2015 Fifth Grade MATHEMATICS - Mr. Smith's...

1 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department June 2014

Fifth Grade

MATHEMATICS Curriculum Map

2014 – 2015

Volusia County Schools

Mathematics Florida Standards


I. Critical Areas for Mathematics in Grade 5……………….………..2 II. Mathematics Florida Standards: Grade 5 Overview……….…….3

III. Standards for Mathematical Practice………………………….……4 IV. Common Addition and Subtraction Situations……………….…..5 V. Common Multiplication and Division Situations…………………6 VI. 5E Learning Cycle: An Instructional Model………………………7

VII. Domains A. Operations and Algebraic Thinking…………………………………..8 B. Numbers and Operations in Base Ten…………………………..…..8 C. Numbers and Operations – Fractions………………………………15 D. Measurement and Data……………………………………….…..….21 E. Geometry……………………………………………………….……...21

VIII. Appendices Appendix A: Formative Assessment Strategies…………………….40 Appendix B: Intervention / Remediation Guide……………………..50

IX. Glossary of Terms for the Mathematics Curriculum Map…….51

Table of Contents


Critical Areas for Mathematics in Grade 5 Gradetandards

Mathematics Grade 5 In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (i.e., unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations; and (3) developing understanding of volume.

(1) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike

denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaning of fractions, of multiplication and division, and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

(2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. Students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense. They compute products and quotients of decimals to hundredths efficiently and accurately.

(3) Students recognize volume as an attribute of three-dimensional space. They understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or overlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. They select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume. They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determine volumes to solve real world and mathematical problems.


Domain: Operations and Algebraic Thinking

Cluster 1: Write and interpret numerical expressions.

Cluster 2: Analyze patterns and relationships.

Domain: Number and Operations in Base Ten

Cluster 1: Understand the place value system.

Cluster 2: Perform operations with multi-digit whole numbers and with decimals to hundredths.

Domain: Number and Operations—Fractions

Cluster 1: Use equivalent fractions as a strategy to add and subtract fractions.

Cluster 2: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Domain: Measurement and Data

Cluster 1: Convert like measurement units within a given measurement system.

Cluster 2: Represent and interpret data.

Cluster 3: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

Domain: Geometry

Cluster 1: Graph points on the coordinate plane to solve real-world and mathematical problems.

Cluster 2: Classify two-dimensional figures into categories based on their properties.

Grade 5 Overview


Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (SMP.1)

Solving a mathematical problem involves making sense of what is known and applying a thoughtful and logical process which

sometimes requires perseverance, flexibility, and a bit of ingenuity.

2. Reason abstractly and quantitatively. (SMP.2)

The concrete and the abstract can complement each other in the development of mathematical understanding: representing a

concrete situation with symbols can make the solution process more efficient, while reverting to a concrete context can help make

sense of abstract symbols.

3. Construct viable arguments and critique the reasoning of others. (SMP.3)

A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting

evidence.

4. Model with mathematics. (SMP.4)

Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (SMP.5)

Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical

understanding.

6. Attend to precision. (SMP.6)

Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical

explanations.

7. Look for and make use of structure. (SMP.7)

Recognizing a structure or pattern can be the key to solving a problem or making sense of a mathematical idea.

8. Look for and express regularity in repeated reasoning. (SMP.8)

Recognizing repetition or regularity in the course of solving a problem (or series of similar problems) can lead to results more

quickly and efficiently.


Common Addition and Subtraction Situations

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Addend Unknown Both Addends Unknown1

Put Together/

Take Apart2

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5, 5 – 3 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Difference Unknown Bigger Unknown Smaller Unknown

Compare 3

(“How many more?” version):

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

(“How many fewer?” version):

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5, 5 – 2 = ?

(Version with “more”):

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

(Version with “fewer”):

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ?, 3 + 2 = ?

(Version with “more”):

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

(Version with “fewer”):

Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have? 5 – 3 = ?, ? + 3 = 5

1 These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left of the equal sign, help children understand

that the = sign does not always mean makes or results in, but always does mean is the same number as. 2 Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this basic situation, especially for small numbers

less than or equal to 10. 3 For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown and using less for the smaller unknown). The

other versions are more difficult.


Common Multiplication and Division Situations4

4The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples.

5The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are

in 3 rows and 6 columns. How m any apples are in there? Both forms are valuable. 6Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement

situations.

Unknown Product

Group Size Unknown (“How many in each group?” Division)

Number of Groups Unknown (“How many groups?” Division)

3 × 6 = ? 3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all?

Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag?

Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed?

Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays5, Area6

There are 3 rows of apples with 6 apples in each row. How many apples are there?

Area example. What is the area of a 3 cm by 6 cm rectangle?

If 18 apples are arranged into 3 equal rows, how many apples will be in each row?

Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be?

Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Compare

A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost?

Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue hat cost?

Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as longs as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?

Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

General a × b = ? a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ?


ENGAGEMENT EXPLORATION EXPLANATION ELABORATION EVALUATION The engagement phase of the model

is intended to capture students’ interest and focus their thinking on the concept, process, or skill

that is to be learned.

During this engagement phase, the teacher is on center stage.

The exploration phase of the model is intended to provide students with a common set of experiences from

which to make sense of the concept, process or skill that is to be learned.

During the exploration phase, the students come to center stage.

The explanation phase of the model is intended to grow students’

understanding of the concept, process, or skill and its associated

academic language.

During the explanation phase, the teacher and students

share center stage.

The elaboration phase of the model is intended to construct a deeper understanding of the concept, process, or skill through the exploration of related ideas.

During the elaboration phase, the teacher and students

share center stage.

The evaluation phase of the model is intended to be used during all phases

of the learning cycle driving the decision-making process and

informing next steps.

During the evaluation phase, the teacher and students

share center stage.

What does the teacher do?

create interest/curiosity

raise questions

elicit responses that uncover student thinking/prior knowledge (preview/process)

remind students of previously taught concepts that will play a role in new learning

familiarize students with the unit


provide necessary materials/tools

pose a hands-on/minds-on problem for students to explore

provide time for students to “puzzle” through the problem

encourage students to work together

observe students while working

ask probing questions to redirect student thinking as needed


ask for justification/clarification of newly acquired understanding

use a variety of instructional strategies

use common student experiences to: o develop academic language o explain the concept

use a variety of instructional strategies to grow understanding

use a variety of assessment strategies to gage understanding


provide new information that extends what has been learned

provide related ideas to explore

pose opportunities (examples and non-examples) to apply the concept in unique situations

remind students of alternate ways to solve problems

encourage students to persevere in solving problems


observe students during all phases of the learning cycle

assess students’ knowledge and skills

look for evidence that students are challenging their own thinking

present opportunities for students to assess their learning

ask open-ended questions: o What do you think? o What evidence do you have? o How would you explain it?

