GRADE 3 MATHEMATICS CURRICULUM GUIDE · LCPS Grade 3 Mathematics Curriculum Guide 2016-2017 Quarter...

GRADE 3 MATHEMATICS

CURRICULUM GUIDE

Loudoun County Public Schools 2016-2017

Overview, Scope and Sequence, Unit Summaries, The First 20 Days Classroom Routines, Curriculum Framework, Learning Progressions

(additional attachments: Intervention Ideas, NCSM Great Tasks SOL alignment, Math Literature Connections)

Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the

Elementary Math Resources VISION site: http://loudounvision.net/. Search: Math—Elementary Resources; Enrollment key: MATH (all caps)

http://loudounvision.net/

LCPS Grade 3 Mathematics Curriculum Guide 2016-2017

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the

Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes excerpts from documents published by the Virginia Department of Education. Other statements, such as

suggestions on the incorporation of technology and essential questions, represent the professional consensus of Loudoun’s teachers concerning the implementation of these standards.

This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.

NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE

The Curriculum Guide is created to link different components of the guide to related information from the Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources.

To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource.

If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button. Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlates with the objectives of the lesson and provide students with the appropriate challenge.


2009 Virginia SOL Testing Blueprint: Test Items by Strand Dates of LCPS Quarters SOL Reporting

Category Grade 3 SOL Number of Test

Items (CAT) Number of Test

Items

(Traditional)

Number and Number Sense

3.1a-c, 3.2, 3.3a-c 7 10

Computation and

Estimation 3.4, 3.5, 3.6, 3.7 7 10

Measurement and

Geometry

3.8, 3.9a-d, 3.10a-b,

3.11a-b, 3.12, 3.13, 3.14,

3.15, 3.16

8 11

Probability, Statistics,

Patterns, Functions,

and Algebra

3.17a-c, 3.18, 3.19, 3.20a-b

6 9

2016 – 2017 School Calendar

Starts Ends

First Quarter August 29 November 4

Second Quarter November 9 January 26

Third Quarter January 30 April 6

Fourth Quarter April 17 June 9

Quarter 1 Quarter 2 Quarter 3 Quarter 4

P = Teacher Workday/Planning Day H = Holiday/ No School F = First Day of School TI = Teacher Institute for new professionals NH = New Hire Workday SD = In School Staff Development days CS = County Wide Staff Development Days


Grade 3 Nine Weeks Overview 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs

Unit 2-Place Value 3.1 Place Value, Round, Compare

Unit 3-Computation With Whole Numbers (addition/subtraction)

3.2 Related Facts to Solve Problems 3.4 Single- & Multistep Problems (add/subtract) 3.20 Identity/Commutative Properties (addition)

Unit 4-Money 3.8 Count & Compare Money, Making Change

Unit 1-Classroom Routines: NUMBER TALKS 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature 3.17 Data and Graphs

Unit 5-Computation With Whole Numbers (multiplication/division) 3.5 Multiplication & Division Facts 3.6 Model Multiplication & Division, Create & Solve Story Problems 3.19 Patterns (see unit summary) 3.20 Identity/Commutative Properties (multiplication)

Unit 6-Patterns and Data 3.17 Collect, Display, & Interpret Data 3.19 Patterns

Unit 7-Geometry 3.14 Plane & Solid Geometric Figures 3.15 2D Geometry 3.16 Congruent/Non-congruent Geometric Figures


Unit 8-Fractions, Probability, and Measurement (length) 3.3 Model, Name, & Compare Fractions 3.18 Probability 3.9ad Length to Nearest ½ Inch, Area/Perimeter

Unit 9-Computation with Fractions 3.7 Add/Subtract Fractions With Like Denominators

Unit 10-Elapsed Time and Temperature 3.11 Time/Elapsed Time 3.12 Equiv. Periods of Time 3.13 Temperature


Unit 11-Measuring My World 3.9 Measure Length, Weight, Liquid Volume, Area/Perimeter 3.10 Area/Perimeter

Review for SOL Assessment & Post SOL Topics

48 days 45 days 48 days 39 days


Grade 3 Scope & Sequence Quarter 1: 48 days

Days UNIT Standard Content Strand Topic

All year Unit 1-Classroom

Routines

“The First 20 Days Classroom Routines”

& NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature, Data/Graphs

12 Unit 2-Place Value 3.1 Number and Number

Sense Place Value, Round, Compare

22 Unit 3-Computation With

Whole Numbers (addition/subtraction)

3.2 Number and Number

Sense Related Facts to Solve Problems

3.4 Computation and

Estimation Single- and Multistep Problems (add/subtract)

3.20 Patterns, Functions,

and Algebra Identity/Commutative Properties (addition)

10 Unit 4-Money 3.8 Measurement Count and Compare Money, Make Change

4 Assessment, Review, and Intervention


Quarter 2: 45 days



Routines NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature, Data/Graphs

21 Unit 5-Computation With

Whole Numbers (multiplication/division)

3.5 Computation and

Estimation Multiplication and Division Facts

3.6 Computation and

Estimation Model Multiplication and Division, Create and

Solve Story Problems


and Algebra Patterns (see unit summary)


and Algebra Identity/Commutative Properties (multiplication)

10 Unit 6-Patterns & Data

3.17 Probability and

Statistics Collect, Display, and Interpret Data


and Algebra Patterns

10 Unit 7-Geometry

3.14 Geometry Plane and Solid Geometric Figures

3.15 Geometry 2D Geometry

3.16 Geometry Congruent/Non-congruent Geometric Figures



Quarter 3: 48 days



Routines

NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature,

Data/Graphs

22 Unit 8-Fractions, Probability, and

Measurement (length)

3.3 Number and Number

Sense Model, Name, and Compare Fractions

3.18 Probability and

Statistics Probability

3.9ad Measurement Length to Nearest ½ inch, Area/Perimeter

12 Unit 9-Computation

With Fractions 3.7

Computation and Estimation

Add/Subtract Fractions With Like Denominators

10 Unit 10-Elapsed Time &

Temperature

3.11 Measurement Time/Elapsed Time

3.12 Measurement Equivalent Periods of Time

3.13 Measurement Temperature



Quarter 4: 39 days



Routines

NUMBER TALKS, Time/Elapsed Time, Equiv. Periods of Time, Temperature,

Data/Graphs

18 Unit 11-Measuring My

World

3.9 Measurement Measure Length, Weight, Liquid Volume,

Area/Perimeter

3.10 Measurement Area/Perimeter


SOL Tests

LCPS MATH Unit Summary Grade 3 2016-2017

Unit: 1 Quarters 1-4

Classroom Routines

VDOE Standards of Learning:

1st quarter: The First 20 Days Classroom Routines 3.11 The student will

a) tell time to the nearest minute, using analog and digital clocks

3.12 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.

3.13 The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.

3.17 The student will a) collect and organize data, using observations, measurements, surveys, or

experiments; b) construct a line plot, a picture graph, or a bar graph to represent the

data; and c) read and interpret the data represented in line plots, bar graphs, and

picture graphs and write a sentence analyzing the data.

VDOE Process Goals: Problem Solving, Communication, Connections, Reasoning, Representations

Learning Targets:

I can tell time to the nearest minute using different clock models.

I can identify equivalent periods of time and recognize the relationships between the different periods of time.

I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.

I will collect data, and represent the data in graphs to write a sentence explaining the results.

Big Ideas Essential Questions

Classroom routines (about 10 minutes each day) can be used to introduce, support, and extend topics throughout the yearly curriculum in order to provide students with regular practice in important mathematical ideas.

Can you compare and contrast analog and digital clocks?

Can you explain and justify how to determine time on an analog clock? elapsed time?

How is a calendar organized to measure time?

Can you describe the relationships that exist among periods of time within a calendar year?

When and why do we have a leap year?

What the purpose of a thermometer?

How is temperature related to everyday activities?

How do you explain strategies that can be used to collect, organize, and represent data?

How does the type of data and the questions to be answered influence the choice of graph?

Can you compare and contrast the key elements needed when constructing line plots and graphs?

How do you collect, organize, display, and interpret data to provide different kinds of information?


Prerequisite Skills Vocabulary

VDOE Vertical Alignment document K-3 VDOE Vertical Alignment document 3-6

2.12 The student will tell and write time to nearest 5 min 2.13 The student will a) determine past/future days of the week b) identify days/dates on calendar 2.14 The student will read temperature on thermometer in Celsius and Fahrenheit to nearest 10 degrees 2.17 The student will construct picture/picto/bar graphs

VDOE Vocabulary Word Wall Cards data half-hour days of the week categories quarter hour months of the year survey hours minutes bar graph hour hand time data point minute hand equivalent relationships increments analog clock picture graph digital clock scale a.m. temperature horizontal axis p.m. elapsed time vertical axis Celsius Fahrenheit title thermometer labels legend/key line plot prediction

Achievement Criteria How to Assess Achievement

“The content of the mathematics standards is intended to support the following five process goals for students:

• becoming mathematical problem solvers • communicating mathematically • reasoning mathematically • making mathematical connections and • using mathematical representations to model and

interpret practical situations.” -2009 Mathematics Standards of Learning

Click here for a brief audio PowerPoint slide with more information about the Process Goals

Pre and Post Unit Assessments for each standard

can be found in PowerSchool Assessment (formerly Interactive Achievement)

Sample Math Tasks are available in VISION:

Search: LCPS-Math: K-12 Math Tasks Enrollment key: MATH

NCSM Great Tasks

(available in all LCPS Elementary Schools—click link)

Classroom Routines

1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Number Talks sample flipcharts available on the Elementary Math Resources VISION site Example: http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf INVESTIGATIONS: Mathematical Thinking at Grade 3 Calendar Math p. 87/Exploring Data p. 89

Create an interactive bulletin board. The clock faces will need to be laminated or placed in plastic sleeves so that students will be able to draw hands on them and then erase the hands. In the middle section, the elapsed time will change daily or even during the day. Students will be given a digital start time written on the board. A student will go to the bulletin board and record the digital time on the start time clock face by drawing the hands. The student will then check the elapsed time and determine the end time to draw on the end time clock face. (Note: A geared clock needs to be available for students’ use at this bulletin board. Be careful when giving out start times and elapsed times that the end time does not need to cross over between a.m. and p.m.)

Have students work together in groups of two or three to create, exchange, and solve five word problems dealing with the temperature changes that they have observed over a period of time.

Display graphs around the classroom, and have students keep their individual graphs in binders or folders. Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2011/opening_session/2009sol_vertical_articulation_by_topic_k-3_9-15-11.pdf

http://www.doe.virginia.gov/instruction/mathematics/professional_development/institutes/2011/opening_session/2009sol_vertical_articulation_by_topic_3-6_9-15-11.pdf

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_3.pdf

https://www.dropbox.com/s/ve7sxlqo2ps6cyj/Process%20Goals%20audio%20slide.pptx


https://aa.powerschool.com/Account/Login?redirectUrl=https://aa.powerschool.com/


http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf



Unit: 2 Quarter 1

Place Value


3.1 The student will a) read and write six-digit numerals and identify the place value and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).


Learning Targets:

I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.

I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.

I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).


• Understand that knowledge of place value is essential when comparing numbers. • Understand the relationships in the place value system, where each place is ten times the value of the place to its right. • Understand that rounding gives an estimate to use when exact numbers are not needed for the situation. • Understand the relative magnitude of numbers by comparing numbers. • Understand how to use manipulatives such as base 10 blocks, Digiblocks, etc. • Use patterns in the place value system to read and write numbers.

Can you explain the relationship in the place value system using a six-digit numeral?

Can you compare and contrast written formats for whole numbers (standard, written, and expanded notation)?

What is the magnitude of each 4 in the number 4,444?

Can you explain strategies for comparing two whole numbers?

Can you explain the use of an inequality symbol in an equation?

Why are numbers rounded? Are there other strategies for estimation?

Can you demonstrate and explain how to round a four-digit number using a variety of strategies?



2.1 The student will a) read/write/ID place value in 3‐digit numeral b) round 2‐digit numbers to nearest ten c) compare two whole numbers 0 – 999 with symbols and/or words. 2.4 The student will a) count by 2/5/10 to 100, starting at multiples of 2,5,10 b) count backward by 10 from 100 c) recognize even/odd numbers 2.2 The student will a) ID ordinal positions w/numbers 1st ‐ 20th b) write ordinal numbers

VDOE Vocabulary Word Wall Cards

digit place value number numeral standard form expanded form place value rounding estimation greater than less than equal to compare ones tens hundreds thousands ten thousands hundred thousands














NCSM Great Tasks


Differentiation Resources

Use place value mats to reinforce the concept of place values. Use base-10 blocks to model place values.

Have students demonstrate understanding of place value by changing numbers from standard form into expanded form, and from expanded form into standard form.

Use a number line graphic organizer.

Use color coding and/or underlining to identify the place value position to be rounded.

Use colored markers to emphasize numbers when writing on a number line.

Have students create a human number line to demonstrate how to round a number.

Have students create a set of number cards with various place values underlined, indicating that the number is to be rounded to this place. Then, have students create a second set of number cards that are the rounded numbers matching the first set of cards. Have students play a matching game with the cards.

Have students underline specific place value to look at when determining whether a number is greater than, less than, or equal to another number (e.g., 2,567 > 2,308)

Have students formulate their own “greater than,” “less than,” and “equal to” statements about the location of specific places on a map, using symbols and terms.

Intervention Ideas (available in all LCPS Elementary Schools—click link)

ELL Model Performance Indicators (click to link)

Investigations: Mathematical Thinking at Grade 3 Investigation 1: What is a Hundred? Session1: How Much is 100? Session 2 and 3: Working with 100 Landmarks in the Hundreds Investigation 3: Constructing a 1000 Chart ESS lessons: 3.1a Place Value 3.1 b Rounding Whole Numbers 3.1 c Comparing Numbers Learn Zillion: 3.1a Understand the Value of a Digit in a Multi-Digit Number 3.1b Round to the Nearest Ten Using a Number line 3.1b Round to the Nearest Ten Using Base Ten Blocks 3.1b Round to the Nearest Ten or Hundred Using Real World Situations Brain POP 3.1b Rounding Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1b.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-1c.pdf

http://learnzillion.com/lessons/1783-understand-the-value-of-a-digit-in-a-multidigit-number

http://learnzillion.com/lessons/1783-understand-the-value-of-a-digit-in-a-multidigit-number

http://learnzillion.com/lessons/1786-round-to-the-nearest-ten-using-a-number-line

http://learnzillion.com/lessons/1787-round-to-the-nearest-ten-using-base-ten-blocks

http://learnzillion.com/lessons/1790-round-to-the-nearest-ten-or-hundred-in-real-world-situations

http://learnzillion.com/lessons/1790-round-to-the-nearest-ten-or-hundred-in-real-world-situations

http://www.brainpop.com/math/numbersandoperations/rounding/



Unit: 3 Quarter 1

Computation with Whole Numbers (add/subtract)


3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.

3.4 The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole numbers, each 9,999 or less, with or without regrouping.

3.20 The student will a) investigate the identity and the commutative properties for addition and

multiplication; and b) identify examples of the identity and commutative properties for

addition and multiplication.


Learning Targets:

I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences and solve problems.

I can estimate answers and solve problems involving one or more steps in which I will need to add and/or subtract numbers that are 9,999 or less.

I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.


Understand, model, and explain how addition and subtraction are related.

Equal emphasis should be placed on the structure of problems in solving single- and multi-step practical problems (ie: a part plus a part equals a whole in addition and a whole minus a part equals a part in subtraction).

Recognize that estimation skills are valuable, time-saving tools particularly in practical situations when exact answers are not required or needed and determining the reasonableness of the sum or difference.

Develop and use strategies to estimate whole number sums and differences, while utilizing flexible methods of combining numbers, to determine the reasonableness of an exact answer.

Know that mathematical relationships can be expressed using number sentences. Represent the equals sign as “the same as” by varying the location of the equals sign in number sentences. (ie: 50 = 25 + 25)

Investigate the identity and commutative property for addition.

Include patterns as a connection (ie: 25 + 25 = 50, 26 + 24 = 50, 27 + 23 = 50, etc.)

How do you use the inverse relationships between addition/subtraction to solve related basic fact sentences? For example, 5 + 3 = 8 and 8 – 3 = __

How do you write three related basic fact sentences when given one basic fact sentence for addition/subtraction?

(ie: Given 3+7=10, then solve the related facts: __+ 3 = 10, 10- 7= __, and 10- 3= __.

How do you determine whether an estimate or an exact answer is an appropriate solution for practical addition and subtraction problems?

How do you solve problems involving the sum of two whole numbers, with or without regrouping, paper and pencil, mental computation, or using calculators?

How do you solve problems involving the difference of two whole numbers, with or without regrouping, paper and pencil, mental computation, or using calculators,?

What is the identity property in addition when a number is added to zero? (ie: 0 + 2 = 2, 5 + 0 = 5)

What is the commutative property for addition?

How do you write number sentences to represent equivalent mathematical relationships? (e.g., 4 x 3 = 14 - 2).




2.6 The student when given two whole numbers whose sum is 99 or less will a) estimate the sum 2.7 The student when given two whole numbers each 99 or less will b) find the difference 2.8 The student will create and solve one and two‐step addition and subtraction problems with data from tables and picture or bar graphs.


inverse add addend relationship subtract sum factor difference array number sentence estimate factor related facts regroup product addend property identity identity property commutative property

equal part whole










NCSM Great Tasks



Write number sentences both horizontally and vertically so that students may use multiple strategies for computation.

Have students use grid paper to assist them in lining up columns of numbers vertically when adding and subtracting.

Allow students with designated accommodation to use calculators.

Have students create example and non-example cards for the identity property for addition. Then, have them exchange cards with partners and sort the cards into the correct columns on the Example/Non-Example mat. Have partners check for accuracy.



Investigations: Mathematical Thinking at Grade 3 Investigation 2: Doubles and Halves Investigation 4: Exploring Odds and Evens Combining and Comparing

Investigation 1: Comparisons with Record Numbers

Investigation 3: Adding with Money, Inches, and Time

(Also SOLs 3.8, 3.11)

Investigation 4: Working With Hundreds

ESS lessons: 3.2 Inverse Relationships (Related to SOL 3.4, 3.5) 3.4 Addition and Subtraction (Related to 3.1a)

3.20 Array for the Commutative Property for

Multiplication!