What does the student do?

show interest in the topic

reflect and respond to questions

ask self-reflection questions: o What do I already know? o What do I want to know? o How will I know I have learned

the concept, process, or skill?

make connections to past learning experiences


manipulate materials/tools to explore a problem

work with peers to make sense of the problem

articulate understanding of the problem to peers

discuss procedures for finding a solution to the problem

listen to the viewpoint of others


record procedures taken towards the solution to the problem

explain the solution to a problem

communicate understanding of a concept orally and in writing

critique the solution of others

comprehend academic language and explanations of the concept provided by the teacher

assess own understanding through the practice of self-reflection


generate interest in new learning

explore related concepts

apply thinking from previous learning and experiences

interact with peers to broaden one’s thinking

explain using information and experiences accumulated so far


participate actively in all phases of the learning cycle

demonstrate an understanding of the concept

solve problems

evaluate own progress

answer open-ended questions with precision

ask questions

Evaluation of Engagement The role of evaluation during the

engagement phase is to gain access to students’ thinking during the

pre-assessment event/activity.

Conceptions and misconceptions currently held by students are uncovered during this phase.

These outcomes determine the concept, process, or skill to be

explored in the next phase of the learning cycle.

Evaluation of Exploration The role of evaluation during the exploration phase is to gather an

understanding of how students are progressing towards making sense of

a problem and finding a solution.

Strategies and procedures used by students during this phase are

highlighted during explicit instruction in the next phase.

The concept, process, or skill is formally explained in the next phase

of the learning cycle.

Evaluation of Explanation The role of evaluation during the

explanation phase is to determine the students’ degree of fluency (accuracy

and efficiency) when solving problems.

Conceptual understanding, skill refinement, and vocabulary acquisition

during this phase are enhanced through new explorations.

The concept, process, or skill is elaborated in the next phase

of the learning cycle.

Evaluation of Elaboration The role of evaluation during the

elaboration phase is to determine the degree of learning that occurs

following a differentiated approach to meeting the needs of all learners.

Application of new knowledge in unique problem solving situations

during this phase constructs a deeper and broader understanding.

The concept, process, or skill has been and will be evaluated as part of all phases of the learning cycle.

5E Learning Cycle: An Instructional Model


Standards for Mathematical Practice Students will: (to be embedded throughout instruction as appropriate)

Make sense of problems and

persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and

critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision. Look for and make use of structure.

Look for and express regularity in repeated

reasoning.

SMP.1 SMP.2 SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8

MAFS Domains: Number and Operations in Base Ten Operations and Algebraic Thinking

Pacing: Weeks 1 - 9 August 18 – October 17

Clusters Learning Targets Standards Vocabulary


MAFS: Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

MAFS.5.NBT.1.1 base ten numerals cubed (power of 3) decimal decimal point divide equal to equivalent expanded form exponent expression greater than hundredths less than multiply power of 10 product quotient round squared (power of 2) tenths thousandths whole number word form

Students will:

explain that a digit in one place is 10 times the value of the digit to its right.

explain that a digit in one place is 1/10 the value of the digit to its left.

demonstrate competency with place value concepts in the context of explaining patterns involving powers of 10.

MAFS: Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MAFS.5.NBT.1.2

Students will:

express powers of 10 using whole-number exponents (e.g., 10 = 10¹, 100 = 10², 1000= 10³).

illustrate and explain the pattern for how and why the number of zeros in a product (when multiplying a whole number by a power of 10) relates to the power of 10 (e.g., 5 x 100, and 5 x 10² equal 500).

illustrate and explain the pattern in the placement of the decimal point when a decimal is multiplied by a power of 10. (e.g., multiplying 15.3 by 100, or 15.3 x 10², results in 1530--where the decimal point in the quotient is 2 places to the right of where it was in the factor).

illustrate and explain the pattern in the placement of the decimal point when a decimal is divided by a power of 10 (e.g., dividing 15.3 by 100, or 15.3 ÷ 10², results in 0.153--where the decimal point in the quotient is 2 places to the left of where it was in the dividend).



MAFS: Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form,

e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10) + 9 x (1/100) + 2 x (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and <

symbols to record the results of comparisons.

MAFS.5.NBT.1.3

base ten numerals cubed (power of 3) decimal decimal point divide equal to equivalent expanded form exponent expression greater than hundredths less than multiply power of 10 product quotient round squared (power of 2) tenths thousandths whole number word form

Students will:

represent decimals using place value, models, and graphics of place value through the thousandths place.

E.g., Place Value Charts

represent decimals up to the thousandths place numerically.

E.g., Equivalent forms of 0.34 are: 34/100 3/10 + 4/100 30/100 + 4/100 0.30 + 0.04 340/1000 3 × (1/10) + 4 × (1/100) 3 × (1/10) + 4 × (1/100) + 0 × (1/1000)

read and write decimals up to thousandths in word form, base ten numerals, and expanded form.

compare two decimals up to the thousandths using place value and record the comparison using symbols <, >, or =.

MAFS: Use place value understanding to round decimals to any place. MAFS.5.NBT.1.4 Students will:

explain how to use place value to round decimals to any place.

round decimals, up to thousandths.

demonstrate competency with place value concepts in the context of rounding. HINT: Students will use rounding, benchmark numbers, or number lines, to predict the relative size of answers when adding, subtracting, multiplying or dividing decimals.


Cluster 1: Write and interpret numerical expressions.

MAFS: Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.

MAFS.5.OA.1.1 braces brackets conventional order equality expression operation parentheses

Students will:

perform operations in the conventional order (i.e., multiplication and division before addition and subtraction).

simplify and write numerical expressions that may include parentheses, brackets, and/or braces.

evaluate expressions and determine why the value changes when the order changes

MAFS: Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) as three times as large as 18932 + 921, without having to calculate the indicated sum or product.

MAFS.5.OA.1.2

Students will:

apply an understanding of operations and grouping symbols to write numerical expressions without evaluating (i.e., solving) them.

apply an understanding of operations and grouping symbols to interpret the meaning of numerical expressions without evaluating (i.e., solving) them.