3.20 My Identity Is in My Pocket

3.20 Property Commute








http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-2.pdf


http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-20ab_2.pdf





Learn Zillion: 3.2 Solve Addition Problems Using Complements of Ten 3.2 Use Addition and Subtraction Fact Families to Solve for Unknown Amounts 3.2 Identify Addition and Subtraction Patterns Using a Hundreds Chart 3.2 Find Number Patterns by Using “In” and “Out” Boxes Brain POP Jr.: Adding with Regrouping Subtracting with Regrouping BrainPOP: Commutative Property Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://learnzillion.com/lessons/1580-solve-addition-problems-using-complements-of-ten

http://learnzillion.com/lessons/1579-use-addition-and-subtraction-fact-families-to-solve-for-unknown-amounts

http://learnzillion.com/lessons/1579-use-addition-and-subtraction-fact-families-to-solve-for-unknown-amounts

http://learnzillion.com/lessons/1464-identify-addition-and-subtraction-patterns-using-a-hundreds-chart


http://learnzillion.com/lessons/1531-find-number-patterns-by-using-addition-and-subtraction-to-solve-in-and-out-boxes

http://www.brainpopjr.com/math/additionandsubtraction/addingwithregrouping/

http://www.brainpopjr.com/math/additionandsubtraction/subtractingwithregrouping/



Unit: 4 Quarter 1

Money


3.8 The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of the bills and coins, and make change.


Learning Targets:

I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple strategies to make change.


A collection of coins and bills has a value that can be counted (counting on, beginning with the highest value, and/or by grouping the coins and bills)

Determine the change after a purchase ($5.00 or less), including counting on, using coins and bills, i.e., starting with the amount to be paid (purchase price), counting forward to the next dollar, and then counting forward by dollar bills to reach the amount from which to make change; and mentally calculate the difference.

Can you demonstrate how to count the value of collections of coins and bills up to $5.00.?

How do you compare the values of two sets of coins or bills, up to $5.00, using the terms greater than, less than, and equal to?

Can you show how to make change from $5.00 or less?



2.10 The student will a) count/compare collection of coins with values of $2.00 or less b) use cent/dollar symbols and decimal points


money coin bill value change skip counting collection










NCSM Great Tasks











Allow students to use calculators.

Allow students to use grid paper to line up numbers vertically when showing their work.

Have students work with larger amounts when making change.

Discuss which human resources need to know how to calculate money and make change. List types of capital and natural resources they may choose to spend their money on.

Use Coin Box on the Illuminations website to count, collect, exchange, and make change with virtual coins.



Investigations: Landmarks in the Hundreds Investigation 2: Using Landmarks to Solve Problems Session 4: Solving Problems with Money

Things That Come in Groups: Investigation 5: Problems with Larger Numbers Session 1: Calculate Savings ESS lessons: 3.8 Money Counts BrainPOP Jr.: Counting Coins Dollars and Cents Equivalent Coins Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://illuminations.nctm.org/ActivityDetail.aspx?ID=217

http://illuminations.nctm.org/


http://www.brainpopjr.com/math/money/countingcoins/

http://www.brainpopjr.com/math/money/dollarsandcents/

http://www.brainpopjr.com/math/money/equivalentcoins/



Unit: 5 Quarter 2

Computation with Whole Numbers (multiply/divide)


3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.

3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

3.19 The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms.

3.20 The student will a) investigate the identity and the commutative properties for addition and

multiplication; and b) identify examples of the identity and commutative properties for

addition and multiplication.


Learning Targets:

I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.

I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication problems (one factor 99 or less and the second factor 5 or less).

I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.


Understand and explain how multiplication and division are related.

Recognize that estimation skills are valuable, time-saving tools particularly in practical situations when exact answers are not required or needed. They are also valuable in determining the reasonableness of the product or quotient.

Investigate the identity and commutative property for multiplication.

Know that mathematical relationships can be expressed using number sentences. Represent the equals sign as “the same as” and not a symbol that gives an answer by varying the location of the equals sign in number sentences. (ie: 50 = 25 + 25)

Numerical patterns can be incorporated into the unit through skip counting on a number line, skip counting on a hundred chart, etc.

Partial products and partial quotients are strategies that allow for students to engage in number sense while using computation.

(ie: 57 x 8 = (50 x 8) + (7 x 8) = 400 + 56 = 456)

How do you use the inverse relationships between multiplication/division to solve related basic fact sentences?

How do you write three related basic fact sentences when given one basic fact sentence for multiplication/division?

How do you determine whether an estimate or an exact answer is an appropriate solution for practical multiplication and division problems?

How do you solve problems involving the product of two whole numbers, with or without regrouping, using calculators, paper and pencil, or mental computation?

How do you solve problems involving the quotient of two whole numbers, with or without regrouping, using calculators, paper and pencil, or mental computation?

What is the identity property in multiplication?

What is the commutative property?

How do you write number sentences to represent equivalent mathematical relationships? (e.g., 4 x 3 = 14 - 2).




2.5 The student will recall addition and subtraction facts w/sums to 20 or less 2.9 The student will recognize and describe related facts and inverse relationship between addition and subtraction

VDOE Vocabulary Word Wall Cards numeral factor fact family area number sentence linear array set multiply skip counting product quotient divide dividend equal divisor quotient commutative property identity property










NCSM Great Tasks



Provide multiplication charts, calculators, and additional math aids for students with memory difficulties.

Supply scrap paper/grid paper for students to draw arrays.

Include multistep problems for students (ie: 2 × 3 × 4 or 3 × 6 + 2).

Distribute sheets of grid paper. Brainstorm with students how they could use the grid paper to model the commutative property for multiplication. Ask students what the product of 3 × 5 is. Then, have students shade a 3 × 5 area of blocks on the grid paper and cut out the shaded area. Next, ask students what the product of 5 × 3 is, and have students shade a 5 × 3 area of blocks and cut out the shaded area. Have students compare their two cutouts by placing one on top of the other, and identify that the two cutouts are congruent. Ask why the two shapes are congruent. Write the 3 × 5 = 5 × 3 on the board, and ask students whether they agree or disagree with

Investigations: Things that Come in Groups Landmarks in the Hundreds

Investigation 2: Using Landmarks to Solve Problems

Sessions 5, 6: Real – World Multiplying and Dividing

ESS lessons: 3.5 Multiplication and Division 3.6 Multiplication and Division Representations

3.20 Array for the Commutative Property for

Multiplication!

3.20 My Identity Is in My Pocket

3.20 Property Commute

Learn Zillion: 3.5 Understanding Multiplication and Division Relationships 3.5 Understand Multiplication Using Equal Groups 3.5 Solve Multiplication Using Arrays 3.5 Division Using a Number Line














http://learnzillion.com/lessons/965-understand-multiplication-and-division-relationships

http://learnzillion.com/lessons/965-understand-multiplication-and-division-relationships

http://learnzillion.com/lessons/41-understand-multiplication-problems-using-equal-groups

http://learnzillion.com/lessons/40-solve-multiplication-problems-using-arrays-2

http://learnzillion.com/lessons/1745-interpret-division-as-an-unknown-factor-problem-using-a-number-line


what you just wrote. Have them justify their reasoning. Ask students how the congruence of the two cutouts demonstrates the commutative property for multiplication. The students’ justification must include the fact that the order of the factors does not change the product. Give students an opportunity to work in groups to come up with other examples for the commutative property for multiplication, using the grid paper. (Note: Students could use the “equation mat” to place the grids on the mat and the Commutative Property Model recording sheet to record their examples. (ESS lessons)

Have students create example and non-example cards for the identity property of multiplication. Then, have them exchange cards with partners and sort the cards into the correct columns on the Example/Non-Example mat. Have partners check for accuracy.

Quotient Café activity on the Illuminations site.


ELL Model Performance Indicators

(click to link)

3.5 Solve Division by Drawing Pictures 3.5 Solve Division by Subtracting Equal Groups 3.5 Solve Multiplication and Division Problems Using a Diagram 3.5 Find Number Patterns by Using “In” and “Out” Boxes to 3.5 Solve Multiplication and Division 3.6 Understand Multiplication Problems Representing as

Areas

3.6 Find a Missing Quotient in a Division Problem BrainPOP Jr.: Multiply by 0 and 1 Arrays Making Equal Groups Repeated Addition Repeated Subtraction Dividing with Remainders BrainPOP: Multiplication Division Commutative Property Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)



http://learnzillion.com/lessons/1516-solve-division-problems-by-drawing-pictures

http://learnzillion.com/lessons/49-solve-division-problems-subtracting-equal-groups

http://learnzillion.com/lessons/54-solve-multiplication-and-division-problems-using-a-diagram

http://learnzillion.com/lessons/54-solve-multiplication-and-division-problems-using-a-diagram

http://learnzillion.com/lessons/1532-find-number-patterns-by-using-multiplication-and-division-to-solve-in-and-out-boxes


http://learnzillion.com/lessons/42-understand-multiplication-problems-representing-as-areas

http://learnzillion.com/lessons/42-understand-multiplication-problems-representing-as-areas

http://learnzillion.com/lessons/51-find-a-missing-quotient-in-a-division-problem

http://www.brainpopjr.com/math/multiplicationanddivision/multiplyingby0or1/

http://www.brainpopjr.com/math/multiplicationanddivision/arrays/

http://www.brainpopjr.com/math/multiplicationanddivision/makingequalgroups/

http://www.brainpopjr.com/math/multiplicationanddivision/repeatedaddition/

http://www.brainpopjr.com/math/multiplicationanddivision/repeatedsubtraction/

http://www.brainpopjr.com/math/multiplicationanddivision/dividingwithremainders/

http://www.brainpop.com/math/numbersandoperations/multiplication/

http://www.brainpop.com/math/numbersandoperations/division/

http://www.brainpop.com/math/numbersandoperations/commutativeproperty/



Unit: 6 Quarter 2

Patterns and Data


3.17 The student will a) collect and organize data, using observations, measurements, surveys, or

experiments; b) construct a line plot, a picture graph, or a bar graph to represent the

data; and c) read and interpret the data represented in line plots, bar graphs, and

picture graphs and write a sentence analyzing the data.

3.19 The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. *see Big Ideas


Learning Targets:

I will collect data, and represent the data in graphs to write a sentence explaining the results.

I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete objects, numbers, tables, and pictures and identify mathematical relationships that exist within patterns.


Develop methods of collecting, organizing, describing, displaying, and interpreting data to answer questions they have posed about themselves and their world.

Make connections between data represented in different ways (ie: how data in a bar graph compares and contrasts to the same data in a line plot).

Numerical patterns can be tied into this graphing unit by skip counting by various increments on the scale of the graph and/or by using the key of a picture graph (ie: a symbol stands for 2 votes—if there are 5 symbols in the graph, you would count 2, 4, 6, 8, 10).

How do you explain strategies that can be used to collect, organize, and represent data?

How does the type of data and the questions to be answered influence the choice of graph?

Can you compare and contrast the key elements needed when constructing line plots and graphs?

How do you collect, organize, display, and interpret data to provide different kinds of information?

Can you explain how you know which interpretation of a graph is correct and the remaining interpretations are incorrect?



2.17 The student will construct picture, pictograph, and bar graphs 2.20 The student will identify, create, and extend patterns

VDOE Vocabulary Word Wall Cards data pattern title categories table line plot survey rule labels poll growing bar graph repeating data points extending increments numeric pattern picture graph geometric pattern scale multiples horizontal axis function vertical axis key














NCSM Great Tasks



Enlarge grid paper for students with visual or motor disabilities.

Have students graph the survey results on the computer.

Have students graph the survey results on graph paper.

Have students create a human graph based on their favorite colors or their eye colors.

Have students respond to survey questions, using tactile methods, such as wooden sticks on paper cups.

Have students develop three to five questions to use in interviewing each other, and have them graph the results.

Have students put the vocabulary words into a math glossary that includes the word, a picture, and the definition.

Display graphs around the classroom, and have students keep their individual graphs in binders or folders.

Have students develop pattern sequences on the board, using plastic magnetic numbers.

Have students use calculators to skip count and find new patterns to share with classmates.

Provide each student with a personal hundred chart marked with color-coded patterns to keep in their notebooks (e.g., 2, 4, 6, 8… in red, 1, 3, 5, 7… in blue).

Intervention Ideas



Investigations: Mathematical Thinking in Grade 3 Investigation 3: “Data and Handfuls”, Sessions 1,2: Collecting and Representing Data Sessions 3,4: Handfuls of Cubes and Other Objects Things That Come in Groups Investigation 5: Problems with Larger Numbers Session 2: Many, Many Legs Session 3: Data Tables and Line Plots ESS lessons: 3.17 Data Mania 3.17 Statistics Through the Year 3.19 Patterns in a Staircase 3.19 Patterns on the Hundreds Chart 3.19 Exploring Multiples 3.19 The Ins and Outs of Patterns 3.19 Tunneling Through Patterns Learn Zillion: 3.19 Identify Addition and Subtraction Patterns Using a Hundreds Chart 3.19 Find Number Patterns by Using “In” and “Out” Boxes to Solve Addition and Subtraction 3.19 Find Number Patterns by Using “In” and “Out” Boxes to Solve Multiplication and Division BrainPOP Jr.: 3.17 Tally Charts and Bar Graphs 3.17 Line Graphs 3.17 Picture Graphs BrainPOP: Math Literature Connections (click link) 3.17 Graphs 3.19 Problem Solving Using Tables Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-19_2.pdf











http://www.brainpopjr.com/math/data/tallychartsandbargraphs/

http://www.brainpopjr.com/math/data/linegraphs/

http://www.brainpopjr.com/math/data/pictographs/

http://www.brainpop.com/math/dataanalysis/graphs/

http://www.brainpop.com/math/dataanalysis/problemsolvingusingtables/



Unit: 7 Quarter 2

Geometry


3.14 The student will identify, describe, compare and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.

3.15 The student will identify and draw representations of points, line segments, rays, angles, and lines.

3.16 The student will identify and describe congruent and noncongruent plane figures.


Learning Targets:

I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.

I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.

I can will identify and describe congruent and noncongruent plane figures and justify the identification.


Identify and describe plane and solid geometric figures by using relevant characteristics.

Recognize the similarities and differences between plane and solid figures, and compare the figures to objects in everyday life.

Line segments and angles are components of plane polygons.

Recognize that congruent plane figures remain congruent even if they are in different spatial orientations, while noncongruent plane figures remain noncongruent even if they are in different spatial orientations.

Can you identify models and pictures of plane geometric figures (circle, square, rectangle, and triangle) and solid geometric figures (cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by name?

How can you identify, describe, compare, and contrast plane geometric figures by counting the number of sides and angles?

How do you identify, describe, compare, and contrast solid geometric figures by counting the number of angles, vertices, edges, and by the number and shape of faces?

Can you identify characteristics of solid geometric figures (cylinder, cone, cube, square pyramid, and rectangular prism)?

How do you identify examples of points, line segments, rays, angles, and lines?

How do you draw representations of points, line segments, rays, angles, and lines, using a ruler or straightedge?

When identifying examples of congruent and noncongruent figures, how do you verify their congruence by laying one on top of the other using drawings or models?

Can you determine and explain why plane figures are congruent or noncongruent, using tracing procedures?




2.16 The student will identify, describe, compare, and contrast plane and solid figures. 2.15 The student will a) draw line of symmetry in a figure b) identify and create figures with one line of symmetry.

VDOE Vocabulary Word Wall Cards square point plane rectangle line figures triangle line segment circles circle ray squares right angle angle rectangles opposite endpoint triangles sphere vertex polygon cube vertices sides rectangular prism angles angle size vertices shape edges congruent faces non-congruent solid geometric figure congruency square pyramid cone cylinder plane properties










NCSM Great Tasks



Have student pairs or groups participate in a “real-

world” solid geometric figure scavenger hunt.

Have students record their finds in a chart with

columns in which to list the examples of the solid

geometric figures that they find.

Guide students in constructing models of the solid geometric figures, using different options for materials. One idea is to use toothpicks as the edges and gumdrops as the vertices; another possibility is drinking straws and marshmallows. Students could also create a chart that would help them calculate how many toothpicks or straws and gum drops or marshmallows they would need for each figure.

Investigations: Exploring Solids and Boxes Investigation 1: Sorting and Describing Solids Investigation 2: Building Polygons and Polyhedra Investigation 3: Making Boxes Turtle Paths Investigation 1: Paths and Lengths of Paths Investigation 2: Turns in Paths

Flips, Turns, and Area

Investigation 1: Motions with Tetrominoes









Have students use a drawing software program to create plane geometric figures. Direct students to print them, cut them out, and label them.

Once figures are cut out and labeled, have students trace them on paper. Some students find that tracing a shape is helpful for remembering it. Have students label each traced figure.

Create poster-size geometric figures, and display them in the classroom. Use various fabrics and other materials to create a variety of tactile edges and vertices.

Have students create a notebook of geometry terms. Direct them to divide each page into two sections and to draw a geometric shape (or paste a cut-out shape) in one section and label the shape in the other. Use of color to distinguish the terms may be helpful for some students.

Have students use a Venn diagram to compare the different geometric shapes according to their properties.

Provide a set of congruent/noncongruent figures on cards and two hula hoops, one for congruent figures and the other for noncongruent figures. Have students form two teams to compete at placing the figure cards into the correct hoops.

Distribute pattern blocks, and have each student use them to create a picture or model to trade with a partner. Each student must then create an image that is congruent with the traded picture or model. Allow students to trace the outlines of the pictures or models in order to create their congruent images.



(click to link)

ESS lessons: 3.14 What Am I? 3.14 Plane Geometry Sort 3.15 Folded Geometry 3.15 Secret Sort for Geometry 3.16 Fit to be Congruent

BrainPOP Jr.: Plane Shapes Solid Shapes Points, Line Segments, Rays Congruent and Similar Shapes BrainPOP: Geometry Circles Angles Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.brainpopjr.com/math/geometry/planeshapes/

http://www.brainpopjr.com/math/geometry/solidshapes/

http://www.brainpopjr.com/math/geometry/pointslinessegmentsrays/

http://www.brainpopjr.com/math/geometry/congruentandsimilarshapes/

http://www.brainpop.com/math/geometryandmeasurement/geometry/

http://www.brainpop.com/math/geometryandmeasurement/circles/

http://www.brainpop.com/math/geometryandmeasurement/angles/



Unit: 8 Quarter 3

Fractions, Probability, & Measurement (length)


3.3 The student will: a) name and write fractions (including mixed numbers) represented by a

model b) model fractions (including mixed numbers) and write fractions’ names c) compare fractions having like and unlike denominators using words and

symbols (>,<, or =)

3.18 The student will investigate and describe the concept of probability as chance and list possible results of a given situation.

3.9ad The student will estimate and use U.S. Customary and metric units to measure

a) length to the nearest 12 inch, inch, foot, yard, centimeter, and meter;

b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams, and kilograms; and d) area and perimeter.


Learning Targets:

I can label and create multiple pictures / models of a given fraction. * Parameters: 1. Proper Fractions, Improper Fractions, and Mixed Numbers

2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Pictures / Models – Set, Area, Linear

I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions. * Parameters: 1. Only Proper Fractions

2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Like and Unlike Denominators 4. Pictures / Models: Set, Area, Linear

I can explore the idea of probability as chance and identify possible outcomes of a situation.

I can use Customary and Metric Units to measure length, volume, weight, area, and perimeter.


The whole must be defined. Parts of a whole can be renamed as the definition of the whole changes (ie: using pattern blocks, a trapezoid is ½ of a whole hexagon, but if the whole is defined as two hexagons, then the trapezoid is ¼ of the whole).

Fractions represent parts of wholes and students need to be flexible in how they view these numbers. Area models, set models, and linear models should all be used in addition to symbols and numerals in developing a conceptual understanding of fractions.

How do you name and write fractions (including mixed numbers) represented by a model to include halves, thirds, fourths, eighths, tenths, and twelfths?

Can you explain how you would use concrete materials and pictures to model at least halves, thirds, fourths, eighths, tenths, and twelfths?

Can you compare fractions using the terms greater than, less than, or equal to and the symbols ( >, <, and =), using models, concrete materials and pictures?

What is the definition of probability?


There are many strategies for comparing fractions including using models (same size whole), comparing to a benchmark, comparing numerators when denominators are the same, etc.

Explain that the value of a fraction is dependent on both the number of parts in a whole (denominator) and the number of those parts being considered (numerator).

Define that a proper fraction is a fraction whose numerator is less than its denominator.

Define that an improper fraction is a fraction whose numerator is greater than or equal to the denominator, is one or greater than one, and can be expressed as a whole number or a mixed number.

A mixed number is written as a whole number and a proper fraction.

Investigate, understand, and apply basic concepts of probability. Understand that probability is the chance of an event happening and can be represented as a fraction.

Estimate and measure length (to the nearest ½ inch) using rational numbers (fractions).

Perimeter is a measure of the distance around a polygon and area is a measure of square units needed to cover a surface. Rational numbers (fractions) can be used when measuring perimeter and area.

What are all possible outcomes for a given situation? How can you represent the outcome as a fraction?

Which vocabulary word would you use to Identify the degree of likelihood of an outcome occurring? (impossible, unlikely, as likely as, equally likely, likely, and certain.)

How do you estimate and determine the U.S. Customary and metric units to measure lengths

of objects to the nearest 12 of an inch, inch, foot,

yard, centimeter, and meter?

How do you estimate and use U.S. Customary and metric units to measure area and perimeter?

How do you determine the actual measure of area or perimeter using U.S. Customary and metric units?



2.3 The student will a) Identify halves, thirds, fourths, sixths, eighths, tenths b) write halves, thirds, fourths, sixths, eighths, tenths c) compare halves, thirds, fourths, sixths, eighths, tenths 2.18 The student will predict outcomes if an experiment Is repeated 2.11 The student will a) estimate and measure length to nearest centimeter and inch b) estimate and measure weight/mass c) estimate and measure liquid volume


fraction outcome foot greater than event inch less than predict length equal to probability measure compare impossible yard numerator unlikely centimeter denominator equally likely meter whole number likely as likely as mixed number certain most likely least likely area square units perimeter measure part whole














NCSM Great Tasks



Have students use grid paper to assist them in drawing representations of fractions.

Provide blank fraction bars or fraction circles for students to use to practice modeling fractions and mixed numbers.

Use pre‐made fraction strips for students with kinesthetic difficulties.

Have students use fraction strips for adding and subtracting fractions.

Use larger counters for students with gross-motor deficits.

Use counters with indentations for students with visual deficits.

Group students in pairs, and have each student cut a piece of adding machine tape to match his/her partner’s height. Then, have each student measure his/her own tape (the one that matches his/her height) with a ruler, yardstick, or meter stick. Next, have each student calculate how many toothpicks, cubes, or popsicle sticks must be laid end-to-end to equal the length of his/her tape.

Have students make measurement estimates before giving them the measuring tools to measure the designated objects.

Investigations: Fair Shares

From Paces to Feet Investigation 1: Measuring with Paces and Steps Investigation 2: From Paces to Feet

Flips, Turns, and Area

Investigation 2: Finding Area ESS lessons: 3.3a Naming and Writing Fractions 3.3b Modeling Fractions 3.3c Comparing Fractions (Related to 3.1 a,b,c) 3.18 Is There Probability in THIRD? 3.18 Probability Boxes

3.18 Two-Color-Counter-Toss

3.9a Measuring Length 3.9d Measuring Area and Perimeter (Also use with SOL 3.10) Learn Zillion: 3.3 Recognize Fractions by Breaking Shapes Into Equal Parts 3.3 Write Fractions with a Numerator Other Than 1 3.3 Write Fractions with a Numerator and a Denominator 3.3 Write Fractions Using Shapes 3.3 Write Fractions of a Set (1) 3.3 Write Fractions of a Set (2) 3.3 Identify a Fraction as a Point on a Number Line Using 3.3 Area Models 3.3 Identify Equivalent Fractions Using Models 3.3 Identify Equivalent Fractions Using a Number Line












http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-9d.pdf

http://learnzillion.com/lessons/72-recognize-fractions-breaking-shapes-into-equal-parts

http://learnzillion.com/lessons/72-recognize-fractions-breaking-shapes-into-equal-parts

http://learnzillion.com/lessons/76-write-fractions-with-a-numerator-other-than-one

http://learnzillion.com/lessons/717-write-fractions-with-numerator-and-denominator

http://learnzillion.com/lessons/73-write-fractions-using-shapes-1

http://learnzillion.com/lessons/78-write-fractions-of-a-set-2

http://learnzillion.com/lessons/75-write-fractions-of-a-set-1

http://learnzillion.com/lessons/1729-identify-a-fraction-as-a-point-on-a-number-line-using-area-models

http://learnzillion.com/lessons/1729-identify-a-fraction-as-a-point-on-a-number-line-using-area-models

http://learnzillion.com/lessons/1731-identify-equivalent-fractions-using-fraction-models

http://learnzillion.com/lessons/1732-identify-equivalent-fractions-using-a-number-line


Give students a list of measurements, and have them locate objects in the classroom that have those exact measurements.

Have students measure distances on maps, and use the map scale to determine the actual distances between various pairs of places.

Use larger grid paper to assist students with fine motor issues.

Use appropriate graphic organizers helpful to particular groups of learners.



(click to link)

3.3 Identify Equivalent Fractions Using Fraction Strips 3.3 Generate Equivalent Fractions Using Fraction Models 3.3 Express Fractions Equivalent to 1 Using Fractions Strips 3.3 Understand Fractions: Create Mini Stories 3.3 Place Fractions on a Number Line 3.3 Count Fractions to Make 1 Whole 3.3 Compare Fractions with the Same Denominator by Reasoning About Their Size 3.3 Express Whole Numbers as Fractions 3.9d Find the Area of a Shape Using Square Units 3.9d Cover Area of a Shape Using Square Units 3.9d Use Grid Paper to Find the Area 3.9d Find the Perimeter 3.9d Find the Perimeter with Missing Sides BrainPOP Jr.: Basic Parts of a Whole More Fractions Equivalent Fractions Mixed Fractions Measurement: Inches and Feet Measurement: Centimeters, Meters, Kilometers Area Perimeter Basic Probability Probability Combinations BrainPOP: Fractions Customary Units Metric Units Metric Vs. Customary Basic Probability Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://learnzillion.com/lessons/1733-identify-equivalent-fractions-using-fraction-strips

http://learnzillion.com/lessons/1734-generate-equivalent-fractions-using-fraction-models

http://learnzillion.com/lessons/1736-express-fractions-equivalent-to-1-using-fraction-strips

http://learnzillion.com/lessons/1736-express-fractions-equivalent-to-1-using-fraction-strips

http://learnzillion.com/lessons/81-understand-fractions-create-ministories

http://learnzillion.com/lessons/74-place-fractions-on-a-number-line-1

http://learnzillion.com/lessons/79-count-fractions-to-make-1-whole

http://learnzillion.com/lessons/1740-compare-fractions-with-the-same-denominator-by-reasoning-about-their-size

http://learnzillion.com/lessons/1740-compare-fractions-with-the-same-denominator-by-reasoning-about-their-size

http://learnzillion.com/lessons/1738-express-whole-numbers-as-fractions

http://learnzillion.com/lessons/1155-find-the-area-of-a-shape-using-square-units

http://learnzillion.com/lessons/1154-cover-the-area-of-a-shape-using-square-units

http://learnzillion.com/lessons/1157-use-grid-paper-to-find-the-area

http://learnzillion.com/lessons/1166-find-the-perimeter-of-a-polygon-with-more-than-4-sides

http://learnzillion.com/lessons/1320-find-perimeter-with-missing-side-lengths

http://www.brainpopjr.com/math/fractions/basicpartsofawhole/

http://www.brainpopjr.com/math/fractions/morefractions/

http://www.brainpopjr.com/math/fractions/equivalentfractions/

http://www.brainpopjr.com/math/fractions/mixednumbers/

http://www.brainpopjr.com/math/measurement/inchesandfeet/

http://www.brainpopjr.com/math/measurement/centimetersmeterskilometers/

http://www.brainpopjr.com/math/measurement/area/

http://www.brainpopjr.com/math/measurement/perimeter/

http://www.brainpopjr.com/math/data/basicprobability/

http://www.brainpopjr.com/math/data/probability/

http://www.brainpopjr.com/math/data/combinations/

http://www.brainpop.com/math/numbersandoperations/fractions/

http://www.brainpop.com/math/numbersandoperations/customaryunits/

http://www.brainpop.com/math/numbersandoperations/metricunits/

http://www.brainpop.com/math/numbersandoperations/metricvscustomary/

http://www.brainpop.com/math/geometryandmeasurement/angles/



Unit: 9 Quarter 3

Computation with Fractions


3.7 The student will add and subtract proper fractions having like denominators of 12 or less.


Learning Targets:

I can use pictures / models to add and subtract fractions. * Parameters: 1. Only Proper Fractions 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Only Like Denominators 4. Pictures / Models: Set, Area, Linear


The whole must be defined. Parts of a whole can be renamed as the definition of the whole changes (ie: using pattern blocks, a trapezoid is ½ of a whole hexagon, but if the whole is defined as two hexagons, then the trapezoid is ¼ of the whole).

A proper fraction is a fraction whose numerator is smaller than its denominator.

An improper fraction is a fraction whose numerator is greater than or equal to the denominator and is one or greater than one.

An improper fraction can be expressed as a whole number or a mixed number.

A mixed number is written as a whole number and a proper fraction. A mixed number is the sum of a whole number and the proper fraction.

Computation with fractions can be compared and contrasted with whole number computation.

How can you model fraction operations using…

region/area models (e.g., pie pieces, pattern blocks, geoboards, drawings);

set models (e.g., chips, counters, cubes, drawings); and

length/measurement models (e.g., nonstandard units such as rods, connecting cubes, and drawings)?

How do you add and subtract with proper fractions having like denominators of 12 or less, using concrete materials and pictorial models representing area/regions (circles, squares, and rectangles), length/measurements (fraction bars and strips), and sets (counters)?



2.6 The student, when given two whole numbers whose sum is 99 or less, will find the sum.


fraction whole number

proper fraction numerator

improper fraction denominator

sum difference

part whole














NCSM Great Tasks



Have students use fraction strips and fraction circles to solve word problems.

Have students complete Exit Cards to check for understanding.

Have students use grid paper to assist them in drawing representations of fractions.

Provide blank fraction bars or fraction circles for students to use to practice modeling fractions and mixed numbers.



Investigations: Fair Shares

Investigation 1: Sharing Brownies

Session 4: The Fraction Cookie Game

Sessions 5, 6: Backward Sharing

ESS lessons: 3.7 Adding and Subtracting Fractions

Learn Zillion: 3.7 Add and Subtract Fractions with Like Denominators 3.7 Solve Fraction Word Problems Using Key Words and Pictures BrainPOP: Adding and Subtracting Fractions Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://learnzillion.com/lessons/120-add-and-subtract-fractions-with-like-denominators

http://learnzillion.com/lessons/80-solve-fraction-word-problems-using-key-words-and-pictures

http://learnzillion.com/lessons/80-solve-fraction-word-problems-using-key-words-and-pictures

http://www.brainpop.com/math/numbersandoperations/addingandsubtractingfractions/



Unit: 10 Quarter 3

Elapsed Time & Temperature


3.11 The student will a) tell time to the nearest minute, using analog and digital clocks; and b) determine elapsed time in one-hour increments over a 12-hour period.

3.12 The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes and hours.

3.13 The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real thermometers and physical models of thermometers will be used.


Learning Targets:


I can tell time to the nearest minute and how many hours have passed (using a clock) when given a scenario involving the passing of time

I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.


Skip counting and computation strategies can be used to calculate elapsed time.

Identifying equivalent periods of time can be integrated into classroom routines and practical problems in other units.

Patterns can be observed when reading temperature from a thermometer (often increments of 10’s or 2’s).

Can you compare and contrast analog and digital clocks?

Can you explain and justify how to determine time on an analog clock?

Can you explain and justify how to determine elapsed time?

How is a calendar organized to measure time?

Can you describe the relationships that exist among periods of time within a calendar year?

When and why do we have a leap year?

How can you use patterns to help read temperature on a thermometer?



2.12 tell and write time to nearest 5 min 2.13 a) determine past/future days of the week; b) ID days/dates on calendar 2.14 read temperature on thermometer in C or F to nearest 10 degrees


analog clock one-half hour digital clock calendar hours months of the year minutes days of the week seconds quarter hour hour hand minute hand a.m. p.m. temperature thermometer degrees scale/increments Fahrenheit Celsius














NCSM Great Tasks



Show students times on analog and digital clocks, and have them respond verbally or use a response board to tell the times.

Have students use manipulatives, such as plastic clocks, to set different times to become skillful at using the minute and hour hands.

Have students cut out pictures of clocks and watches from magazines and flyers, glue them in their notebooks, and write the displayed times next to them.

Model elapsed time in a variety of ways including on a number line or elapsed time ruler.

Provide a felt calendar and numbers with Velcro backs. Have students construct a calendar for a given month. Ask students to point to a particular day that has happened or will happen and relate it to a class event on that day.

Have students collect weather information for the local area from newspapers, television news, and/or the Internet. Have students practice depicting the listed temperatures on physical models of thermometers.

Have students use two different colors to indicate temperatures in Celsius and temperatures in Fahrenheit.

Have students work together in groups of two or three to create, exchange, and solve five word problems dealing with the temperature changes that they have observed during the unit.



Investigations: 3.11 Mathematical Thinking at Grade 3 Ten Minute Math, pages 87-90 Combining and Comparing

Investigation 5: Calendar Comparisons Session 1: How Much Longer? Sessions 2, 3: School Days ESS lessons: 3.11—It’s About Time 3.11—Where Did the Time Go? 3.11—Hoppin’ on the Elapsed Time Line 3.12—Calendar Math 3.13—Was the Groundhog Correct? Learn Zillion: 3.11 Reading the Exact Time on a Clock to the Minute 3.11 Reading the Exact Time on a Clock 3.11 Drawing Exact Time on a Clock 3.11 Elapsed Time to the Nearest Minute Brain Pop: 3.11 Time to the Minute 3.11 Elapsed Time 3.12 Calendar and Dates 3.13 Temperature Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-11b_1.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-11b_2.pdf



http://learnzillion.com/lessons/836-reading-the-exact-minute-on-a-clock

http://learnzillion.com/lessons/837-reading-the-exact-time-on-a-clock

http://learnzillion.com/lessons/838-drawing-the-exact-time-on-a-clock

http://learnzillion.com/lessons/578-solving-elapsed-time-word-problems-to-the-nearest-minute

http://www.brainpopjr.com/math/time/timetotheminute/

http://www.brainpop.com/math/numbersandoperations/elapsedtime/

http://www.brainpopjr.com/math/time/calendaranddates/

http://www.brainpopjr.com/math/measurement/temperature/



Unit: 11 Quarter 4

Measuring My World


3.9 The student will estimate and use U.S. Customary and metric units to measure

a) length to the nearest 12 inch, inch, foot, yard, centimeter, and meter;

b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams, and kilograms; and d) area and perimeter.

3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given surface in

order to determine area.


Learning Targets:

I can use customary and metric units to measure length, volume, weight, area, and perimeter.

I can measure the outside of a shape (perimeter) and count the number of square units on the inside of a shape (area).


Estimate measures of length, liquid volume, weight/mass, area and perimeter.

Determine the actual measure of length, liquid volume, weight/mass, area and perimeter.

Perimeter is a measure of the distance around a polygon.

Area is a measure of square units needed to cover a surface.

While conversions within systems are not necessarily essential in 3rd grade, skip counting and patterns can be integrated into measurement through the use of a double number line:

How do you estimate and use U.S. Customary and metric units to measure lengths of objects

to the nearest 12 of an inch, inch, foot, yard,

centimeter, and meter; liquid volume to the nearest cup, pint, quart, gallon, and liter; weight/mass of objects to the nearest ounce, pound, gram, and kilogram?

How do you determine the actual measure of length using U.S. Customary and metric units to

measure objects to the nearest 12 of an inch,

foot, yard, centimeter, and meter; liquid volume units to measure to the nearest cup, pint, quart, gallon, and liter; weight/mass of objects to the nearest ounce, pound, gram, and kilogram?

How do you estimate and use U.S. Customary and metric units to measure area and perimeter.

How do you determine the actual measure of area or perimeter using U.S. Customary and metric units.




2.11 The student will a) estimate and measure length to nearest centimeter and inch b) estimate and measure weight/mass c) estimate and measure liquid volume

VDOE Vocabulary Word Wall Cards foot cup inch pint length quart measure gallon yard liter centimeter distance meter perimeter grams area kilograms square units mass ruler ounces polygon pounds weight balance scale mass estimate liquid volume










NCSM Great Tasks



Group students in pairs, and have each student cut a piece of adding machine tape to match his/her partner’s height. Then, have each student measure his/her own tape (the one that matches his/her height) with a ruler, yardstick, or meter stick. Next, have each student calculate how many toothpicks, cubes, or popsicle sticks must be laid end-to-end to equal the length of his/her tape.

Have students make measurement estimates before giving them the measuring tools to measure the designated objects.

Provide students with a generic, non-detailed drawing of a person to measure to the nearest one-half inch, and record the measurements on the recording sheet.

Give students a list of measurements, and have them locate objects in the classroom that have those exact measurements.

Investigations: From Paces to Feet Investigation 3: Measuring Project: Do Our Chairs Fit Us? Investigation 4: Measuring Balobbyland

Combining and Comparing Investigation 2: How Much Heavier or Lighter? Session 1: Weighing Fruits and Vegetables Session 2: Comparing the Weights ESS lessons: 3.9a Measuring Length 3.9b Measuring Liquid Volume 3.9c Measuring Weight/Mass 3.9d Measuring Area and Perimeter (Also use with SOL 3.10) 3.10a Determining Perimeter

3.10b Measuring Surface Area











http://www.doe.virginia.gov/testing/solsearch/sol/math/3/mess_3-9d.pdf




Have students measure distances on maps, and use the map scale to determine the actual distances between various pairs of places.

Use larger grid paper to assist students with fine motor issues.

Have high-ability students draw shapes that correspond to given areas or perimeters.

Discuss how area and perimeter are used in sports

Use appropriate graphic organizers helpful to particular groups of learners.