MAFS: Fluently multiply multi-digit whole numbers using the standard algorithm. MAFS.5.NBT.2.5 area model array compatible numbers decompose digit Distributive property divide dividend divisor equal sharing equation expanded notation factor inverse operation multiple multiply partial quotients place value product quotient remainder repeated subtraction

Students will:

recall basic multiplication facts. (I.e., this is a 3rd

grade skill)

describe and demonstrate how the standard algorithm relates to previously taught multiplication strategies based on place value and the properties of operations.

use the standard algorithm for multi-digit whole number multiplication with ease (3-digit by 2-digit.

HINT: Even though the standard leads more towards computation, the connection to story contexts is critical.

E.g., {[24 ÷ (3 + 5)] – 1}

{[24 ÷ 8] – 1}

{3 – 1} 2



MAFS: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.5.NBT.2.6 area model array compatible numbers decompose digit Distributive property divide dividend divisor equal sharing equation expanded notation factor inverse operation multiple multiply partial quotients place value product quotient remainder repeated subtraction

Students will:

explain the inverse relationship between multiplication and division.

describe and demonstrate the process of division using a variety of models (e.g., expanded notation, partial quotients, repeated subtraction, equal sharing, place-value, properties).

illustrate and explain calculations by using equations, rectangular arrays, and/or area models.

model and apply a variety of strategies to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

HINT: Even though the standard leads more towards computation, the connection to story contexts is critical. The standard algorithm is not taught until 6

th grade.

E.g., Expanded notation is the use of the Distributive property in division problems, for

example, 639 3 can be expressed as:

(600 + 30 + 9) 3 = (600 3) + (30 3) + (9 3). Partial quotients is a strategy for long division using groupings of multiples of the divisor and then adding the partial quotients to find the answer.

26 r 4 partial quotients

5 134

- 50 10 84 - 50 10 34 - 25 5 9 - 5 1

4

interpret remainders in the context of a story.

use an understanding of the relationship between multiplication and division to check the quotient.

Multiples of 5 Find compatible numbers for use with the strategy of partial quotients. 1 × 5 = 5 2 × 5 = 10 5 × 5 = 25 10 × 5 = 50 20 × 5 = 100


Suggested Instructional Resources – Unit 1 MAFS enVisionMATH AIMS Lakeshore Internet

MAFS.5.NBT.1.1

Whole number place value magnets

cpalms.org Shift the Place, Shift the Value Understanding Place Value

www.k-5mathteachingresources.com Comparing Digits

grade5commoncoremath.wikispaces.hcpss.org 5.NBT.1 Assessment Tasks

www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx

5th grade Unit 1 Framework 5th grade Unit 2 Framework

MAFS.5.NBT.1.2

Step-up lesson 1


cpalms.org Seeking Patterns Using Base Ten and Powers of Ten Intro to Multiplying Decimals by 10, 100, 1000

www.k-5mathteachingresources.com Multiplying a Whole Number by a Power of 10 Multiplying a Decimal by a Power of 10 Dividing a Whole Number by a Power of 10 Dividing a Decimal by a Power of 10

grade5commoncoremath.wikispaces.hcpss.org 5.NBT.2



MAFS.5.NBT.1.3

Deducing Decimals Dealing with Decimals

Decimal place value magnets Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Decimals Have a Point! Batting a Thousand(th)

www.k-5mathteachingresources.com Representing Decimals with Base Ten Blocks



5th grade Unit 2 Framework

http://www.cpalms.org/Public

http://www.cpalms.org/Public/PreviewResource/Preview/28707


http://www.k-5mathteachingresources.com/

http://www.k-5mathteachingresources.com/support-files/comparing-digits.pdf

https://grade5commoncoremath.wikispaces.hcpss.org/5.NBT.1

https://grade5commoncoremath.wikispaces.hcpss.org/Assessing+5.NBT.1

http://www.georgiastandards.org/Common-Core/Pages/Math-K-5.aspx

https://www.georgiastandards.org/Common-Core/Common%20Core%20Frameworks/CCGPS_Math_5_Unit1FrameworkSE.pdf






http://www.k-5mathteachingresources.com/support-files/multiplying-a-whole-number-by-a-power-of-10.pdf

http://www.k-5mathteachingresources.com/support-files/multiplying-a-decimal-by-a-power-of-10.pdf

http://www.k-5mathteachingresources.com/support-files/dividing-a-whole-number-by-a-power-of-10.pdf

http://www.k-5mathteachingresources.com/support-files/dividing-a-decimal-by-a-power-of-10.pdf









http://www.k-5mathteachingresources.com/support-files/representingdecimalswithbase105.nbt3.pdf





MAFS enVisionMATH AIMS Lakeshore Internet

MAFS.5.NBT.1.4

6-1 Decimal place value magnets Gr. 5 Daily Dose of Fractions & Decimals

www.k-5mathteachingresources.com Rounding Decimals to the Nearest Hundredth




MAFS.5.OA.1.1

cpalms.org Watch Out for Parentheses Order of Operations Bingo

www.k-5mathteachingresources.com Target Number Dash Numerical Expressions Clock

grade5commoncoremath.wikispaces.hcpss.org 5.OA.1



MAFS.5.OA.1.2

Willie the Wheel Man

cpalms.org Words to Expressions Video Game Scores

www.k-5mathteachingresources.com Comparing Digits

grade5commoncoremath.wikispaces.hcpss.org 5.OA.2




http://www.k-5mathteachingresources.com/support-files/roundingdecimalstothenearesthundredth.pdf








http://www.k-5mathteachingresources.com/support-files/targetnumberdash5.oa1.pdf

http://www.k-5mathteachingresources.com/support-files/numercialexpressionswallclock.pdf

https://grade5commoncoremath.wikispaces.hcpss.org/5.OA.1







http://www.k-5mathteachingresources.com/support-files/comparing-digits.pdf






MAFS.5.NBT.2.5

cpalms.org Chance Product

www.k-5mathteachingresources.com Make the Largest Product Make the Smallest Product




MAFS.5.NBT.2.6

1-1 1-3 1-5 1-6 3-1 3-8


cpalms.org What Are They Thinking? Understanding Division.

www.k-5mathteachingresources.com Partial Quotients Partition the Dividend Multiplying Up







http://www.k-5mathteachingresources.com/support-files/makethelargestproduct.pdf

http://www.k-5mathteachingresources.com/support-files/makethesmallestproduct.pdf







http://www.k-5mathteachingresources.com/support-files/division-strategy-partial-quotients3.pdf

http://www.k-5mathteachingresources.com/support-files/division-strategy-partition-the-dividend.pdf

http://www.k-5mathteachingresources.com/support-files/division-strategy-multiplying-up.pdf















reasoning.


MAFS Domains: Number and Operations in Base Ten Number and Operations - Fractions

Pacing: Weeks 10 - 18 October 21 – December 19

Learning Targets Standards Vocabulary


MAFS: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

MAFS.5.NBT.2.7 addition strategies decimal divide division strategies hundredths multiplication strategies multiply place value product quotient subtraction strategies tenths

Students will:

add decimals, to hundredths, using concrete models, drawings, strategies based on place value, and properties of operations.

represent and justify addition strategies and reasoning used to solve problems.

subtract decimals, to hundredths, using concrete models, drawings, strategies based on place value, properties of operations and the relationship between addition and subtraction.

represent and justify subtraction strategies and reasoning used to solve problems.

multiply decimals using area model and drawings.

multiply decimals using strategies based on an understanding of place value and properties of operations.

represent and justify multiplication strategies and reasoning used to solve problems.

divide decimals using area model and drawings.

divide decimals using strategies based on an understanding of place value and properties of operations.

represent and justify division strategies and reasoning used to solve problems. HINT: This standard requires students to extend the models and strategies developed for operations with whole numbers.

E.g., Use a model to solve 3 – 0.6.




MAFS: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) / bd.)

MAFS.5.NF.1.1 benchmark fractions common factors denominator difference divisible equivalent factor fraction fraction greater than

one (

)

like denominator mixed number numerator prime reasonableness sum unlike denominator whole number

Students will:

apply concepts of factors, multiples, and equivalent fractions to find common denominators. (4

th grade skill)

represent addition and subtraction of fractions, including mixed numbers, with unlike denominators using concrete models, graphical models, and equations. HINT: Subtrahends may not be greater than the minuends and cannot be a negative number.

HINT: Concrete models include, but are not limited to, fraction strips, fraction circles, pattern blocks, Geoboards, rulers, and other tangible objects. Graphical models include, but are not limited to, pictures of base-ten blocks, drawings, and linear models (number lines).



MAFS: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

MAFS.5.NF.1.2

common factors denominator difference equivalent estimate factor fraction like denominator numerator prime reasonableness sum unlike denominator

Students will:

solve word problems involving addition and subtraction of fractions with like and unlike denominators using visual fraction models or equations.

use benchmark fractions and number sense of fractions to estimate and assess reasonableness of answers. HINT: Subtrahends may not be greater than the minuends and cannot be a negative number.


MAFS: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

MAFS.5.NF.2.3 array denominator equation equivalent formula fraction mixed number multiply numerator partition product quotient repeated addition represent unit fraction whole number

Students will: explain that fractions (a/b) can be represented as a division of the numerator by the

denominator (a ÷ b). For example, 5/3 = 5 ÷ 3

HINT: In Grade 4 students connected fractions with addition and multiplication, understanding that 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 5 x 1/3; therefore 5 ÷ 3 = 5 x 1/3

illustrate that the denominator represents the number of equal portions needed. illustrate that the numerator represents the total amount being divided. express why a ÷ b can be represented by the fraction a/b. solve word problems involving the division of whole numbers.

o predict whether the quotient will be a whole number, mixed number, or fraction. o illustrate a solution strategy using visual fraction models or equations that

represent the problem. o interpret and explain why the quotient is a whole number, mixed number, or

fraction. E.g., Show how 3 ÷ 7 can also be represented as 3/7. Divide each of 3 rectangles into 7 equal parts resulting in a total of 21 equal parts. Divide the 21 parts into 7 equal groups. The result is 3/7 of 1 whole.



MAFS: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a

sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)


Students will:

extend the fundamental understanding of multiplication as repeated addition, to multiplication of a fraction by a whole number as repeated addition of a unit fraction (e.g., 2 x (1/4) = 1/4 + 1/4) .

develop a fundamental understanding that the multiplication of a fraction by a whole number could be represented as repeated addition of a unit fraction (e.g., 2 x (1/4) = 1/4 + 1/4).

extend the understanding of multiplication by a unit fraction to the multiplication of any quantity by a fraction (i.e., Just as 1/3 of 5 is one part when 5 is partitioned (divided) into 3 equal parts, so 2/3 of 5 is 2 parts when 5 is partitioned into 3 equal parts.).

use the understanding of multiplication by a fraction to develop the general formula for the product of two fractions, a/b x c/d = ac/bd. HINT: Grade 5 students do NOT need to express the formula in the general algebraic form (a/b x c/d = ab/cd). They need to reason out many examples using fraction strips and number line diagrams. 2/3 x 5/2 = 2x5/3x2

create story contexts for problems involving multiplication of a fraction and a whole number or multiplication of two fractions.

MAFS: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit

fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

MAFS.5.NF.2.4

divide a rectangle with fractional side lengths into rectangles whose sides are the corresponding unit fractions.

use an array of square units to calculate the area of a rectangle with fractional sides.

use unit fraction squares to prove the area of rectangles with fractional side lengths.

I.e., 2/3 x 4/5 represented using an area model:



MAFS.5.NBT.2.7

6-4 6-5 6-6 6-11B 6-11C 6-11D 6-11F 6-11G

Pack and Post Operation Decimals

Write and wipe graphing boards Decimal Operations Grids Decimals Activity Stations Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Dividing Decimals Investigations Base Blocks Decimals

www.k-5mathteachingresources.com Base Ten Pictures with Decimals

www.slideshare.net/bujols/model-multiplication-of-decimals How to Model Multiplication of Decimals

fractionbars.com/CommonCore/Gd5Les/CCSSDSDivStep3Gd5.pdf

Dividing Decimals by Decimals




MAFS.5.NF.1.1

8-1 8-2

Fraction Time Fractions with Pattern Blocks Fraction Action: 4 Fraction Action: 5 Fraction Action: 9

Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Using Models to Add Fractions Making S'mores

www.k-5mathteachingresources.com Creating Equivalent Fractions to Add Unlike Fractions Creating Equivalent Fractions to Subtract Unlike Fractions

grade5commoncoremath.wikispaces.hcpss.org 5.NF.1



MAFS.5.NF.1.2

8-3 8-4 8-6

Royal Rugs Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Do These Add Up? Estimating Using Benchmark Fractions

www.k-5mathteachingresources.com Subtracting Mixed Numbers (Unlike Denominators)