Use grid paper instead of construction paper for polygon cutouts.

Have students connect the linking cubes instead of just placing them on the polygon to make it easier to keep the cubes inside the shape.

Have students look through magazines, newspapers, and books to find examples of surfaces measured using square units.

Provide students with cloth measuring tapes to use for wrapping instead of string.

Provide students with string cut to the exact length of the perimeter of each polygon.

Provide students with a variety of rulers to use.

Display two or three large United States maps of different scales. Group students into small groups of three or four, and assign each group a state. (Note: The more regularly shaped states will work best.) Have each group use string to measure the perimeter of the assigned state on each map. Then, have students in each group compare their various perimeter measurements of the same state, discussing why they are so different. Use their findings to lead into a class discussion of map scale—how it plays a vital role in map design and why it is important to pay close attention to the scale of a map.



(click to link)

Learn Zillion: 3.9b Understanding Volume & How Volume is Measured 3.9b Estimate Volume in Liters 3.9b Measure Volume in Liters 3.9c Understand Mass & How Mass is Measured 3.9c Estimate Mass in Grams 3.9c Measure Mass in Grams 3.9c Estimate Mass in Kilograms 3.9c Measure Mass in Kilograms 3.9d, 3.10 Find the Area of a Shape Using Square Units 3.9d, 3.10 Cover Area of a Shape Using Square Units 3.9d, 3.10 Use Grid Paper to Find the Area 3.9d, 3.10 Find Area Using Multiplication 3.9d, 3.10 Find the Perimeter 3.9d, 3.10 Find the Perimeter with Missing Sides BrainPOP Jr.: Measurement: Inches and Feet Measurement: Centimeters, Meters, Kilometers Measurement: Ounces, Pounds, Tons Measurement: Grams, Kilograms Measurement: Cups, Pints, Quarts, Gallons Area Perimeter BrainPOP: Customary Units Metric Units Metric Vs. Customary Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://learnzillion.com/lessons/1270-understand-volume-and-how-volume-is-measured

http://learnzillion.com/lessons/1271-estimate-volume-in-liters

http://learnzillion.com/lessons/1272-measure-volume-in-liters

http://learnzillion.com/lessons/1273-understand-mass-and-how-mass-is-measured

http://learnzillion.com/lessons/1274-estimate-mass-in-grams

http://learnzillion.com/lessons/1276-measure-mass-in-grams

http://learnzillion.com/lessons/1275-estimate-mass-in-kilograms-using-benchmarks

http://learnzillion.com/lessons/1277-measure-mass-in-kilograms

http://learnzillion.com/lessons/1155-find-the-area-of-a-shape-using-square-units

http://learnzillion.com/lessons/1154-cover-the-area-of-a-shape-using-square-units

http://learnzillion.com/lessons/1157-use-grid-paper-to-find-the-area

http://learnzillion.com/lessons/1170-find-area-using-multiplication-in-real-world-problems

http://learnzillion.com/lessons/1166-find-the-perimeter-of-a-polygon-with-more-than-4-sides

http://learnzillion.com/lessons/1320-find-perimeter-with-missing-side-lengths

http://www.brainpopjr.com/math/measurement/inchesandfeet/

http://www.brainpopjr.com/math/measurement/centimetersmeterskilometers/

http://www.brainpopjr.com/math/measurement/ouncespoundsandtons/

http://www.brainpopjr.com/math/measurement/gramsandkilograms/

http://www.brainpopjr.com/math/measurement/cupspintsquartsgallons/

http://www.brainpopjr.com/math/measurement/area/

http://www.brainpopjr.com/math/measurement/perimeter/

http://www.brainpop.com/math/numbersandoperations/customaryunits/

http://www.brainpop.com/math/numbersandoperations/metricunits/

http://www.brainpop.com/math/numbersandoperations/metricvscustomary/


The First 20 Days Classroom Routines: Establishing a Mathematics Classroom Community

Overview: The mini lessons included in this guide are intended to be used in conjunction with your first unit of study. The daily 10-15 minute lessons will help

you set routines, develop references for students, establish protocols, and create norms for an engaging math classroom community. The lessons may be

modified or extended based on students’ need or grade level. The routines, protocols, and experiences should be revisited throughout the school year in order

to maintain a productive math community.

Goals:

Build a classroom community of learners

Support students’ understanding of math content by establishing guidelines related to the VA process goals (problem solving, communication,

reasoning, connections, and representation).

Develop routines that will help students become reflective problem solvers and engage in a rigorous study of mathematics.

Background: This guide is based on a document developed by Austin Independent School District. Their document was modeled after the First 20 Days of Independent Reading by Fountas & Pinnell. Many of the suggested routines will also connect to other effective protocols used in Being a Writer and Responsive Classroom. This guide was adapted from a resource created by Arlington Public Schools.

Mini Lesson Key Ideas Essential Understandings

Anchor Charts/Supports Resources Teacher Notes

Day 1 Management: Classroom Procedures/ Community Guidelines

Establish routines, procedures, and student expectations for daily math lessons.

Students develop criteria for a “Being a Mathematician” chart that will be posted in the classroom. Students understand that the information posted in the classroom will be a valuable reference for them.

Develop a “Being a Mathematician” anchor chart to which students can refer. The chart should have less than 6 criteria to be effective and manageable. Example behaviors:

• Remain on task • Participate/stay engaged • Listen actively • Discuss math ideas • Treat materials with respect • Always try your best

*Brainstorm the list with the students

Chart paper, Markers Have a discussion about routines and procedures with the students. This is a good time to have students talk about expectations for engaging in classroom discussions and completing their work.

Day 2 Management: Mathematical Tools VA Process Goals: Problem Solving & Representation

Mathematicians can utilize math tools to help them solve problems.

Tools are a valuable resource for mathematicians. Students are aware of the tools that are available in the classroom.

Brainstorm a list of mathematical tools and discuss how they can be used and stored. Add additional information to the “Being a Mathematician” chart about placing materials in their proper storage containers and location after use. Examples: Base ten blocks Cubes Number cubes Hundreds chart Two-colored counters

Emphasize how and why materials are to be used during math instruction.



Day 3 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Norms for classroom discussions need to be established in order to engage in respectful discourse and have equitable participation.

In order to communicate and learn from each other, mathematicians must listen to, as well as speak, with their classmates. We will function as a respectful classroom community in order to learn.

Create an anchor chart for “Norms for a Math Discussion” or “Rights and Obligations During Discussions” Example norms include: Speak respectfully Take turns (equitable participation) Give others time to think Eyes on the speaker

Norms may be similar to those you establish in other content areas. These established routines should be revisited all year long.

Day 4 Math Talk/ Classroom Discourse VA Process Goal: Communication

Mathematicians communicate orally about their work. Different talk moves can be used while facilitating classroom discussions. Students learn content through the process goal of communication.

Math can be more rigorous when you communicate with others. There are sentence starters that can be used to help one engage in discussions.

Post and discuss Talk Moves to encourage students to share their thinking. Identify 1 or 2 moves to begin the year with (based on your first units of study).

- Talk bubbles or Talk move sticks

Introduce talk moves

- Turn and Talk (also called partner talk, or think-pair-share)

- Say More: You ask an individual student to expand on what he or she said

- Revoicing (also called verify and clarify)

- Repeat - Agree/Disagree and why?

Encourage students to speak in complete thoughts when communicating orally. The utilization and introduction of talk moves is a continuous process. This day is one way to introduce moves, but it should be ongoing.



Day 5 Collaboration (Game) VA Process Goal: Communication

Mathematicians can work collaboratively while playing a game in order to learn important math concepts.

Students understand that they can work with others to explore math content. Cooperation is a key component of working with a partner.

Establish rules for working with a partner while playing a math game. Try the “Say it to Play it” guideline: When playing a game in partners, the students must state their move and/or provide an explanation for why they are playing that move (Ex: In the game Compare, a student may say “9 is greater than 5, so I win the cards”).

Post rules and directions for engaging in a game with a partner. Consider utilizing a fact fluency game for this mini lesson.

Rules and clear directions will help make group work successful. After the mini lesson, have students practice a game during the math lesson for the day.

Day 6 Collaborative/ Independent Work (Rotations) VA Process Goal: Communication

Mathematicians can explore/ engage in a variety of experiences within a math period. Work may be collaborative or independent.

In order to have a variety of activities during a math block, it is important to be mindful of procedures, noise level, expectations, etc.

Review procedures for moving around the classroom to different centers Consider utilizing visual time reminders Use cues for sound control/reminders

Post clear directions at independent centers. Provide a materials checklist.



Day 7 Real Life Connections to Math VA Process Goal: Connections

Mathematicians make connections between math ideas and the world around them.

Math connects to other content areas/disciplines (i.e. Science). Students relate math to the world around them.

Brainstorm a list of math concepts that relate to the real world. Consider using the following discussion prompts: Where in the world do you see numbers? When do you use math in your everyday life?

Chart paper Calendar / Daily Schedule

Consider connecting this discussion to everyday events in their life.

Day 8 Representing Thinking VA Process Goals: Representation, Communication

Mathematicians can represent ideas in multiple ways. Mathematicians use words to explain their thinking. Mathematicians can explain their thinking verbally or in writing in order to process information.

Students will become more familiar with ways they can represent math ideas. Students can show their math thinking in written words.

In order to fully communicate their understanding, mathematicians may provide written explanations of their reasoning.

Brainstorm ways that students can represent their thinking. Ex: Pictures/drawing Words Numbers Symbols Manipulative models

Utilize sentence frames: “This is a ______________. It is a ______ because it ______________. “ This example shows a picture, numbers, and a written explanation.

Encourage students to show math concepts in a variety of ways. Encourage students to write about their understanding or show their thinking using words, pictures, numbers, etc.



Day 9 Recording & Reflecting in Math

VA Process Goal: Communication

Mathematicians keep a record of their daily experiences (i.e. math game).

Students will understand how to utilize a recording sheet or guide as they play a game or solve a problem. Students will record and reflect upon their work to communicate their understanding in writing.

Example of Game Recording Sheet:

Introduce a Recording Sheet as a student tool.

Day 10 Academic Language of Math VA Process Goal: Communication

Specialized language is used in math. Mathematical language can be modeled and explicitly taught.

Students will develop an understanding of specific math terminology. Conceptual understanding is developed as students use math terminology.

Post examples of key vocabulary terms with visual examples.

Math Word Wall, Word Banks, VDOE Vocabulary Cards http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml The vocabulary terms introduced are then posted for class reference.

New vocabulary should be explicitly introduced and utilized within daily lessons. This is a continuous routine/ element for all units of study.

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/index.shtml





Day 11 Vocabulary Development VA Process Goals: Representation, Communication, Connections

Mathematicians use a variety of strategies to build vocabulary.

Students will utilize a tool to reinforce their math vocabulary.

Select model to implement with students (i.e. Frayer).

Student math journal VDOE Math Vocabulary Cards Frayer Model

Students can utilize math journals to keep a record of math vocabulary. Their journals can also serve as a valuable resource in addition to the Word Wall or class references (see Day 10).

Day 12 Math Strategies VA Process Goals: Problem Solving, Representation, Connections

A variety of strategies can be used to solve problems and explore mathematical concepts.

Students develop a repertoire of strategies. Students see connections between different strategies used to solve problems.

Build or add to a strategy wall showing models of strategies for various skills or concepts.

Anchor charts can be developed for a wide variety of strategies depending on the grade level. Examples are shown to the left.



Day 13 Connections VA Process Goals: Connections, Communication

Mathematicians make and recognize connections among mathematical ideas.

Students understand that they can make connections among math ideas. Math can be related to the world outside the classroom.

Discussion questions: How is that answer like the one you modeled yesterday? Where have you seen that before?

Consider having students glue question/ comment starters in the back of their math journal. They can refer to it during class discussions.

Day 14 Justification VA Process Goals: Reasoning, Representation

Mathematicians verify their thinking by showing it multiple ways.

Students will develop a deeper understanding of content when asked to justify their thinking.

Create an anchor chart that depicts ways that students can justify their thinking.

Justify means: explain, defend,

describe, prove, give reasons, show

you understand, validate…

Using verbal explanation first can help facilitate written justification.



Day 15 Problem Solving Strategies VA Process Goals: Problem Solving, Communication

Mathematicians choose from a variety of strategies to solve problems.

Students have a resource of strategies to help them solve problems . Sample strategies: -find a pattern - estimate and check -make an organized list -draw a diagram -write an equation -work backward -solve a simpler problem -read a table/chart

Introduce problem solving strategies (a variety of strategies can be used). Explain that the different strategies can be used to help students with problem solving. Choose 1 strategy to explain/highlight for the mini lesson. You will continue to model/introduce/use the strategies throughout the year.

Students can create their own problem solving strategy icons or bookmarks as well as refer to a class anchor chart of strategies.

During classroom instruction, teachers can engage students in discourse about their problem solving strategy.

Day 16 Problem Solving Protocol VA Process Goals: Problem Solving, Communication

There are processes that can be used to help solve problems.

Students will be introduced to a problem solving protocol. Students will become familiar with the protocol steps.

Develop and post a problem solving protocol.

Post the protocol in the classroom for student reference.

Consider trying a problem as a class to model how the protocol is used. The emphasis should be on the steps, so it may be easiest to select content that is readily accessible to all learners.

Step 1: Read and quietly think on your own – release your pencils. Step 2: Talk about the problem. What is your plan to solve? Pick your strategy. Step 3: Share your strategy. Step 4: Solve the problem and communicate your thinking.



Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections

There are tools mathematicians use to monitor and assess their work or behavior.

Students understand how to use a rubric to assess themselves/ their work.

Create a class rubric that is not math related. The topic should be something relevant to an everyday student activity in the classroom or school. Examples include: Lunchroom behavior Morning routine Dismissal Cubbie/desk organization

Day 18 Reflection/ Self-Monitoring VA Process Goal: Reasoning

Mathematicians modify their work as needed.

Students reflect upon and revise their work to demonstrate their full understanding.

Introduce a criteria chart and rubric for self- monitoring of work.

Sample Rubric:

Rubric & Problem Solving Protocol Create an anchor chart with “How to Self-Correct or Modify Your Work”

Help students develop a clear understanding of the criteria and how upcoming math tasks will be scored. Emphasize how this is similar to the revisions they do during the writing process.



Day 19 Collaboration (Task) VA Process Goal: Communication

Mathematicians can work collaboratively on a problem solving task to learn important math concepts.

Students understand that they can work with others to solve problems and learn new information.

Review roles that pairs or small groups should follow/hold when working together on a task. Examples: Materials manager Recorder Reporter Time keeper

Develop an anchor chart with roles/procedures for group work on a task/problem. Self-assess/reflect upon collaborative work experiences. Students can use the problem solving protocol together (See Day 16).

Save time at the end of the lesson to debrief the experience. What went well? What could be improved next time they are working in a group?

Day 20

Process Goals

VA Process Goals: Problem Solving, Reasoning, Communication, Connections, & Representation

“The content of the mathematics standards is intended to support the following five process goals for students: *becoming mathematical problem solvers *communicating mathematically *reasoning mathematically *making mathematical connections and *using mathematical representations to model and interpret practical situations.”

-2009 Mathematics Standards of Learning

Student-friendly process goals poster (can be a poster for the classroom and/or a small version can be taped to desks or in math journals) Process Goals bookmark (click on picture to the left to access the file for the poster and bookmark)

Students should be engaged in process goals throughout every mathematical task and lesson throughout the year.

https://www.dropbox.com/s/t2pvle6rn86heu2/Process Goals student-friendly.docx

Mathematics Standards of Learning Curriculum Framework 2009: Grade 3

VDOE Technical Assistance Document

to be used in conjunction with the VDOE Curriculum Framework (click title above to link to document)

Virginia Mathematics Standards of Learning

Curriculum Framework 2009 Introduction

The 2009 Mathematics Standards of Learning Curriculum Framework is a companion document to the 2009 Mathematics Standards of Learning and amplifies the Mathematics Standards of Learning by defining the content knowledge, skills, and understandings that are measured by the Standards of Learning assessments. The Curriculum Framework provides additional guidance to school divisions and their teachers as they develop an instructional program appropriate for their students. It assists teachers in their lesson planning by identifying essential understandings, defining essential content knowledge, and describing the intellectual skills students need to use. This supplemental framework delineates in greater specificity the content that all teachers should teach and all students should learn. Each topic in the Mathematics Standards of Learning Curriculum Framework is developed around the Standards of Learning. The format of the Curriculum Framework facilitates teacher planning by identifying the key concepts, knowledge and skills that should be the focus of instruction for each standard. The Curriculum Framework is divided into two columns: Essential Understandings and Essential Knowledge and Skills. The purpose of each column is explained below. Essential Understandings This section delineates the key concepts, ideas and mathematical relationships that all students should grasp to demonstrate an understanding of the Standards of Learning. Essential Knowledge and Skills Each standard is expanded in the Essential Knowledge and Skills column. What each student should know and be able to do in each standard is outlined. This is not meant to be an exhaustive list nor a list that limits what is taught in the classroom. It is meant to be the key knowledge and skills that define the standard. The Curriculum Framework serves as a guide for Standards of Learning assessment development. Assessment items may not and should not be a verbatim reflection of the information presented in the Curriculum Framework. Students are expected to continue to apply knowledge and skills from Standards of Learning presented in previous grades as they build mathematical expertise.

http://www.doe.virginia.gov/instruction/mathematics/resources/mathematics_sol_technical_assistance.pdf


3.1

The student will

a) read and write six-digit numerals and identify the place value and value of each digit;

b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and

c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).

UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)

ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

The structure of the Base-10 number system is

based upon a simple pattern of tens, where each

place is ten times the value of the place to its right.

This is known as a ten-to-one place value

relationship.

The structure of the Base-10 blocks is based on the

ten-to-one place value relationship (e.g., 10 units

make a long, 10 longs make a flat, 10 flats make a

cube).

Place value refers to the value of each digit and

depends upon the position of the digit in the

number. In the number 7,864, the eight is in the

hundreds place, and the value of the 8 is eight

hundred.

Flexibility in thinking about numbers — or

“decomposition” of numbers (e.g., 12,345 is 123

hundreds, 4 tens, and 5 ones) — is critical and

supports understandings essential to multiplication

and division.

Whole numbers may be written in a variety of

formats:

All students should

Understand that knowledge of place value is

essential when comparing numbers.

Understand the relationships in the place value

system, where each place is ten times the value of

the place to its right.

Understand that rounding gives an estimate to use

when exact numbers are not needed for the

situation.

Understand the relative magnitude of numbers by

comparing numbers.

The student will use problem solving, mathematical

communication, mathematical reasoning,

connections, and representations to

Investigate and identify the place and value for

each digit in a six-digit numeral, using Base-10

manipulatives (e.g., Base-10 blocks).

Use the patterns in the place value system to read

and write numbers.

Read six-digit numerals orally.

Write six-digit numerals that are stated verbally or

written in words.