Addition Word Problems with Fractions








http://www.k-5mathteachingresources.com/support-files/base-10-pictures-with-decimals.pdf

http://www.slideshare.net/bujols/model-multiplication-of-decimals


http://fractionbars.com/CommonCore/Gd5Les/CCSSDSDivStep3Gd5.pdf










http://www.k-5mathteachingresources.com/support-files/creating-equivalent-fractions-to-add-unlike-fractions.pdf

http://www.k-5mathteachingresources.com/support-files/creating-equivalent-fractions-to-subtract-unlike-fractions.pdf

https://grade5commoncoremath.wikispaces.hcpss.org/5.NF.1







http://www.k-5mathteachingresources.com/support-files/subtracting-mixed-numbers-with-unlike-denominators.pdf

http://www.k-5mathteachingresources.com/support-files/fractionwordproblem1.pdf






MAFS.5.NF.2.3

9-7A Area Tiles


cpalms.org Picture This! Fractions as Division

www.k-5mathteachingresources.com Relating Fractions to Division

www.engageny.org Grade 5 Module 4 grade5commoncoremath.wikispaces.hcpss.org 5.NF.3 5.NF.B.3 Lesson Dividing it Up.doc



MAFS.5.NF.2.4

9-7B 9-7C 12-3A

Fraction Action: 6 Fair Squares

Fraction Multipliers Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Modeling Fraction Multiplication Multiplying a Fraction by a Fraction Area Models: Multiplying Fractions Painting a Wall

www.k-5mathteachingresources.com Multiplying Fractions by Dividing Rectangles Fraction X Fraction Word Problems

lessonplanspage.com Multiplying Fractions Using Manipulatives







http://www.k-5mathteachingresources.com/support-files/relating-fractions-to-division-problems.pdf

http://www.engageny.org/sites/default/files/resource/attachments/math-g5-m4-full-module.pdf


https://grade6commoncoremath.wikispaces.hcpss.org/Grade+5+Numbers+and+Operations+-+Fractions









http://www.k-5mathteachingresources.com/support-files/multiplyingfractionsbydividingrectangles5.nf4a.pdf

http://www.k-5mathteachingresources.com/support-files/fraction-x-fraction-word-problems.pdf

http://lessonplanspage.com/mathmultiplyingfractionsmanipulatives46-htm/














reasoning.


MAFS Domains: Number and Operation - Fractions Measurement and Data Geometry

Pacing: Weeks 19 - 29 January 6 – March 19



MAFS: Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor,

without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the

given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.


Students will:

interpret the relationship between the size of the factors and the size of the product without performing the actual multiplication.

HINT: This standard calls for students to examine the magnitude of products in terms of the relationship between two types of problems.

explain why multiplying a given number by a number or fraction greater than 1 results in a product greater than the given number (e.g., if 3/4 is the given number and it is multiplied by 5, the product will be larger than 3/4).

explain why multiplying a given number by a fraction less than 1 results in a product less than the given number (e.g., if 5 is the given number and it is multiplied by 3/4, the product results in a fraction that is less than 5).

multiply a given fraction by 1 to find an equivalent fraction (e.g., 3/4 x 2/2 = 6/8). (this is a 4

th grade skill)

relate the principle of fraction equivalence to the effect of multiplying a fraction by 1. E.g.,

Example 1: Mrs. Jones teaches in a room that is 60 feet wide and 40 feet long. Mr. Thomas teaches in a room that is half as wide, but has the same length. How do the dimensions and area of Mr. Thomas’ classroom compare to Mrs. Jones’ room? Draw a picture to prove your answer.

Example 2: How does the product of 225 x 60 compare to the product of 225 x 30? How do you know? Since 30 is half of 60, the product of 22 5x 60 will be double or twice as large as the product of 225 x 30.



MAFS: Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem.


Students will:

solve real world problems involving multiplication of fractions and mixed numbers and interpret the product in the context of the problem.

explain or illustrate solution strategies using visual fraction models or equations that represent the problem.

MAFS: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.)

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4÷(1/5) = 20 because 20 x (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

MAFS.5.NF.2.7

Students will:

apply an understanding of the division of whole numbers to the concept of dividing with fractions (e.g., 1/3 ÷ 4 can be interpreted as sharing a 1/3 slice of pizza with 4 people).

divide unit fractions by whole numbers (e.g., 1/3 ÷ 4) using visual models.

create and solve story contexts where a unit fraction is divided by a whole number (not zero) using a visual model.

divide whole numbers by unit fractions (e.g., 4 ÷ 1/5) using visual models.

create and solve story contexts where a whole number (not zero) is divided by a unit fraction using a visual model.

solve real world problems involving division of unit fractions by whole numbers using fraction models and equations.

solve real world problems involving division of whole numbers by unit fractions using fraction models and equations.

E.g., Angelo has 4 lbs of peanuts. He wants to give each of his friends 1/5 lb. How many friends can receive 1/5 lb. of peanuts?

1 lb. of peanuts

𝟏

𝟓 lb.

1

3

1

12


Cluster 1: Convert like measurement units within a given measurement system.

MAFS: Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

MAFS.5.MD.1.1 accurate balance convert conversion customary units feet grams hours inches kilogram kilometer length line plot liters mass meters metric units miles milligrams milliliters millimeters minutes ounces pounds precise ruler scale seconds time tons volume weight yards

Students will:

compare units of measure within the same system and same dimensions (i.e., inches to feet, ounces to pounds, millimeters to meters, grams to kilograms, seconds to minutes).

convert units within the same system (customary or metric)

apply knowledge of length, weight, mass, and time to solve multi-step word problems using measurement conversions.

Cluster 2: Represent and interpret data.

MAFS: Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

MAFS.5.MD.2.2

Students will:

measure and record objects to the nearest 1/2, 1/4, or 1/8 unit.

HINT: Measures for length, mass, and liquid volume will be the focus for this standard.

record and display a set of measurements in fractions of a unit on a line plot

E.g., Ten beakers, measured in liters, are filled with a liquid.

solve problems involving information presented in line plots.

HINT: Refer to pages 5-6 in the Fifth Grade Mathematics Curriculum Map for clarification of Common Addition, Subtraction, Multiplication and Division situations. It is expected that students will become proficient in finding the unknown number for all situations.


Cluster 3: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

MAFS: Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be

used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n

cubic units.

MAFS.5.MD.3.3

additive attribute attribute B= area of base composite solid cubic units formula height length rectangular prism solid figure volume width

Students will:

identify volume as an attribute of a solid figure.

explain that a cube with 1 unit side length is “one cubic unit” of volume.

explain a process for finding the volume of a solid figure by filling it with unit cubes without gaps and overlaps.

MAFS: Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. MAFS.5.MD.3.4

Students will:

measure the volume of a hollow three-dimensional figure (i.e., rectangular prism and cube) by filling it with unit cubes without gaps and counting the number of unit squares.

determine the appropriate size unit to measure the volume of a rectangular prism or cube (e.g., base 10 units, wooden cubes, centimeter cubes, base 10 thousands cube, etc.).


Cluster 3, cont: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.

MAFS: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base.

a. Represent threefold whole-number products as volumes, e.g.,to represent the associative property of multiplication.

b. Apply the formula V= l x w x h and V= B x h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of non-overlapping parts, applying this technique to solve real world problems.

MAFS.5.MD.3.5

additive attribute attribute B= area of base composite solid cubic units formula height length rectangular prism solid figure volume width

Students will:

relate finding the product of three numbers (length, width, and height) to finding volume.

use the formula for area (3rd

grade skill) to develop an understanding of volume.

relate the associative property of multiplication to finding volume.

calculate volume of rectangular prisms and cubes, with whole number edge lengths, using the formula for volume (V = bwh or V = Bh) in real world and mathematical problems.

E.g., 1. Find the area of the base by multiplying its length by its width (B = l × w). 2. Multiply the area of the base by the height (V = Bh).

label appropriate units of measure for volume.

decompose a composite solid into non-overlapping rectangular prisms to find the volume of the solid by finding the sum of the volumes of each of the decomposed prisms.

E.g., What is the volume of water needed to fill the pool in the diagram?

solve real world problems involving volume.

(3 x 2) is represented by the first layer

(3 x 2) x 5 is represented by the number of 3 x 2 layers

(3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) =

6 + 6 + 6 + 6 + 6 = 30

6 representing the size/area of one layer

The deep end of the pool measures 14 ft. × 10 ft. × 5 ft. making the volume 700 cubic feet.

The shallow end of the pool measures 6 ft. × 5 ft. × 5 ft. making the volume 150 cubic feet.

700 cubic feet + 150 cubic feet = 850 cubic feet


Cluster 2: Classify two-dimensional figures into categories based on their properties.

MAFS: Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angle.

MAFS.5.G.2.3 2-dimensional acute angle attribute category circle classify concave congruent convex edge half-circle hexagon intersecting irregular kite obtuse angle octagon parallel parallelogram pentagon perpendicular polygon quadrilateral quarter circle rectangle regular rhombus right angle side square symmetry trapezoid triangle Venn diagram vertex

Students will:

compare and describe the geometric attributes of two-dimensional figures (i.e., triangle, quadrilateral, rectangle, square, rhombus, trapezoid, kite, pentagon, hexagon, octagon, circle, half-circle, quarter circle).

categorize two-dimensional figures according to their individual and shared geometric attributes.

HINT: Geometric attributes include properties of sides (i.e., parallel, perpendicular, congruent), properties of angles (i.e., type, measurement, congruent), and properties of symmetry (i.e., point and line).

explain the reasoning for the determined categories.

MAFS: Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. MAFS.5.G.2.4

organize figures into a Venn diagram based on determined attributes.

E.g.,



MAFS.5.NF.2.5

9-7D Fraction Action: 6 Fair Squares

Fraction Multipliers Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Multiplying a Fraction by a Fraction Fractions - Rectangle Multiplication

www.k-5mathteachingresources.com Multiplication and Scale Problems

nlvm.usu.edu Rectangle Multiplication of Fractions



Reasoning with Fractions p.110-117

MAFS.5.NF.2.6

9-7E Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Garden Variety Fractions To multiply or not to multiply? Making Cookies

www.k-5mathteachingresources.com Fraction x Mixed Number Word Problems Whole Number x Mixed Number Models Mixed Number x Fraction Models



Comparing MP3s p.90-101

http://www.cpalms.org/Uploads/resources/26674/1/4/docs/Mary%20Thon%20Schedule.docx



http://www.k-5mathteachingresources.com/support-files/multiplication-and-scale-problems.pdf

http://nlvm.usu.edu/en/nav/frames_asid_194_g_2_t_1.html?open.instructions







http://www.k-5mathteachingresources.com/support-files/fraction-x-mixed-no.-word-problems-5nf6.pdf

http://www.k-5mathteachingresources.com/support-files/Whole-Number-x-Mixed-Number-Models.pdf

http://www.k-5mathteachingresources.com/support-files/Mixed-Number-x-Fraction-Models.pdf





MAFS.5.NF.2.7

9-7F 9-7G 9-7H

Straw Planes Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Painting a Room Origami Stars Models for the Multiplication and Division of Fractions

www.k-5mathteachingresources.com Divide a Unit Fraction by a Whole Number Dividing a Whole Number by a Unit Fraction Divide a Whole Number by a Unit Fraction Division of Fractions Word Problems

ccgpsmathematicsk-5.wikispaces.com Where are the Cookies?



Dividing with Unit Fractions p.119-124

MAFS.5.MD.1.1

cpalms.org Conversion Excursion Stand Up and Cheer

k-5mathteachingresources.com Comparing Units of Metric Linear Measure Metric Conversion Word Problems

grade5commoncoremath.wikispaces.hcpss.org 5.MD.1



MAFS.5.MD.2.2

15-1A cpalms.org What's the Plot?

k-5mathteachingresources.com Fractions on a Line Plot Sacks of Flour







http://www.k-5mathteachingresources.com/support-files/Divide-a-Unit-Fraction-by-a-Whole-Number.pdf

http://www.k-5mathteachingresources.com/support-files/dividing-a-whole-number-by-a-unit-fraction-5.nf7b.pdf

http://www.k-5mathteachingresources.com/support-files/Divide-a-whole-number-by-a-unit-fraction.pdf

http://www.k-5mathteachingresources.com/support-files/divisionoffractionwordproblems.pdf

http://ccgpsmathematicsk-5.wikispaces.com/K-5+Formative+Assessment+Lessons+%28FALs%29





http://www.k-5mathteachingresources.com/support-files/comparingunitsofmetriclinearmeasure.pdf

http://www.k-5mathteachingresources.com/support-files/measurementwordproblemsmetric.pdf

https://grade5commoncoremath.wikispaces.hcpss.org/5.MD.1



http://www.k-5mathteachingresources.com/support-files/fractionsonalineplot.pdf

http://www.k-5mathteachingresources.com/support-files/sacksofflour.pdf






MAFS.5.MD.3.3

Essential Math: Measurement of Rectangles (some pieces of the lesson)

Hands-On Volume Center

cpalms.org Finding Volume (Utah Education Network) Manipulating Cubic Units Houses with Height Numbers Volume

k-5mathteachingresources.com Exploring Volume Building Rectangular Prisms with a Given Volume