Round a given whole number, 9,999 or less, to the

nearest ten, hundred, and thousand.

Solve problems, using rounding of numbers, 9,999

or less, to the nearest ten, hundred, and thousand.

Determine which of two whole numbers between 0

and 9,999 is greater.

Determine which of two whole numbers between 0

and 9,999 is less.

Compare two whole numbers between 0 and 9,999,

using the symbols >, <, or =.

Use the terms greater than, less than, and equal to

when comparing two whole numbers.


– Standard: 123,456;

– Written: one hundred twenty-three thousand,

four hundred fifty-six; and

– Expanded: (1 100,000) + (2 10,000) + (3

1,000) + (4 100) + (5 10) + (6 1).

Numbers are arranged into groups of three places

called periods (ones, thousands, millions, and so

on). Places within the periods repeat (hundreds,

tens, ones). Commas are used to separate the

periods. Knowing the place value and period of a

number helps students find the value of a digit in

any number as well as read and write numbers.

To read a whole number through the hundred

thousands place,

– read the digits to the first comma;

– say the name of the period (e.g., “thousands”);

then

– read the last three digits, but do not say the

name of the ones period.

Reading and writing large numbers should be

related to numbers that have meanings (e.g.,

numbers found in the students’ environment).

Concrete materials, such as Base-10 blocks may be

used to represent whole numbers through

thousands. Larger numbers may be represented on

place value charts.

Rounding is one of the estimation strategies that is

often used to assess the reasonableness of a

solution or to give an estimate of an amount.

Students should explore reasons for estimation,

using practical experiences, and use rounding to

solve practical situations.


3.1

The student will

a) read and write six-digit numerals and identify the place value and value of each digit;

b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and

c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).



The concept of rounding may be introduced

through the use of a number line. When given a

number to round, locate it on the number line.

Next, determine the multiple of ten, hundred, or

thousand it is between. Then identify to which it is

closer.

A procedure for rounding numbers to the nearest

ten, hundred, or thousand is as follows:

– Look one place to the right of the digit to

which you wish to round.

– If the digit is less than 5, leave the digit in the

rounding place as it is, and change the digits

to the right of the rounding place to zero.

– If the digit is 5 or greater, add 1 to the digit in

the rounding place, and change the digits to

the right of the rounding place to zero.

A procedure for comparing two numbers by

examining may include the following:

– Line up the numbers by place value by lining

up the ones.

– Beginning at the left, find the first place value

where the digits are different.

– Compare the digits in this place value to

determine which number is greater (or

which is less).

– Use the appropriate symbol > or < or the words

greater than or less than to compare the

numbers in the order in which they are

presented.

– If both numbers are the same, use the symbol =

or the words equal to.


3.2

The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to

complete basic fact sentences. The student will use these relationships to solve problems.



Addition and subtraction are inverse operations, as

are multiplication and division.

In building thinking strategies for subtraction, an

emphasis is placed on connecting the subtraction

fact to the related addition fact. The same is true for

division, where the division fact is tied to the

related multiplication fact. Building fact sentences

helps strengthen this relationship.

Addition and subtraction should be taught

concurrently in order to develop understanding of

the inverse relationship.

Multiplication and division should be taught

concurrently in order to develop understanding of

the inverse relationship.

All students should

Understand how addition and subtraction are

related.

Understand how multiplication and division are

related.




Use the inverse relationships between

addition/subtraction and multiplication/division to

solve related basic fact sentences. For example,

5 + 3 = 8 and 8 – 3 = __;

4 3 = 12 and 12 ÷ 4 = __.

Write three related basic fact sentences when given

one basic fact sentence for addition/subtraction and

for multiplication/division. For example, given

3 2 = 6, solve the related facts __ 3 = 6,

6 ÷ 3 = __, and 6 ÷ __ = 3.


3.3

The student will

a) name and write fractions (including mixed numbers) represented by a model;

b) model fractions (including mixed numbers) and write the fractions’ names; and

c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).



A fraction is a way of representing part of a whole

(as in a region/area model or a length/measurement

model) or part of a group (as in a set model).

Fractions are used to name a part of one thing or a

part of a collection of things. Models can include

pattern blocks, fraction bars, rulers, number line,

etc.

In each area/region and length/measurement model,

the parts must be equal-sized (congruent). Wholes

are divided or partitioned into equal-sized parts. In

the set model, each member of the set is an equal

part of the set. The members of the set do not have

to be equal in size.

The denominator tells how many equal parts are in

the whole or set. The numerator tells how many of

those parts are being considered.

Provide opportunities to make connections among

fraction representations by connecting concrete or

pictorial representations with oral language and

symbolic representations.

Informal, integrated experiences with fractions at

this level will help students develop a foundation

for deeper learning at later grades. Understanding

the language of fractions (e.g., thirds means “three

equal parts of a whole,” 1

3 represents one of three

equal-size parts when a pizza is shared among three

students, or three-fourths means “three of four

equal parts of a whole”) furthers this development.

All students should

Understand that the whole must be defined.

Understand that the denominator tells the number

of equal parts that represent a whole.

Understand that the numerator is a counting

number that tells how many equal size parts are

being considered.

Understand that the value of a fraction is dependent

on both the number of parts in a whole

(denominator) and the number of those parts being

considered (numerator).

Understand that a proper fraction is a fraction

whose numerator is smaller than its denominator.

Understand that an improper fraction is a fraction

whose numerator is greater than or equal to the

denominator and is one or greater than one.

Understand that an improper fraction can be

expressed as a whole number or a mixed number.

Understand that a mixed number is written as a

whole number and a proper fraction.




Name and write fractions (including mixed

numbers) represented by a model to include halves,

thirds, fourths, eighths, tenths, and twelfths.

Use concrete materials and pictures to model at

least halves, thirds, fourths, eighths, tenths, and

twelfths.

Compare fractions using the terms greater than,

less than, or equal to and the symbols ( <, >, and

=). Comparisons are made between fractions with

both like and unlike denominators, using models,

concrete materials and pictures.


3.3

The student will

a) name and write fractions (including mixed numbers) represented by a model;

b) model fractions (including mixed numbers) and write the fractions’ names; and

c) compare fractions having like and unlike denominators, using words and symbols (>, <, or =).



Comparing unit fractions (a fraction in which the

numerator is one) builds a mental image of

fractions and the understanding that as the number

of pieces of a whole increases, the size of one

single piece decreases (e.g., 1

5 of a bar is smaller

than 1

4 of a bar).

Comparing fractions to a benchmark on a number

line (e.g., close to 0, less than 1

2 , exactly

1

2 , greater

than 1

2 , or close to 1) facilitates the comparison of

fractions when using concrete materials or pictorial

models.


3.4

The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole

numbers, each 9,999 or less, with or without regrouping.



Addition is the combining of quantities; it uses the

following terms:

addend 423

addend + 246

sum 669

Subtraction is the inverse of addition; it yields the

difference between two numbers and uses the

following terms:

minuend 7,698

subtrahend – 5,341

difference 2,357

An algorithm is a step-by-step method for

computing.

An example of an approach to solving problems is

Polya’s four-step plan:

– Understand: Retell the problem; read it twice;

take notes; study the charts or diagrams;

look up words and symbols that are new.

– Plan: Decide what operation(s) and sequence

of steps to use to solve the problem.

– Solve: Follow the plan and work accurately. If

the first attempt does not work, try another

plan.

– Look back: Does the answer make sense?

Knowing whether to find an exact answer or to

make an estimate is learned through practical

experiences in recognizing which is appropriate.

When an exact answer is required, opportunities to

explore whether the answer can be determined

mentally or must involve paper and pencil or

All students should

Understand that estimation skills are valuable,

time-saving tools particularly in practical situations

when exact answers are not required or needed.

Understand that estimation skills are also valuable

in determining the reasonableness of the sum or

difference when solving for the exact answer is

needed.

Develop and use strategies to estimate whole

number sums and differences to determine the

reasonableness of an exact answer.

Develop flexible methods of adding whole

numbers by combining numbers in a variety of

ways, most depending on place values.




Determine whether an estimate or an exact answer

is an appropriate solution for practical addition and

subtraction problems situations involving single-

step and multistep problems.

Determine whether to add or subtract in practical

problem situations.

Estimate the sum or difference of two whole

numbers, each 9,999 or less when an exact answer

is not required.

Add or subtract two whole numbers, each 9,999 or

less.

Solve practical problems involving the sum of two

whole numbers, each 9,999 or less, with or without

regrouping, using calculators, paper and pencil, or

mental computation in practical problem situations.

Solve practical problems involving the difference

of two whole numbers, each 9,999 or less, with or

without regrouping, using calculators, paper and

pencil, or mental computation in practical problem

situations.

Solve single-step and multistep problems involving

the sum or difference of two whole numbers, each

9,999 or less, with or without regrouping.


3.4

The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole

numbers, each 9,999 or less, with or without regrouping.



calculators help students select the correct

approach.

Determining whether an estimate is appropriate and

using a variety of strategies to estimate requires

experiences with problem situations involving

estimation.

There are a variety of mental mathematics

strategies for each basic operation, and

opportunities to practice these strategies give

students the tools to use them at appropriate times.

For example, with addition, mental mathematics

strategies include

– Adding 9: add 10 and subtract 1; and

– Making 10: for column addition, look for

numbers that group together to make 10.

Using Base-10 materials to model and stimulate

discussion about a variety of problem situations

helps students understand regrouping and enables

them to move from the concrete to the abstract.

Regrouping is used in addition and subtraction

algorithms.

Conceptual understanding begins with concrete

experiences. Next, the children must make

connections that serve as a bridge to the symbolic.

One strategy used to make connections is

representations, such as drawings, diagrams, tally

marks, graphs, or written comments.


3.5

The student will recall multiplication facts through the twelves table, and the corresponding division facts.



The development of computational fluency relies

on quick access to number facts.

A certain amount of practice is necessary to

develop fluency with computational strategies;

however, the practice must be motivating and

systematic if students are to develop fluency in

computation, whether mental, with manipulative

materials, or with paper and pencil.

Strategies to learn the multiplication facts through

the twelves table include an understanding of

multiples/skip counting, properties of zero and one

as factors, pattern of nines, commutative property,

and related facts.

In order to develop and use strategies to learn the

multiplication facts through the twelves table,

students should use concrete materials, hundred

chart, and mental mathematics.

To extend the understanding of multiplication,

three models may be used:

– The equal-sets or equal-groups model lends

itself to sorting a variety of concrete objects

into equal groups and reinforces repeated

addition or skip counting.

– The array model, consisting of rows and

columns (e.g., 3 rows of 4 columns for a 3-

by-4 array) helps build the commutative

property.

– The length model (e.g., a number line) also

reinforces repeated addition or skip

counting.

All students should

Develop fluency with number combinations for

multiplication and division.

Understand that multiplication is repeated addition.

Understand that division is the inverse of

multiplication.

Understand that patterns and relationships exist in

the facts.

Understand that number relationships can be used

to learn and retain the facts.




Recall and state the multiplication and division

facts through the twelves table.

Recall and write the multiplication and division

facts through the twelves table.


3.6

The student will represent multiplication and division, using area, set, and number line models, and create and solve problems

that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.



The multiplication and division facts through the

twelves tables should be modeled.

Multiplication is a shortcut for repeated addition.

The terms associated with multiplication are listed

below:

factor 54

factor 3

product 162

Creating real-life problems and solving them

facilitates the connection between mathematics and

everyday experiences (e.g., area problems).

The use of Base-10 blocks and repeated addition

can serve as a model. For example, 4 12 is read

as four sets consisting of one rod and two units.

The sum is renamed as four rods and eight units or

48. This can be thought of as

12 + 12 + 12 + 12 = (SET)

The use of Base-10 blocks and the array model can

be used to solve the same problem. A rectangle

array that is one rod and two units long by four

units wide is formed. The area of this array is

represented by 4 rods and 8 units.

The number line model can be used to solve a

multiplication problem such as 3 4. This is

represented on the number line by three jumps of

four.

The number line model can be used to solve a

division problem such as 6 ÷ 3 and is represented

on the number line by noting how many jumps of

three go from 6 to 0.

All students should

Understand the meanings of multiplication and

division.

Understand the models used to represent

multiplying and dividing whole numbers.




Model multiplication, using area, set, and number

line models.

Model division, using area, set, and number line

models.

Solve multiplication problems, using the

multiplication algorithm, where one factor is 99 or

less and the second factor is 5 or less.

Create and solve word problems involving

multiplication, where one factor is 99 or less and

the second factor is 5 or less.


3.6

The student will represent multiplication and division, using area, set, and number line models, and create and solve problems

that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.



The number of jumps (two) of a given length (three) is the answer to the question.

An algorithm is a step-by-step method for computing.

0 1 2 3 4 5 6


3.7

The student will add and subtract proper fractions having like denominators of 12 or less.



A proper fraction is a fraction whose numerator is

less than the denominator. A proper fraction is a

fraction that is always less than one.

An improper fraction is a fraction whose numerator

is greater than or equal to the denominator. An

improper fraction is a fraction that is equal to or

greater than one.

An improper fraction can be expressed as a mixed

number. A mixed number is written as a whole

number and a proper fraction.

The strategies of addition and subtraction applied

to fractions are the same as the strategies applied to

whole numbers.

Reasonable answers to problems involving addition

and subtraction of fractions can be established by

using benchmarks such as 0, 1

2 , and 1. For

example, 3

5 and

4

5 are each greater than

1

2 , so their

sum is greater than 1.

Concrete materials and pictorial models

representing area/regions (circles, squares, and

rectangles), length/measurements (fraction bars and

strips), and sets (counters) can be used to add and

subtract fractions having like denominators of 12 or

less.

All students should

Understand that a proper fraction is a fraction

whose numerator is smaller than its denominator.

Understand that an improper fraction is a fraction

whose numerator is greater than or equal to the

denominator and is one or greater than one.

Understand that an improper fraction can be

expressed as a whole number or a mixed number.

Understand that a mixed number is written as a

whole number and a proper fraction. A mixed

number is the sum of a whole number and the

proper fraction.

Understand that computation with fractions uses the

same strategies as whole number computation.




Demonstrate a fractional part of a whole, using

– region/area models (e.g., pie pieces, pattern

blocks, geoboards, drawings);

– set models (e.g., chips, counters, cubes,

drawings); and

– length/measurement models (e.g., nonstandard

units such as rods, connecting cubes, and

drawings).

Name and write fractions and mixed numbers

represented by drawings or concrete materials.

Represent a given fraction or mixed number, using

concrete materials, pictures, and symbols. For

example, write the symbol for one-fourth and

represent it with concrete materials and/or pictures.

Add and subtract with proper fractions having like

denominators of 12 or less, using concrete

materials and pictorial models representing

area/regions (circles, squares, and rectangles),

length/measurements (fraction bars and strips), and

sets (counters).


3.8

The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare

the value of the bills and coins, and make change.



The value of a collection of coins and bills can be

determined by counting on, beginning with the

highest value, and/or by grouping the coins and

bills.

A variety of skills can be used to determine the

change after a purchase, including

– counting on, using coins and bills, i.e., starting

with the amount to be paid (purchase price),

counting forward to the next dollar, and then

counting forward by dollar bills to reach the

amount from which to make change; and

– mentally calculating the difference.

All students should

Understand that a collection of coins and bills has a

value that can be counted.

Understand how to make change from $5.00 or

less.




Count the value of collections of coins and bills up

to $5.00.

Compare the values of two sets of coins or bills, up

to $5.00, using the terms greater than, less than,

and equal to.

Make change from $5.00 or less.


3.9

The student will estimate and use U.S. Customary and metric units to measure

a) length to the nearest 1

2 inch, inch, foot, yard, centimeter, and meter;

b) liquid volume in cups, pints, quarts, gallons, and liters;

c) weight/mass in ounces, pounds, grams, and kilograms; and

d) area and perimeter.


ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND

SKILLS

Weight and mass are different. Mass is the amount

of matter in an object. Weight is determined by the

pull of gravity on the mass of an object. The mass of

an object remains the same regardless of its location.

The weight of an object changes dependent on the

gravitational pull at its location. In everyday life,

most people are actually interested in determining an

object’s mass, although they use the term weight

(e.g., “How much does it weigh?” versus “What is

its mass?”).

The concept of a standard measurement unit is one

of the major ideas in understanding measurement.

Familiarity with standard units is developed through

hands-on experiences of comparing, estimating,

measuring, and constructing.

Benchmarks of common objects need to be

established for each of the specified units of measure

(e.g., the mass of a mathematics book is about one

kilogram). Practical experience measuring the mass

of familiar objects helps to establish benchmarks and

facilitates the student’s ability to estimate measures.

One unit of measure may be more appropriate than

another to measure an object, depending on the size

of the object and the degree of accuracy desired.

Correct use of measurement tools is essential to

understanding the concepts of measurement.

All students should

Understand how to estimate measures of length,

liquid volume, weight/mass, area and perimeter.

Understand how to determine the actual measure of

length, liquid volume, weight/mass, area and

perimeter.

Understand that perimeter is a measure of the

distance around a polygon.

Understand that area is a measure of square units

needed to cover a surface.

The student will use problem solving,

mathematical communication, mathematical

reasoning, connections, and representations to

Estimate and use U.S. Customary and metric

units to measure lengths of objects to the nearest 1

2 of an inch, inch, foot, yard, centimeter, and

meter.

Determine the actual measure of length using

U.S. Customary and metric units to measure

objects to the nearest 1

2 of an inch, foot, yard,

centimeter, and meter.


units to measure liquid volume to the nearest

cup, pint, quart, gallon, and liter.

Determine the actual measure of liquid volume

using U.S. Customary and metric units to

measure to the nearest cup, pint, quart, gallon,

and liter.


units to measure the weight/mass of objects to

the nearest ounce, pound, gram, and kilogram.


3.9

The student will estimate and use U.S. Customary and metric units to measure

a) length to the nearest 1

2 inch, inch, foot, yard, centimeter, and meter;

b) liquid volume in cups, pints, quarts, gallons, and liters;

c) weight/mass in ounces, pounds, grams, and kilograms; and

d) area and perimeter.


ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND

SKILLS

Perimeter is the distance around any two-

dimensional figure and is found by adding the

measures of the sides.

Area is a two-dimensional measure and is therefore

measured in square units.

Area is the number of square units needed to cover a

figure, or more precisely, it is the measure in square

units of the interior region of a two-dimensional

figure.

Determine the actual measure of weight/mass

using U.S. Customary and metric units to

measure the weight/mass of objects to the

nearest ounce, pound, gram, and kilogram.


units to measure area and perimeter.

Determine the actual measure of area or

perimeter using U.S. Customary and metric

units.


3.10

The student will

a) measure the distance around a polygon in order to determine perimeter; and

b) count the number of square units needed to cover a given surface in order to determine area.



A polygon is a closed plane figure composed of at

least three line segments that do not cross. None of

the sides are curved.

Perimeter is a measure of the distance around a

polygon and is found by adding the measures of the

sides.