Differentiating Area and Volume p.14-19 How Many Ways p.22-27

MAFS.5.MD.3.4

Hands-On Volume Center

cpalms.org Volume: It's All About the Count Pump Up the Volume

k-5mathteachingresources.com 3D Structures Roll a Rectangular Prism Four Open Boxes



Books, Books, and More Books p.40-43

MAFS.5.MD.3.5

Luggage Limits Hands-On Volume Center

cpalms.org Volume: Let's Be Efficient Formulating Volume

k-5mathteachingresources.com Comparing Volumes of Cereal Boxes Project What's the Volume? Ordering Rectangular Prisms by Volume



Super Solids p.44-47





http://www.k-5mathteachingresources.com/support-files/exploringvolume.pdf

http://www.k-5mathteachingresources.com/support-files/buildingrectangularprismswithagivenvolume.pdf






http://www.k-5mathteachingresources.com/support-files/3d-structures.pdf

http://www.k-5mathteachingresources.com/support-files/rollarectangularprism.pdf

http://www.k-5mathteachingresources.com/support-files/rollarectangularprism.pdf

http://www.k-5mathteachingresources.com/support-files/four-open-boxes.pdf





http://www.k-5mathteachingresources.com/support-files/comparing-volumes-of-cereal-boxes-project-and-rubric.pdf

http://www.k-5mathteachingresources.com/support-files/whats-the-volume.pdf

http://www.k-5mathteachingresources.com/support-files/orderingrectangularprismsbyvolume.pdf





MAFS.5.G.2.3

12-1A Classifying Quadrilaterals

2-D geometric shapes tub

cpalms.org Analyzing Polyhedra Triangles are Plane Easy:

k-5mathteachingresources.com Quadrilateral Criteria Constructing Quadrilaterals

grade5commoncoremath.wikispaces.hcps.org 5.G.3



MAFS.5.G.2.4

12-1A 12-1B

2-D geometric shapes tub

cpalms.org Analyzing Polyhedra Sets and The Venn Diagram (Beginner) Where in the Venn are the Quadrilaterals? "

k-5mathteachingresources.com Triangle Hierarchy Diagram Triangle Hierarchy Diagram 2 Regular/Irregular Hierarchy Diagram

grade5commoncoremath.wikispaces.hcpss.org 5.G.4





http://www.k-5mathteachingresources.com/support-files/quadrilateralcriteria.pdf

http://www.k-5mathteachingresources.com/support-files/constructingquadrilaterals.pdf

https://grade5commoncoremath.wikispaces.hcpss.org/5.G.3






http://www.k-5mathteachingresources.com/support-files/triangle-hierarchy-diagram1.pdf

http://www.k-5mathteachingresources.com/support-files/trianglehierarchydiagram2.pdf

http://www.k-5mathteachingresources.com/support-files/regularirregularhierarchydiagram.pdf














reasoning.


MAFS Domains: Geometry Operations and Algebraic Thinking Numbers and Operations in Base Ten Numbers and Operations - Fractions

Pacing: Weeks 30 - 39 March 30 – June 3


Cluster 1: Graph points on the coordinate plane to solve real-world and mathematical problems.

MAFS: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

MAFS.5.G.1.1 coordinate grid coordinate plane coordinates equidistant horizontal increasing intervals ordered pairs origin plot point quadrant vertical x- and y-coordinates x-axis y-axis

Students will:

draw a coordinate plane with two intersecting perpendicular lines.

identify the intersection as the origin and the point where 0 lies on each of the lines.

label the horizontal axis as the x-axis, and the vertical axis as the y-axis.

identify an ordered pair such as (3,2) as an x-coordinate followed by a y-coordinate. explain the relationship between an ordered pair and its location on the coordinate plane.

HINT: The first quadrant includes only positive numbers.

MAFS: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

MAFS.5.G.1.2

Students will:

determine when a mathematical problem has a set of ordered pairs.

use appropriate tools strategically to identify, locate and plot ordered pairs of whole numbers on a graph in the first quadrant of the coordinate plane.

describe the horizontal and vertical movements necessary to get from one point to another on a coordinate plane.

determine the distance between two ordered pairs using appropriate tools or strategies.

relate the coordinate values of any graphed point to the context of the problem.


Cluster 2: Analyze patterns and relationships.

MAFS: Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

MAFS.5.OA.2.3 compare coordinate coordinate plane corresponding terms graph horizontal numerical pattern plot rule ordered pairs trend vertical x-axis y-axis

Students will:

generate two numerical patterns with the same starting number for two given rules.

E.g., Today, both Melissa and Joe have no fish. They both go fishing each day. Melissa catches 2 fish each day. Joe catches 4 fish each day.

explain the relationship between the two numerical patterns by comparing how each pattern grows or by comparing the relationship between each of the corresponding terms from each pattern.

E.g., Since Joe catches 4 fish each day, and Melissa catches 2 fish, the amount of Joe’s fish is always greater. Joe catches twice as many fish as Melissa.

form ordered pairs out of corresponding terms from each pattern and graph them on a coordinate plane.

observe and explain patterns and trends represented in the coordinate plane.

E.g.,

02468

101214161820

0 1 2 3 4 5

Fish

Day

Catching Fish

Melisa

Joe



MAFS: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

MAFS.5.NBT.2.6 area model array compatible numbers decompose digit Distributive property divide dividend divisor equal sharing equation expanded notation factor inverse operation multiple multiply partial quotients place value product quotient remainder repeated subtraction

Students will:

explain the inverse relationship between multiplication and division. describe and demonstrate the process of division using a variety of models (e.g., expanded notation, partial quotients, repeated subtraction, equal sharing, place-value, properties).

E.g., Expanded notation is the use of the Distributive property in division problems, for

example, 639 3 can be expressed as:

(600 + 30 + 9) 3 = (600 3) + (30 3) + (9 3). Partial quotients is a strategy for long division using groupings of multiples of the divisor and then adding the partial quotients to find the answer.

26 r 4 partial quotients

5 134

- 50 10 84 - 50 10 34 - 25 5 9 - 5 1

4

illustrate and explain calculations by using equations, rectangular arrays, and/or area models.

model and apply a variety of strategies to find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors.

interpret remainders in the context of a story. HINT: Even though the standard leads more towards computation, the connection to story contexts is critical. The standard algorithm is not taught until 6

th grade.

use an understanding of the relationship between multiplication and division to check the quotient.