Area is the number of iterations of a two-

dimensional unit needed to cover a surface. The

two-dimensional unit is usually a square, but it

could also be another shape such as a rectangle or

an equilateral triangle.

Opportunities to explore the concepts of perimeter

and area should involve hands-on experiences (e.g.,

placing tiles (units) around a polygon and counting

the number of tiles to determine its perimeter and

filling or covering a polygon with cubes (square

units) and counting the cubes to determine its area).

All students should

Understand the meaning of a polygon as a closed

figure with at least three sides. None of the sides

are curved and there are no intersecting lines.

Understand that perimeter is a measure of the

distance around a polygon.

Understand how to determine the perimeter by

counting the number of units around a polygon.

Understand that area is a measure of square units

needed to cover a surface.

Understand how to determine the area by counting

the number of square units.




Measure each side of a variety of polygons and add

the measures of the sides to determine the

perimeter of each polygon.

Determine the area of a given surface by estimating

and then counting the number of square units

needed to cover the surface.


3.11

The student will

a) tell time to the nearest minute, using analog and digital clocks; and

b) determine elapsed time in one-hour increments over a 12-hour period.



While digital clocks make reading time easy, it is

necessary to ensure that students understand that

there are sixty minutes in an hour.

Use of a demonstration clock with gears ensures

that the positions of the hour hand and the minute

hand are precise when time is read.

Students need to understand that time has passed or

will pass.

Elapsed time is the amount of time that has passed

between two given times.

Elapsed time should be modeled and demonstrated

using geared analog clocks and timelines.

It is necessary to ensure that students understand

that there are sixty minutes in an hour when using

analog and digital clocks.

Elapsed time can be found by counting on from the

beginning time to the finishing time.

– Count the number of whole hours between the

beginning time and the finishing time.

For example, to find the elapsed time between

7 a.m. and 10 a.m., students can count on to

find the difference between the times (7 and

10), so the total elapsed time is 3 hours.

All students should

Apply appropriate techniques to determine time to

the nearest minute, using analog and digital clocks.

Understand how to determine elapsed time in one-

hour increments over a 12-hour period.




Tell time to the nearest minute, using analog and

digital clocks.

Match the times shown on analog and digital

clocks to written times and to each other.

When given the beginning time and ending time,

determine the elapsed time in one-hour increments

within a 12-hour period (times do not cross

between a.m. and p.m.).

Solve practical problems in relation to time that has

elapsed.


3.12

The student will identify equivalent periods of time, including relationships among days, months, and years, as well as minutes

and hours.



The knowledge that a year has 365 and 1

4 days will

help students understand the necessity of adding a

full day every fourth year, called a leap year.

The use of a calendar facilitates the understanding

of time relationships between days and months,

days and weeks, days and years, and months and

years. Recognize that students need to know the

relationships, such as if there are 24 hours in one

day, how many hours are in three days? If the date

is January 6, what date would it be in two weeks?

How many weeks are in March, April, and May?

The use of an analog clock facilitates the

understanding of time relationships between

minutes and hours and hours and days.

All students should

Understand the relationship that exists among

periods of time, using calendars, and clocks.




Identify equivalent relationships observed in a

calendar, including the number of days in a given

month, the number of days in a week, the number

of days in a year, and the number of months in a

year.

Identify the number of minutes in an hour and the

number of hours in a day.


3.13

The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real

thermometers and physical models of thermometers will be used.



Estimating and measuring temperatures in the

environment in Fahrenheit and Celsius require the

use of real thermometers.

A physical model can be used to represent the

temperature determined by a real thermometer.

The symbols for degrees in Celsius (C) and

degrees in Fahrenheit (F) should be used to write

temperatures.

Celsius and Fahrenheit temperatures should be

related to everyday occurrences by measuring the

temperature of the classroom, the outside, liquids,

body temperature, and other things found in the

environment.

All students should

Understand how to measure temperature in Celsius

and Fahrenheit with a thermometer.




Read temperature to the nearest degree from real

Celsius and Fahrenheit thermometers and from

physical models (including pictorial

representations) of such thermometers.


3.14

The student will identify, describe, compare, and contrast characteristics of plane and solid geometric figures (circle, square,

rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics,

including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models.



The van Hiele theory of geometric understanding

describes how students learn geometry and provides a

framework for structuring student experiences that

should lead to conceptual growth and understanding.

– Level 0: Pre-recognition. Geometric figures are

not recognized. For example, students cannot

differentiate between three-sided and four-

sided polygons.

– Level 1: Visualization. Geometric figures are

recognized as entities, without any awareness

of parts of figures or relationships between

components of a figure. Students should

recognize and name figures and distinguish a

given figure from others that look somewhat

the same (e.g., “I know it’s a rectangle

because it looks like a door, and I know that

the door is a rectangle.”).

– Level 2: Analysis. Properties are perceived, but

are isolated and unrelated. Students should

recognize and name properties of geometric

figures (e.g., “I know it’s a rectangle because

it’s closed, it has four sides and four right

angles, and opposite sides are parallel.”).

A plane geometric figure is any two-dimensional

closed figure. Circles and polygons are examples of

plane geometric figures.

All students should

Understand how to identify and describe plane

and solid geometric figures by using relevant

characteristics.

Understand the similarities and differences

between plane and solid figures.




Identify models and pictures of plane geometric

figures (circle, square, rectangle, and triangle) and

solid geometric figures (cube, rectangular prism,

square pyramid, sphere, cone, and cylinder) by

name.

Identify and describe plane geometric figures by

counting the number of sides and angles.

Identify and describe solid geometric figures by

counting the number of angles, vertices, edges, and

by the number and shape of faces.

Compare and contrast characteristics of plane and

solid geometric figures (e.g., circle/sphere,

square/cube, triangle/square pyramid, and

rectangle/rectangular prism), by counting the

number of sides, angles, vertices, edges, and the

number and shape of faces.

Compare and contrast characteristics of solid

geometric figures (i.e., cube, rectangular prism,

square pyramid, sphere, cylinder, and cone) to

similar objects in everyday life (e.g., a party hat is

like a cone).

Identify characteristics of solid geometric figures

(cylinder, cone, cube, square pyramid, and

rectangular prism).


3.14






Three-dimensional figures are called solid figures or

simply solids. Solids enclose a region of space. The

interior of both plane and solid figures are not part of

the figure. Solids are classified by the types of

surfaces they have. These surfaces may be flat,

curved, or both.

The study of geometric figures must be active, using

visual images and concrete materials.

Access to a variety of concrete tools such as graph

paper, pattern blocks, geoboards, and geometric

solids is greatly enhanced by computer software tools

that support exploration.

Opportunity must be provided for building and using

geometric vocabulary to describe plane and solid

figures.

A cube is a solid figure with six congruent square

faces and with every edge the same length. A cube

has 8 vertices and 12 edges.

A cylinder is a solid figure formed by two congruent

parallel circles joined by a curved surface.

A cone is a solid, pointed figure that has a flat, round

face (usually a circle) that is joined to a vertex by a

curved surface.

A rectangular prism is a solid figure in which all six

faces are rectangles with three pair of parallel

congruent opposite faces.


3.14






A sphere is a solid figure with all of its points the

same distance from its center.

A square pyramid is a solid figure with one square

face and four triangular faces that share a common

vertex.

A face is a polygon that serves as one side of a solid

figure (e.g., a square is a face of a cube).

An angle is formed by two rays with a common

endpoint. This endpoint is called the vertex. Angles

are found wherever lines intersect. An angle can be

named in three different ways by using

– three letters to name, in this order, a point on one

ray, the vertex, and a point on the other ray;

– one letter at the vertex; or

– a number written inside the rays of the angle.

An edge is the line segment where two faces of a

solid figure intersect.

A vertex is the point at which two lines, line

segments, or rays meet to form an angle. It is also the

point on a three dimensional figure where three or

more faces intersect.

Students should be reminded that a solid geometric

object is hollow rather than solid. The “solid”

indicates a three-dimensional figure.


3.15

The student will identify and draw representations of points, line segments, rays, angles, and lines.



A point is an exact location in space. It has no

length or width. Usually, a point is named with a

capital letter.

A line is a collection of points going on and on in

both directions. It has no endpoints. When a line is

drawn, at least two points on it can be marked and

given capital letter names. The line can also be

named with a single, lower-case letter. Arrows

must be drawn to show that the line goes on in both

directions infinitely.

A line segment is part of a line. It has two

endpoints and includes all the points between those

endpoints. The endpoints are used to name a line

segment.

A ray is part of a line. It has one endpoint and

continues on and on in one direction.

An angle is formed by two rays having a common

endpoint. This endpoint is called the vertex. Angles

are found wherever lines and line segments

intersect. An angle can be named in three different

ways by using

– three letters to name, in this order, a point on

one ray, the vertex, and a point on the other

ray;

– one letter at the vertex; or

– a number written inside the rays of the angle.

Angle rulers may be particularly useful in

developing the concept of an angle.

All students should

Understand that line segments and angles are

fundamental components of plane polygons.

Understand that a line segment is a part of a

line, has two end points, and contains all the

points between those two endpoints.

Understand that points make up a line.

Understand that a line continues indefinitely in two

opposite directions.

Understand that a ray is part of a line, has one

endpoint, and continues indefinitely in only one

direction.

Understand that an angle is formed by two rays

having a common endpoint.




Identify examples of points, line segments, rays,

angles, and lines.

Draw representations of points, line segments, rays,

angles, and lines, using a ruler or straightedge.


3.16

The student will identify and describe congruent and noncongruent plane figures.



Congruent plane figures are figures having exactly

the same size and shape. Noncongruent plane

figures are figures that are not exactly the same size

and shape. Opportunities for exploring figures that

are congruent and/or noncongruent can best be

accomplished by using physical models.

Have students identify figures that are congruent or

noncongruent by using direct comparisons and/or

tracing procedures.

All students should

Understand that congruent plane figures match

exactly.

Understand that noncongruent plane figures do not

match exactly.

Understand that congruent plane figures remain

congruent even if they are in different spatial

orientations.

Understand that noncongruent plane figures remain

noncongruent even if they are in different spatial

orientations.




Identify examples of congruent and noncongruent

figures. Verify their congruence by laying one on

top of the other using drawings or models.

Determine and explain why plane figures are

congruent or noncongruent, using tracing

procedures.


3.17

The student will

a) collect and organize data, using observations, measurements, surveys, or experiments;

b) construct a line plot, a picture graph, or a bar graph to represent the data; and

c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the

data.



Investigations involving data should occur

frequently and relate to students’ experiences,

interests, and environment.

Formulating questions for investigations is student-

generated at this level. For example: What is the

cafeteria lunch preferred by students in the class

when four lunch menus are offered?

The purpose of a graph is to represent data gathered

to answer a question.

Bar graphs are used to compare counts of different

categories (categorical data). Using grid paper

ensures more accurate graphs.

– A bar graph uses parallel, horizontal or vertical

bars to represent counts for categories. One

bar is used for each category, with the

length of the bar representing the count for

that category.

– There is space before, between, and after the

bars.

– The axis displaying the scale representing the

count for the categories should extend one

increment above the greatest recorded piece

of data. Third grade students should collect

data that are recorded in increments of

All students should

Understand how data can be collected and

organized.

Understand that data can be displayed in different

types of graphs depending on the data.

Understand how to construct a line plot, picture

graph, or bar graph.

Understand that data sets can be interpreted and

analyzed to draw conclusions.




Formulate questions to investigate.

Design data investigations to answer formulated

questions, limiting the number of categories for

data collection to four.

Collect data, using surveys, polls, questionnaires,

scientific experiments, and observations.

Organize data and construct a bar graph on grid

paper representing 16 or fewer data points for no

more than four categories.

Construct a line plot with no more than 30 data

points.

Read, interpret and analyze information from line

plots by writing at least one statement.

Label each axis on a bar graph and give the bar

graph a title. Limit increments on the numerical

axis to whole numbers representing multiples of 1,

2, 5, or 10.

Read the information presented on a simple bar or

picture graph (e.g., the title, the categories, the

description of the two axes).


3.17

The student will

a) collect and organize data, using observations, measurements, surveys, or experiments;

b) construct a line plot, a picture graph, or a bar graph to represent the data; and

c) read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the

data.



whole numbers, usually multiples of 1, 2, 5, or 10.

– Each axis should be labeled, and the graph

should be given a title.

– Statements representing an analysis and

interpretation of the characteristics of the data

in the graph (e.g., similarities and differences,

least and greatest, the categories, and total

number of responses) should be written.

A line plot shows the frequency of data on a

number line. Line plots are used to show the spread

of the data and quickly identify the range, mode,

and any outliers.

Number of Books Read

Each x represents one student

When data are displayed in an organized manner,

the results of the investigations can be described

and the posed question answered.

Recognition of appropriate and inappropriate

statements begins at this level with graph

interpretations.

Analyze and interpret information from picture and

bar graphs, with up to 30 data points and up to 8

categories, by writing at least one sentence.

Describe the categories of data and the data as a

whole (e.g., data were collected on four ways to

cook or prepare eggs — scrambled, fried, hard

boiled, and egg salad — eaten by students).

Identify parts of the data that have special

characteristics, including categories with the

greatest, the least, or the same (e.g., most students

prefer scrambled eggs).

Select a correct interpretation of a graph from a set

of interpretations of the graph, where one is correct

and the remaining are incorrect. For example, a bar

graph containing data on four ways to cook or

prepare eggs — eaten by students show that more

students prefer scrambled eggs. A correct answer

response, if given, would be that more students

prefer scrambled eggs than any other way to cook

or prepare eggs.


3.18

The student will investigate and describe the concept of probability as chance and list possible results of a given situation.



A spirit of investigation and experimentation

should permeate probability instruction, where

students are actively engaged in explorations and

have opportunities to use manipulatives.

Investigation of experimental probability is

continued at this level through informal activities

using two-colored counters, spinners, and random

number generators (number cubes).

Probability is the chance of an event occurring.

The probability of an event occurring is the ratio of

desired outcomes to the total number of possible

outcomes. If all the outcomes of an event are

equally likely to occur, the probability of the event

= number of favorable outcomes

total number of possible outcomes .

The probability of an event occurring is represented

by a ratio between 0 and 1. An event is

“impossible” if it has a probability of 0 (e.g., the

probability that the month of April will have 31

days). An event is “certain” if it has a probability of

1 (e.g., the probability that the sun will rise

tomorrow morning).

When a probability experiment has very few trials,

the results can be misleading. The more times an

experiment is done, the closer the experimental

probability comes to the theoretical probability

(e.g., a coin lands heads up half of the time).

Students should have opportunities to describe in

informal terms (i.e., impossible, unlikely, as likely

as, equally likely, likely, and certain) the degree of

likelihood of an event occurring. Activities should

include real-life examples.

All students should

Investigate, understand, and apply basic concepts

of probability.

Understand that probability is the chance of an

event happening.




Define probability as the chance that an event will

happen.

List all possible outcomes for a given situation

(e.g., heads and tails are the two possible outcomes

of flipping a coin).

Identify the degree of likelihood of an outcome

occurring using terms such as impossible,

unlikely, as likely as, equally likely, likely, and certain.


3.18

The student will investigate and describe the concept of probability as chance and list possible results of a given situation.



For any event, such as flipping a coin, the equally

likely things that can happen are called outcomes.

For example, there are two equally likely outcomes

when flipping a coin: the coin can land heads up, or

the coin can land tails up.

A sample space represents all possible outcomes of

an experiment. The sample space may be organized

in a list, table, or chart.


3.19

The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the

patterns, using the same or different forms.



Exploring patterns requires active physical and

mental involvement.

The use of materials to extend patterns permits

experimentation or trial-and-error approaches that

are almost impossible without them.

Reproduction of a given pattern in a different

representation, using symbols and objects, lays the

foundation for writing numbers symbolically or

algebraically.

The simplest types of patterns are repeating

patterns. In each case, students need to identify the

basic unit of the pattern and repeat it. Opportunities

to create, recognize, describe, and extend repeating

patterns are essential to the primary school

experience.

Growing patterns are more difficult for students to

understand than repeating patterns because not only

must they determine what comes next, they must

also begin the process of generalization. Students

need experiences with growing patterns in both

arithmetic and geometric formats.

Create an arithmetic number pattern. Sample

numeric patterns include

– 6, 9, 12, 15, 18, (growing pattern);

– 1, 2, 4, 7, 11, 16, (growing pattern);

– 20, 18, 16, 14,…(growing pattern); and

– 1, 3, 5, 1, 3, 5, 1, 3, 5 (repeating pattern).

All students should

Understand that numeric and geometric patterns

can be expressed in words or symbols.

Understand the structure of a pattern and how it

grows or changes.

Understand that mathematical relationships exist in

patterns.

Understand that patterns can be translated from one

representation to another.




Recognize repeating and growing numeric and

geometric patterns (e.g., skip counting, addition

tables, and multiplication tables).

Describe repeating and growing numeric and

geometric patterns formed using numbers, tables,

and/or pictures, using the same or different forms.

Extend repeating and growing patterns of numbers

or figures using concrete objects, numbers, tables,

and/or pictures.


3.19

The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the

patterns, using the same or different forms.



In geometric patterns, students must often

recognize transformations of a figure, particularly

rotation or reflection. Rotation is the result of

turning a figure around a point or a vertex, and

reflection is the result of flipping a figure over a

line.

Sample geometric patterns include

– O Δ O O Δ Δ O O O Δ Δ Δ ; and

– □□★★□★□□★★□★.

A table of values can be analyzed to determine the

pattern that has been used, and that pattern can then

be used to find the next value.


3.20

The student will

a) investigate the identity and the commutative properties for addition and multiplication; and

b) identify examples of the identity and commutative properties for addition and multiplication.



Investigating arithmetic operations with whole

numbers helps students learn about several

different properties of arithmetic relationships.

These relationships remain true regardless of the

numbers.

The commutative property for addition states that

changing the order of the addends does not affect

the sum (e.g., 4 + 3 = 3 + 4). Similarly, the

commutative property for multiplication states that

changing the order of the factors does not affect the

product (e.g., 2 3 = 3 2).

The identity property for addition states that if zero

is added to a given number, the sum is the same as

the given number. The identity property of

multiplication states that if a given number is

multiplied by one, the product is the same as the

given number.

A number sentence is an equation with numbers

(e.g., 6 + 3 = 9; or 6 + 3 = 4 + 5).

All students should

Understand that mathematical relationships can be

expressed using number sentences.

Understand the identity property for addition.

Understand the identity property for multiplication.

Understand the commutative property of addition.

Understand the commutative property of

multiplication.

Understand that quantities on both sides of an

equals sign must be equal.

Understand that quantities on both sides of the not

equal sign are not equal.




Investigate the identity property for addition and

determine that when the number zero is added to

another number or another number is added to the

number zero, that number remains unchanged.

Examples of the identity property for addition are

0 + 2 = 2; 5 + 0 = 5.

Investigate the identity property for multiplication

and determine that when the number one is

multiplied by another number or another number is

multiplied by the number one, that number remains

unchanged. Examples of the identity property for

multiplication are 1 x 3 = 3; 6 x 1 = 6.

Recognize that the commutative property for

addition is an order property. Changing the order

of the addends does not change the sum (5 + 4 = 9

and 4 + 5 = 9).

Recognize that the commutative property for

multiplication is an order property. Changing the

order of the factors does not change the product (2

3 = 3 2).

Write number sentences to represent equivalent

mathematical relationships (e.g., 4 x 3 = 14 - 2).

Identify examples of the identity and commutative

properties for addition and multiplication.

Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 3

Learning Progressions The following pages are the Learning Progressions for the curriculum. More information about the Learning Progressions can be found on VISION. The Grading and Assessment, Module 3: Learning Progressions is about what Learning Progressions are, how they were developed, and how they are used to support instruction and build student learning.


LP 3.1a SOL 3.1: The student will:

a) read and write six-digit numerals and identify the place value and value of each digit; Learning Target: I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.

Learning Progression The student will use problem solving, mathematical communication,

mathematical reasoning, connections, and representations at each level of the learning progression.

Advanced Proficient

I can take the relationship of the places in the place value system (the value of each place is ten times the value of the place to its right) and extend this relationship to places more than one place to the right or left and give a correct proof of this relationship.

Proficient

I can read, write, and model six-digit numerals and identify the place value positions, value of each digit, and the relationship of each place value position to the next.

Intermediate

I can read, write, or model six-digit numerals.

Beginner

I can understand that different digits in a multi-digit number have different values depending on their place value position.


LP 3.1b SOL 3.1: The student will:

b) round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand; and Learning Target: I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.



Advanced Proficient

I can compare and contrast the accuracy of rounding compared to other forms of estimations (compatible number, front-end estimation, etc.).

Proficient

I can round whole numbers, 9,999 or less, to the nearest ten, hundred, and thousand and represent my thinking using pictures, numbers, and words.

Intermediate

I can determine whether a number is closer to one landmark number or another using a model (for example: on a number line, visualizing that 571 is closer to 600 than 500).

Beginner

I understand that if I don’t need an exact answer, I can round numbers as one way to estimate.


LP 3.1c SOL 3.1: The student will: c) compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to). Learning Target: I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less than, or equal to).



Advanced Proficient

I can determine two numbers and how they compare when given clues (for example: What two 4 digit numbers could I be thinking of when one number is 300 less than the other and the digits in the hundreds place are both even?).

Proficient

I can compare two whole numbers between 0 and 9,999, using symbols (>, <, or = ) and words (greater than, less

than, or equal to).

Intermediate

I understand that, when comparing numbers, the largest place value of each number should be evaluated first, followed by each consecutive place value (for example: when comparing 569 and 837, the digits in the hundreds place should be evaluated first).

Beginner

I understand the magnitude of numbers (500 is more than 50).


LP 3.2 SOL 3.2: The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic

fact sentences. The student will use these relationships to solve problems. Learning Target: I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences and solve problems.



Advanced Proficient

I can create problems involving inverse fact relationships and analyze a model of why the facts are related.

Proficient

I can use inverse relationships between addition/subtraction and multiplication/division to complete basic fact

sentences and solve problems.

Intermediate

I can find a subtraction fact when given a related addition fact/find a division fact when given a multiplication fact.

Beginner

I know that addition facts are related to subtraction facts and that multiplication facts are related to division facts.


LP 3.3ab SOL 3.3: The student will:

d) name and write fractions (including mixed numbers) represented by a model e) model fractions (including mixed numbers) and write fractions’ names

Learning Target: I can label and create multiple pictures / models of a given fraction. * Parameters: 1. Proper Fractions, Improper Fractions, and Mixed Numbers 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 2. Pictures / Models – Set, Area, Linear



Advanced Proficient

Using pictures / models and words, I can create and explain a real life example of how fractions are used.

Proficient

I can create and label multiple pictures / models of a given fraction.

Intermediate

I can identify the part (numerator) and whole (denominator) in a picture / model.


Beginner

I understand that the value of a fraction can be greater than 1 and can explain what improper fractions (3/2) and mixed numbers (1 ½) mean.

LP 3.3c SOL 3.3: The student will c) compare fractions having like and unlike denominators using words and symbols (>,<, or =) Learning Target: I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions.

* Parameters: 1. Only Proper Fractions

2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Like and Unlike Denominators 2. Pictures / Models: Set, Area, Linear



Advanced Proficient

Using pictures / models and words, I can create and explain a real life example of fractional pieces being compared and the strategy used to determine which is greater.

Proficient

I can develop and use a variety of strategies (pictures / models, benchmark numbers) to compare fractions.


Intermediate

I can describe the value of a fraction compared to a benchmark number (close to 0, less than 1/2, exactly 1/2, greater than 1/2, close to 1).

Beginner

I understand that when working with unit fractions, the larger the denominator (number of pieces that make up the whole), the smaller the pieces and therefore the smaller the value of the fraction. I understand that I only need to compare the numerators of fractions that have like denominators.

LP 3.4 SOL 3.4: The student will estimate solutions to and solve single-step and multistep problems involving the sum or difference of two whole

numbers, each 9,999 or less, with or without regrouping. Learning Target: I can estimate answers and solve problems involving one or more steps in which I will need to add and/or subtract numbers that

are 9,999 or less.



Advanced Proficient

I can create multi-step contexts and solve for a solution, using and comparing/contrasting multiple strategies.

Proficient

I can estimate answers and solve problems involving one or more steps in which I will need to add and/or

subtract numbers that are

9,999 or less.


Intermediate

I can estimate and solve problems involving one step in which I will need to add and/or subtract numbers that are 9,999 or less.

Beginner

I can understand that some contexts represent addition (combining) and others represent subtraction (separating).

LP 3.5 SOL 3.5: The student will recall multiplication facts through the twelves table, and the corresponding division facts. Learning Target: I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.



Advanced Proficient

I can generalize patterns I observe from models of multiplication and compare them to patterns and models of division.

Proficient

I can understand models and patterns of multiplication in order to recall multiplication facts and relate them to division facts.


Intermediate

I can create models (arrays, number lines, equal group pictures, etc.) to represent repeated addition and repeated subtraction.

Beginner

I understand the inverse relationship between addition and subtraction and use that relationship to help recall those number facts.

LP 3.6 SOL 3.6: The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that

involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less. Learning Target: I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication problems (one factor

99 or less and the second factor 5 or less).



Advanced Proficient

I can compare and contrast models of multiplication and justify the use of a particular model as it relates to solving practical, real-life problems.


Proficient

I can create and use models (area, set, and number lines) of multiplication to create and solve multiplication

problems (one factor 99 or less and the second factor 5 or less).

Intermediate

I can create area, set, and number line models for multiplication.

Beginner

I can identify area, set, and number line models and use them to model addition and subtraction problems.

LP 3.7 SOL 3.7: The student will add and subtract proper fractions having like denominators of 12 or less. Learning Target: I can use pictures / models to add and subtract fractions. * Parameters: 1. Only Proper Fractions 2. Halves, Thirds, Fourths, Fifths, Sixths, Eighths, Tenths, and Twelfths. 3. Only Like Denominators 4. Pictures / Models: Set, Area, Linear




Advanced Proficient

Using pictures / models and words, I can create and explain a real life situation involving adding and subtracting fractions and correctly explain how I would solve the problem.

Proficient

I can use pictures / models to add and subtract fractions.

Intermediate

I understand that when adding and subtracting fractions with like denominators, I can use the same whole number computation strategies with the numerators.

Beginner

I understand that fractions with the like denominators have the same size pieces that make up the whole.

LP 3.8 SOL 3.8: The student will determine, by counting, the value of a collection of bills and coins whose total value is $5.00 or less, compare the value of

the bills and coins, and make change. Learning Target: I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple strategies to make change.

Learning Progression

The student will use problem solving, mathematical communication,



Advanced Proficient

I can apply strategies for making change to real-life situations and explain the most efficient strategy depending on the practical problem.

Proficient

I can count the value of a collection of coins ($5.00 or less), compare the value of bills and coins, and use multiple

strategies to make change.

Intermediate

I can count the value of a collection of coins and count up when an additional set of coins is given.

Beginner

I can recognize coins and bills and compare their values.

LP 3.9 SOL 3.9: The student will estimate and use US Customary and metric units to measure

a) length to the nearest ½ inch, inch. Foot, yard, centimeter, and meter; b) liquid volume in cups, pints, quarts, gallons, and liters; c) weight/mass in ounces, pounds, grams and kilograms; and d) area and perimeter.

Learning Target: The student can measure in US Customary and metric units and apply length measurements to find areas and perimeters.




Advanced Proficient

I can compare and contrast area and perimeter.

Proficient I can measure in US Customary and metric units and apply length measurements to find areas and perimeters.

Intermediate I can measure length, mass, and liquid volume in US Customary and metric (standard) units and determine benchmarks for some measurements.

Beginning I can estimate length (centimeter and inch); weight/mass (pounds, ounces, kilograms, grams); and liquid volume (cups, pints, quarts, gallons, and liters). (Grade 2)

LP 3.10 SOL 3.10: The student will

a) measure the distance around a polygon in order to determine perimeter; and b) count the number of square units needed to cover a given surface in order to determine area.


Learning Target: I can find the perimeter of a polygon by adding the lengths of the line segments forming the polygon and the area of the region inside the polygon (polygonal region) by covering the polygon with square units.



Advanced Proficient

I can investigate strategies and solve problems involving both perimeter and area (ie: create a representation for a polygon with a perimeter of 20 and an area of 25).

Proficient

I can find the perimeter of a polygon by adding the lengths of the line segments forming the polygon and the area of the region inside the polygon (polygonal region) by covering the polygon with square units.

Intermediate I can explore perimeter and area of polygons using several representations.

Beginning I can describe/define polygon and know that a polygon does not include the area inside the polygon, only the line segments forming the polygon.

LP 3.11a SOL 3.11: The student will:

a) tell time to the nearest minute, using analog and digital clocks


Learning Target: I can tell time to the nearest minute using different clock models.



Advanced Proficient

I can create a model for an analog and digital clock when given a time.

Proficient


Intermediate

I can use skip counting by 5’s and 1’s to tell time by using one or more clock models.

Beginner

I can match a written time to a time shown on a clock, to the nearest minute.

LP 3.11b SOL 3.11: The student will:

b) determine elapsed time in one-hour increments over a 12-hour period.


Learning Target: I can tell time to the nearest minute and how many hours have passed (using a clock) when given a scenario involving the passing of time.



Advanced Proficient

I can create my own situation involving the passing of time and can describe a situation when it would be important to know the time to the nearest minute.

Proficient

I can tell time to the nearest minute and how many hours have passed (using a clock or elapsed time ruler) when given a scenario involving the passing of time.

Intermediate I can determine how many hours have passed by using a clock.

Beginning I can tell time to the nearest 5 minutes using analog and digital clocks and I understand that there are 60 minutes in an hour.

LP 3.13 SOL 3.13: The student will read temperature to the nearest degree from a Celsius thermometer and a Fahrenheit thermometer. Real

thermometers and physical models of thermometers will be used.


Learning Target: I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial models.



Advanced Proficient

I can create a model of a thermometer to fit an everyday situation involving temperature.

Proficient

I can read and write temperatures to the nearest degree using Celsius and Fahrenheit thermometers and pictorial

models.

Intermediate

I can use a thermometer or pictorial model to estimate temperatures in Celsius and Fahrenheit.

Beginner

I understand that thermometers are used to measure temperature and that there are two units of temperature measurement (Celsius and Fahrenheit).

LP 3.14


SOL 3.14: The student will identify, describe, compare and contrast characteristics of plane and solid geometric figures (circle, square, rectangle, triangle, cube, rectangular prism, square pyramid, sphere, cone, and cylinder) by identifying relevant characteristics including the number of angles, vertices, and edges, and the number and shape of faces, using concrete models. Learning Target: I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.



Advanced Proficient

I can justify characteristics of solid figures based on characteristics of plane figures.

Proficient I can identify, describe, compare and contrast characteristics of plane and solid geometric figures.

Intermediate I can identify, compare and contrast characteristics of solid geometric figures.

Beginning I can identify, compare and contrast characteristics of plane geometric figures.


LP 3.15 SOL 3.15: The student will identify and draw representations of points, line segments, rays, angles, and lines. Learning Target: I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.



Advanced Proficient

I can compare and contrast points, line segments, rays, angles, and lines, with justifications.

Proficient

I can identify and draw representations of points, line segments, rays, angles, and lines and name them as mathematicians do.

Intermediate I can identify examples of points, line segments, rays, angles, and lines in my environment and justify my identification.

Beginning I can identify line segments, angles, and points as fundamental parts of polygons.


LP 3.16 SOL 3.16: The student will identify and describe congruent and non-congruent plane figures. Learning Target: I can will identify and describe congruent and non-congruent plane figures and justify the identification.



Advanced Proficient

I can explain why figures with different spatial orientations are congruent or not congruent, using multiple strategies.

Proficient I can identify and describe congruent and noncongruent plane figures and justify my identification.

Intermediate I can use direct comparison or tracing to determine congruence.

Beginning I can describe congruence as same shape and same size.

Mathematics Learning Progressions: Grade 3

LP 3.19 SOL 3.19: The student will recognize and describe a variety of patterns formed using numbers, tables, and pictures, and extend the patterns, using the same or different forms. Learning Target: I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete objects, numbers,

tables, and pictures and identify mathematical relationships that exist within patterns.



Advanced Proficient

I can compare and contrast similar patterns using different models and generalize a pattern by extending the pattern even when it does not begin with 1.

Proficient

I can recognize, describe, and extend numeric and geometric patterns (repeating or growing) using concrete

objects, numbers, tables, and pictures and identify mathematical relationships that exist within patterns (for

example, skip counting on a hundreds chart models multiplication).

Intermediate

I can extend repeating and growing numeric and growing patterns and describe the pattern.

Beginner

I can recognize repeating and growing numeric and growing patterns.

Mathematics Learning Progressions: Grade 3

LP 3.20 SOL 3.20: The student will

a) investigate the identity and the commutative properties for addition and multiplication; and b) identify examples of the identity and commutative properties for addition and multiplication.

Learning Target: I can investigate the identity and commutative properties for addition and multiplication and identify examples of the properties.



Advanced Proficient

I can compare and contrast properties and justify why each property holds true.

Proficient

I can investigate the identity and commutative properties for addition and multiplication and identify examples of

the properties.

Intermediate

I can recognize patterns of number properties and match an example with its correct property.

Beginner

I can recognize a number sentence and know that both sides of a number sentence are equivalent expressions when I use an equal sign.

Grade 3 Math Intervention Ideas

Unit 2 – Place Value

Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games

Number and Operations Lessons 1-2 Game #1: The $1,000 Club Game #4: Try for $5,000 Game #7: Rounding Game (tens place) Game #11: Double Trouble(hundreds place) Game #17: Number Maker(thousands place) Game #19: From Here to There

Unit 3 – Computation With Whole Numbers (addition/subtraction)


Number and Operations Lessons 3-4 Algebra Lesson 5

Game #2: Doubles & Doubles Plus One Game #3: Teen Take-Away Game #5: Fast Ten-Yes or No? Game #6: Empty the Bank

Unit 4 – Money


Game #9: Pocket Money Game #18: Try for $5.00

Unit 5 – Computation With Whole Numbers (multiplication/division)


Number and Operations Lessons 5-7, 11-12 Algebra Lesson 6

Game #8: Groups Galore Game #10: Fishy Multiplication Game #11: Double Trouble Game #12: Array Game Game #13: Product Comparing Game #14: Side By Side

Unit 6 – Patterns & Data

Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games Algebra Lessons 1-2, 10 Data Analysis and Probability Lessons 2-3

Unit 7 – Geometry


Geometry Lessons 1-3, 5, 8-9

Unit 8 – Fractions, Probability, & Measurement


Number and Operations Lessons 15-19 Data Analysis and Probability Lessons 6-9

Game #16: Make a Pound

Unit 9 – Computation With Fractions


Number and Operations Lesson 20 Game #16: Make a Pound

Unit 10 – Elapsed Time & Temperature


Measurement Lesson 2

Unit 11 – Measuring My World


Measurement Lessons 3-6, 8-9, 11 Game #16: Make a Pound

Resources available in all LCPS Elementary Schools

Hands-On Standards books Every Day Counts Partner Games

NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)

VA SOL Alignment

Kindergarten Math

Domino Addition and Subtraction

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Activity

SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

Counting Sheep

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.

Activity SOL K.3 The student, given an ordered set of ten objects and/or

pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.

How Big is Your Foot?

Launch & Activity

SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.

1st Grade Math

Bunny Hip Hop

Launch

SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;

and b) group a collection of up to 100 objects into tens and ones and

write the corresponding numeral to develop an understanding of place value.

Activity

SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.

When does it Happen?

Launch & Activity

SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.

Ten is our Friend!

Launch

SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.

Activity SOL 1.6 The student will create and solve one-step story and picture

problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.

2nd Grade Math

Creative Cards

Launch & Activity

SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).

Piggy Banks

Launch & Activity

SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and

quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and

decimal point (.).

Show What You Know!

Launch

SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an

ordered set of objects; and b) write the ordinal numbers.

Activity

SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.

SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.

Pies for Sale

Launch SOL 2.19 The student will analyze data displayed in picture graphs,

pictographs, and bar graphs.

Activity

SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.

SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.

3rd Grade Math

Playful Puppies

Launch

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Activity

SOL 3.5 The student will recall multiplication facts through the twelves table, and the corresponding division facts.

SOL 3.6 The student will represent multiplication and division, using area, set, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor 5 or less.

SOL 3.10 The student will a) measure the distance around a polygon in order to determine

perimeter; and b) count the number of square units needed to cover a given

surface in order to determine area.

SOL 3.20 The student will a) investigate the identity and the commutative properties for

addition and multiplication; and b) identify examples of the identity and commutative properties

for addition and multiplication.

Correcting the Calculator

Launch & Activity

SOL 3.1 The student will a) read and write six-digit numerals and identify the place value

and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,

hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using

symbols (>, <, or = ) and words (greater than, less than, or equal to).

SOL 3.2 The student will recognize and use the inverse relationships between addition/subtraction and multiplication/division to complete basic fact sentences. The student will use these relationships to solve problems.

Fraction Reactions

Launch & Activity

SOL 3.3 The student will a) name and write fractions (including mixed numbers)

represented by a model; b) model fractions (including mixed numbers) and write the

fractions’ names; and c) compare fractions having like and unlike denominators, using

words and symbols (>, <, or =).

4th Grade Math

Bugs, Giraffes, Elephants, and More

Launch

SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.

SOL 4.7 The student will a) estimate and measure length, and describe the result in

both metric and U.S. Customary units; and b) identify equivalent measurements between units within

the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Activity

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Does it Make Sense?

Launch

SOL 4.3 The student will a) read, write, represent, and identify decimals expressed

through thousandths; b) round decimals to the nearest whole number, tenth, and

hundredth; c) compare and order decimals; and

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

Activity

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

The Bigger Half

Launch & Activity


Harry’s Hike

Launch


Activity

SOL 4.5 The student will a) determine common multiples and factors, including least

common multiple and greatest common factor; b) add and subtract fractions having like and unlike

denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving

addition and subtraction with fractions and with decimals.

5th Grade Math

Packed Parking

Launch

SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Activity

SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers

expressed as decimals through thousandths (divisors with only one nonzero digit); and

b) create and solve single-step and multistep practical problems involving decimals.

SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Finding Fractions

Launch

SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form

and vice versa; and b) compare and order fractions and decimals in a given set from

least to greatest and greatest to least.

Activity

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Varying Volumes

Launch & Activity

SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify

whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;

c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.

Customary and metric units; and e) choose an appropriate unit of measure for a given situation

involving measurement using U.S. Customary and metric units.

SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and b) investigate and describe the results of combining and

subdividing plane figures.

Location, Location, Location

Launch

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

Activity

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Mathematics Literature Connections Organized by Curriculum Units

Grade K Math Literature Connections

Unit 2: Counting

One, Two, Skip a Few: First Number Rhymes by Roberta Arenson

98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater

Unit 3: Comparing Sets

20 Hungry Piggies: A Number Book by Trudy Harris

Ten Little Rubber Ducks by Eric Carle

Ten Little Caterpillars by Bill Martin Jr

Henry the Fourth by Stuart J. Murphy

One Monday Morning by Uri Shulevitz

The Napping House by Audrey Wood

Tally O’Malley by Stewart J. Murphy

So you want to be President? By Judith St. George

The Great Graph Contest By Loreen Leedy

Unit 4: Geometry & Sorting

Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy

Unit 5: Shapes in Space

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 6: Geometry & Fractions

Give Me Half by Stuart J. Murphy

Full House by Dayle Ann Dodds

Unit 7: Measuring My World

Measuring Up by J.E. Osborne

Dumpling Soup by Jama Kim Rattigan

How Big is a Foot by Rolf Myller

Big and Little by Steven Jenkins

Time to… by Bruce McMillan

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

Telling Time with Big Mama Cat by D. Harper

Biggest, Strongest, Fastest by Steven Jenkins

Inch by Inch by Leo Lionni

Before and After: A Book of Nature Timescapes by Jan Thornhill

Unit 8: Skip Counting & Money

Arctic Fives Arrive by Elinor J. Pinczes

26 Letters and 99 Cents by Tana Hoban

Unit 9: Combining & Separating

More or Less by Stuart J. Murphy

Animals on Board by Stuart J. Murphy

A Quarter from the Tooth Fairy by Caren Holtzman

Grade 1 Math Literature Connections

Unit 2: Sorting, Ordering, & Patterns

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 3: Developing a Base Ten System

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Is It Larger? Is It Smaller? By T. Hoban

One Hundred Hungry Ants by Elinor J. Pinczes

Ten Sly Piranhas: A Counting Story in Reverse by William Wise

How Many, How Many, How Many by Rick Walton

98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater

Stay in Line by Teddy Slater


Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone

Flat Stanley by J. Brown

The Shapes We Eat by Simone T. Ribke

Give Me Half! By Stuart J. Murphy

Gator Pie by L. Mathews

Unit 5: Time & Fractions


Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Unit 6: Working With Data

Probably Pistachio by Stuart J. Murphy

So You Want to be President? By Judith St. George

The Great Graph Contest by Loreen Leedy

Ready, Set, Hop! By Stuart J. Murphy

Bunches and Bunches of Bunnies by Mathews and Bassett

Unit 7: Combining & Separating

Rooster’s Off to See the World by Eric Carle

Round Trip by A. Jonas

Lemonade For Sale by Stuart J. Murphy


How Do You Measure Weight? by Thomas K. and Heather Adamson

The Greedy Triangle by Marilyn Burns


How Big is a Foot? by Rolf Myller


Biggest, Strongest, Fastest by Steven Jenkins



Best Bug Parade by Stuart J. Murphy

Me and the Measure of Things by J. Sweeney

Unit 9: Applying Place Value

Shoes, Shoes, Shoes by A. Morris

Unit 10: Whole Number Computation

Animals on Board by Stuart J. Murphy

Elevator Magic by Stuart J. Murphy

Ten Black Dots by Donald Crew

Rooster’s Off to See the World by Eric Carle


How High Can a Dinosaur Count? by V. Fisher


The Penny Pot by Stuart J. Murphy


Unit 2: Extending Place Value

The Crayon Counting Book by Pam Munoz

Underwater Counting: Even Numbers by Jerry Pallotta

Unit 3: Computational Fluency

Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell

Mission: Addition by Loreen Leedy

Each Orange Had 8 Slices: A Counting Book by Paul Giganti


Unit 4: Applying Place Value to Computation/Problem Solving

Great Estimations by Bruce Goldstone

How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas

How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns

Sam and the Lucky Money by K. Chinn

Balancing Act by Ellen Stoll Walsh

Betcha by Stuart J. Murphy

Unit 5: Probability & Data

Frog and Toad are Friends by A. Lobel

Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel

Get Up and Go! By Stuart J. Murphy

Unit 6: Data & Problem Solving

So You Want to be President? By Judith St. George

Unit 7: Time & Temperature

Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema

The Grouchy Lady Bug by Eric Carle

Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel

What Time Is It? A Book of Math Riddles by Sheila Keenan


Eating Fractions by Bruce McMillan


Full House by Dayle Ann Dodds

The Patchwork Quilt by Valerie Flournoy



How Big is a Foot? By Rolf Myller



Biggest, Strongest, and Fastest by Steven Jenkins



Jelly Beans for Sale by Bruce McMillan

The Penny Pot by Stuart J. Murphy

The Coin Counting Book by Rosanne Lanczak Williams

Once Upon a Dime by Nancy Kelly Allen


Unit 2: Place Value

Many Is How Many? By Illa Pondendorf

A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein

Counting on Frank by Rod Clement

How Much Is a Million? by David M. Schwartz

If You Made a Million by David M. Schwartz

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Unit 3: Computation With Whole Numbers (addition/subtraction)

Ten Black Dots by Donald Crews

Dealing with Addition Lynette Long

One Duck Stuck by Phyllis Root

One Gorilla by Atsuko Morozumi

A Three Hat Day by Laura Geringer

Unit 4: Money

Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Penny: The Forgotten Coin by Denise Brenna-Nelson

The Coin Counting Book by Rozanne Lanczak Williams

The Penny Pot by Stuart Murphy

Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod

Unit 5: Computation With Whole Numbers (multiplication/division)

Amanda Bean’s Amazing Dream by Cindy Neuschwander

A Remainder of One (*extension) by Elinor J. Pinczes

One Hundred Angry Ants by Elinor J. Pinczes

2 x 2 = Boo by Loreen Leedy

7 x 9 Trouble by Claudia Mills

Too Many Kangaroo Things to Do by Stuart Murphy

Divide and Ride by Stuart Murphy

Bananas Jacqueline Farmer

Centipede’s 100 Shoes by Tony Ross

Ten Times Better by Richard Michelson

Unit 6: Patterns & Data

Emma’s Christmas by Irene Trivias

The Doorbell Rang by Pat Hutchins

One Hundred Angry Ants by Elinor Pinczes

She Came Bringing Me That Little Baby Girl by Eloise Greenfield

Knots on a Counting Rope by Bill Martin Jr.

Berries, Nuts, and Seeds by Diane L. Burns

Lemonade for Sale by Stuart Murphy

Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda

Grapes of Math by Greg Tang

The Quilting Bee by Gail Gibbons

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

Unit 7: Geometry

The Important Book by Margaret Wise Brown

Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone

Pablo’s Tree Pat Mora

If You Were a Polygon Marcie Aboff

It Looked Like Spilt Milk by Charles G. Shaw

Mummy Math by Cindy Neuschwander

Shape Up by David Adler

A Cloak for the Dreamer by Aileen Friedman

Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions

Eating Fractions by Bruce McMillan

Seven Little Hippos by Mike Thaler

Shoes, Shoes, Shoes by Ann Morris

Biggest, Strongest, Fastest Steve Jenkins

The Wolf’s Chicken Stew Keiko Kasza

A Very Improbably Story: A Math Adventure by Edward Einhorn

The Thirteen Days of Halloween Carool Greene

The Doorbell Rang Pat Hutchins

Whole-y Cow, Fractions are Fun! by Taryn Souders

Apple Fractions by Jerry Pallotta

The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta

Fraction Action by Loreen Leedy

Unit 10: Elapsed Time and Temperature

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

What Time is it, Mr. Crocodile? By Judy Sierra

Chimp Math by Ann Whitehead Nagda

Unit 11: Measurement

Spaghetti and Meatballs for All by Marilyn Burns

Perimeter, Area, and Volume David A. Adler

Pastry School in Paris Cindy Neuschwander

Measuring Penny (length) by Loreen Leedy

Biggest, Strongest, Fastest by Steve Jenkins

Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells

Polly’s Pen Pal by Stuart L. Murphy


Room for Ripley by Stuart Murphy


Unit 2: Number Sense: Whole Numbers

A Million Fish…More or Less by Patricia C. McKissack

Unit 3: Whole Number Operations & Applications (adding & subtracting)

Math Curse by Jon Scieszka and Lane Smith

The $1.00 Word Riddle Book by Marilyn Burns

Esio Trot by Roald Dahl

From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine

Giesecke

Anno’s Magic Seeds by Mitsumasa Anno

Equal Shmequal by Virginia Kroll

Unit 4: Whole Number Operations & Applications (multiplication & division)

The King’s Chessboard by David Birch

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Math Curse by Jon Scieszka and Lane Smith

Hottest, Coldest, Highest, Deepest by Steve Jenkins

In the Next Three Seconds…Predictions for the Millenium by Comp. Rowland Morgan

Ten Times Better by Richard Michelson

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

A Remainder of One by Elinor J. Pinczes

Counting on Frank by Rod Clement

Unit 5: Data & Statistics

The Great Graph Contest by Loreen Leedy

Unit 6: Number Sense: Rational Numbers

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

One Riddle, One Answer by Lauren Thompson

Icebergs and Glaciers by Seymour Simon

Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel

Unit 7: Rational Number Operations

Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley

Pizza Counting by Christina Dobson

Piece=Part=Portion by Gifford and Thaler

Fractions=Trouble! By Claudia Mills

Unit 8: Probability & Data Using Rational Numbers

Jumanji by Chris Van Allsburg

A Very Improbable Story by Edward Einhorn and Adam Gustavson

Pigs at Odds by Amy Axelrod and Sharon Nally

Unit 9: Patterns & Measurement

G is for Googol: A Math Alphabet Book by David M. Schwartz

How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen

Nolan

Icebergs and Glaciers by Seymour Simon

If You Hopped Like a Frog by David M. Schwartz

Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells

Biggest, Strongest, Fastest by Steve Jenkins

Unit 10: Plane Geometry & Transformations

Marvelous Math by Lee Bennett Hopkins

The Warlord’s Puzzle by Virginia Walton Pilegard

Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin

Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley

Chickens on the Move (Math Matters!) by Pamela Pollack


Unit 2

A Remainder of One by Elinor Pinczes

My Even Day by Doris Fisher

The Grapes of Math by Greg Tang

Math Appeal by Greg Tang

Among the Odds and Evens by Prescilla Turner


Unit 3

Germs Make Me Sick by Melvin Berger

Bats on Parade by Kathi Appelt

Unit 4

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Fraction Fun by David Adler

Unit 5

Measuring Penny by Loreen Leedy

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Counting On Frank by Rod Clements

How Long? How Wide? by Brian Cleary

Millions to Measure by David Schwartz

Fractions, Decimals, and Percents by David Adler

Unit 6

The Greedy Triangle by Marilyn Burns

Sir Cumference and the Dragon of Pi by Cindy Neuschwander

Unit 7

Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda

A More Perfect Union by Betsy Maestro

Model Performance Indicator Information for Curriculum Guides

Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).

These tables will be useful as you differentiate instruction for all of your learners, but they are especially

helpful for English Language Learners. Below are frequently asked questions about MPI.

What is a Model Performance Indicator (MPI)?

An MPI is a tool that can be used to show examples of how language is processed or produced within a

particular context, including the language with which students may engage during classroom instruction and

assessment.

Each MPI contains three main parts:

Language Function: The first part of an MPI, this shows how students are processing/producing

language at each level of language proficiency

Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge

and skills of the state’s content standards

Support: The final part of an MPI, this highlights the differentiation that should be incorporated for

students at each language level by suggesting appropriate instructional supports for students at each

level of language proficiency

The samples provided also include an example context for language use that provides a brief descriptor of the

activity or task in which students would be engaged, while the inclusion of topic-related language helps to

support the emphasis on imbedding academic language instruction into our content-area teaching practices.

How can these sample MPIs help me?

Educators can use MPI strands in several ways:

to align students’ performance to levels of language development

as a tool for creating language objectives/targets that will help extend students’ level of language

proficiency

as a means for differentiating instruction that incorporates the language of the content area in a way that

meets the needs of students’ levels of language proficiency

An MPI strand helps illustrate the progression of language development from one proficiency level to the next

within a particular context. As these strands are examples, they represent one of many possibilities; therefore,

they can be transformed in order to be made more relevant to the individual classroom context.

Where can I get more information about WIDA, MPIs, etc.?

See My Learning Plan for several WIDA training modules

Introduction to the WIDA ELD Standards

Transforming the WIDA ELD Standards

Interpreting the WIDA ACCESS Score Report

The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at www.wida.us

http://www.wida.us/

SOL Strand and Bullet: 3.17 The student will

a) Collect and organize data, using observations, measurements, surveys, or experiments;

b) Construct a line plot, a picture graph, or a bar graph to represent the data; and

c) Read and interpret the data represented in line plots, bar graphs, and picture graphs and write a sentence analyzing the data.

Example Context for Language Use: Students will gather data from their classmates on a topic of their choice (e.g., birthdays, favorite color,

favorite sport, number of siblings) or data from a newspaper on a topic of their choice (e.g., daily temperatures, sports scores). Students will create a

bar graph, picture graph, or line plot to record their data and write a sentence analyzing the data. As a class, students will practice interpreting

student-graphed or student-plotted data.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE data represented in line plots, picture graphs,

and bar graphs.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify the categories of

data represented in a line

plot, picture graph, or bar

graph using an illustrated

word bank in a small

group

Describe the categories

of data represented in a

line plot, picture graph,

or bar graph using an

illustrated word/phrase

bank and oral sentence

frames with a partner

Discuss data represented

in a line plot, picture

graph, or bar graph using

oral sentence starters and

following a model with a

partner

Present data represented

in a line plot, picture

graph, or bar graph with

a partner

Present and explain

data represented in a


or bar graph with a

partner

RE

AD

ING

Distinguish categories of



graph using an illustrated

and labeled example and

an illustrated word bank

in a small group

Compare categories of

data represented in a


or bar graph using an

illustrated and labeled

example in a small

group

Formulate questions about



graph based on a template

in a small group

Interpret data

represented in a line plot,

picture graph, or bar

graph in a small group

Analyze data

represented in a line

plot, picture graph, or

bar graph in a small

group

WR

ITIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging Lev

el 6-R

each

ing

Create labels for data

represented in line plots,

picture graphs, and bar

graphs using an

illustrated template and

an illustrated word bank

in a small group

Create labels for data

represented in line plots,

picture graphs, and bar

graphs using a template

with a partner

Describe data represented

in line plots, picture

graphs, and bar graphs

using written sentence

frames with a partner

Interpret data represented

in line plots, picture

graphs, and bar graphs

using a written example

and a phrase bank

Analyze data

represented in line

plots, picture graphs,

and bar graphs in a

math journal

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:

data, collect, organize, observations, measurements, surveys, experiments, line plot, picture graph, bar graph, title, axis, key increments, number line,

categories, identify, describe, discuss, present, explain, create, interpret, analyze

SOL Strand and Bullet: 3.18 The student will investigate and describe the concept of probability as chance and list possible results of a give situation Example Context for Language Use: After reviewing the definition of probability (the chance of an event happening), students will explore the

meaning of vocabulary words associated with the concept of probability: certain, likely, equally likely, as likely as, unlikely, impossible. Given a

scenario presented with realia (e.g., a cookie jar has 5 chocolate chip cookies and 15 oreo cookies), students will answer questions about the

probability of reaching into the cookie jar and selecting an oreo (likely) or a chocolate chip cookie (unlikely) or an oatmeal cookie (impossible).

Students will then create their own scenarios and a set of probability questions.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE the concept of probability and all possible

outcomes of a given situation.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Discuss the concept of

probability and all

possible outcomes of a

given situation (e.g.,

different types of cookies

in a cookie jar) using

visuals, realia, and

following a model in a

small group

Discuss the concept of

probability and all



different types of

cookies in a cookie jar)

using realia and oral

sentence frames in a

small group

Ask and answer questions

about the concept of

probability and all




in a cookie jar) using

realia in a small group

Explain the concept of

probability and all




in a cookie jar) with a

partner

Justify a prediction

based on the concept of

probability and all



different types of

cookies in a cookie jar)

with a partner

R

EA

DIN

G

Associate experiment

results with the concept

of probability and all


given situation based on

illustrated text and

labeled illustrations in a

small group using L1

Associate experiment

results with the concept

of probability and all


given situation based on

illustrated text and

labeled illustrations in a

small group

Formulate questions about

the concept of probability

and all possible outcomes

of a given situation from

written scenarios using a

bilingual dictionary with a

partner

Draw conclusions about



of a given situation from

written scenarios with a

partner

Analyze the concept of

probability and all


given situation from

written scenarios

WR

ITIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Describe in a math

journal the concept of

probability and all


given situation using a

template and an

illustrated word/phrase

bank in a small group

using L1 or L2

Describe in a math

journal the concept of

probability and all


given situation using a

writing template and a

word/phrase bank in a

small group

Write questions about the

concept of probability and

all possible outcomes of a

given situation using

question frames and a

bilingual dictionary with a

partner

Create a diagram to show



of a given situation with

a partner

Create written

scenarios to teach the

concept of probability

and all possible

outcomes of a given

situation with a partner

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions such as:

probability, investigate, possible outcome, predict, certain, likely, equally likely, as likely as, unlikely, impossible, counters, spinners, number cubes,

discuss, ask and answer questions, explain, justify, associate, formulate questions, draw conclusions, analyze, describe

GRADE 3 MATHEMATICS CURRICULUM GUIDE · LCPS Grade 3 Mathematics Curriculum Guide 2016-2017 Quarter...

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Transcript of GRADE 3 MATHEMATICS CURRICULUM GUIDE · LCPS Grade 3 Mathematics Curriculum Guide 2016-2017 Quarter...