Multiples of 5 Find compatible numbers for use with the strategy of partial quotients. 1 × 5 = 5 2 × 5 = 10 5 × 5 = 25 10 × 5 = 50 20 × 5 = 100



MAFS: Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

MAFS.5.NBT.2.7 addition strategies decimal divide division strategies hundredths multiplication strategies multiply place value product quotient subtraction strategies tenths

Students will:

add decimals, to hundredths, using concrete models, drawings, strategies based on place value, and properties of operations.

represent and justify addition strategies and reasoning used to solve problems.

subtract decimals, to hundredths, using concrete models, drawings, strategies based on place value, properties of operations and the relationship between addition and subtraction.

represent and justify subtraction strategies and reasoning used to solve problems.

multiply decimals using area model and drawings.

multiply decimals using strategies based on an understanding of place value and properties of operations.

represent and justify multiplication strategies and reasoning used to solve problems.

divide decimals using area model and drawings.

divide decimals using strategies based on an understanding of place value and properties of operations.

represent and justify division strategies and reasoning used to solve problems. HINT: This standard requires students to extend the models and strategies developed for operations with whole numbers.

E.g., Use a model to solve 3 – 0.6.



Cluster 1: Use equivalent fractions as a strategy add and subtract fractions.

MAFS: Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc) / bd.)

MAFS.5.NF.1.1 benchmark fractions common factors denominator difference divisible equivalent factor fraction fraction greater than

one (

)

like denominator mixed number numerator prime reasonableness sum unlike denominator whole number

Students will:

apply concepts of factors, multiples, and equivalent fractions to find common denominators. (4

th grade skill)

represent addition and subtraction of fractions, including mixed numbers, with unlike denominators using concrete models, graphical models, and equations. HINT: Subtrahends may not be greater than the minuends and cannot be a negative number. HINT: Concrete models include, but are not limited to, fraction strips, fraction circles, pattern blocks, Geoboards, rulers, and other tangible objects. Graphical models include, but are not limited to, pictures of base-ten blocks, drawings, and linear models (number lines).

MAFS: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

MAFS.5.NF.1.2

Students will:

solve word problems involving addition and subtraction of fractions with like and unlike denominators using visual fraction models or equations.

use benchmark fractions and number sense of fractions to estimate and assess reasonableness of answers. HINT: Subtrahends may not be greater than the minuends and cannot be a negative number.


Cluster 2: Apply and extend previous understandings of multiplication and division to multiply and divide.

MAFS: Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?


Students will: explain that fractions (a/b) can be represented as a division of the numerator by the

denominator (a ÷ b). For example, 5/3 = 5 ÷ 3 HINT: In Grade 4 students connected fractions with addition and multiplication, understanding that 5/3 = 1/3 + 1/3 + 1/3 + 1/3 + 1/3 = 5 x 1/3; therefore 5 ÷ 3 = 5 x 1/3

illustrate that the denominator represents the number of equal portions needed. illustrate that the numerator represents the total amount being divided. express why a ÷ b can be represented by the fraction a/b. solve word problems involving the division of whole numbers.

o predict whether the quotient will be a whole number, mixed number, or fraction.

o illustrate a solution strategy using visual fraction models or equations that represent the problem.

o interpret and explain why the quotient is a whole number, mixed number, or fraction.

E.g., Show how 3 ÷ 7 can also be represented as 3/7. Divide each of 3 rectangles into 7 equal parts resulting in a total of 21 equal parts. Divide the 21 parts into 7 equal groups. The result is 3/7 of 1 whole.



MAFS.5.G.1.1

5-1 Mark My Words Space Shuttle Coordinates Captain Kid’s Grid Hurkle Hide and Seek Plotting Planes

Write and wipe graphing boards

cpalms.org Cartesian Classroom Human Ordered Pairs: Battle Ship Using Grid Paper:

k-5mathteachingresources.com Coordinate Grid Geoboards Coordinate Shapes Coordinate Grid Swap Coordinate Grid Tangram Assorted Coordinate Grid Paper

beaconlearningcenter.com Beacon Learning Center




MAFS.5.G.1.2

5-2 Willie the Wheel Man Sticking Around Just Drop It!

Write and wipe graphing boards

cpalms.org Map It Out

k-5mathteachingresources.com Geometric Shapes on the Coordinate Grid




http://www.beaconlearningcenter.com/Lessons/Lesson.asp?ID=296



http://www.k-5mathteachingresources.com/support-files/coordinategridgeoboards.pdf

http://www.k-5mathteachingresources.com/support-files/coordinateshapes.pdf

http://www.k-5mathteachingresources.com/support-files/coordinategridswap.pdf

http://www.k-5mathteachingresources.com/support-files/coordinategridtangram.pdf

http://www.k-5mathteachingresources.com/support-files/coordinategridpaperset.pdf

http://www.k-5mathteachingresources.com/support-files/coordinategridpaperset.pdf

http://www.beaconlearningcenter.com/Lessons/




http://www.k-5mathteachingresources.com/support-files/geometricshapesonthecoordinategrid.pdf






MAFS.5.OA.2.3

5-5A cpalms.org Cool School

k-5mathteachingresources.com Function Table and Graph Template Function Table and Coordinate Plane Paper Addition on the Coordinate Plane Subtraction on the Coordinate Plane

grade5commoncoremath.wikispaces.hcps.org 5.OA.3



MAFS.5.NBT.2.6

1-1 1-3 1-5 1-6 3-1 3-8


cpalms.org What Are They Thinking? Understanding Division.

k-5mathteachingresources.com Partial Quotients Partition the Dividend Multiplying Up




MAFS.5.NBT.2.7

6-4 6-5 6-6 6-11B 6-11C 6-11D 6-11F 6-11G

Pack and Post Operation Decimals

Write and wipe graphing boards Decimal Operations Grids Decimals Activity Stations Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Dividing Decimals Investigations Base Blocks Decimals

k-5mathteachingresources.com Base Ten Pictures with Decimals

www.slideshare.net/bujols/model-multiplication-of-decimals

How to Model Multiplication of Decimals

fractionbars.com/CommonCore/Gd5Les/CCSSDSDivStep3Gd5.pdf

Dividing Decimals by Decimals





http://www.k-5mathteachingresources.com/support-files/functiontableandgraph.pdf

http://www.k-5mathteachingresources.com/support-files/functiontableandcoordinategridpaper.pdf

http://www.k-5mathteachingresources.com/support-files/additiononthecoordinateplane.pdf

http://www.k-5mathteachingresources.com/support-files/subtractiononthecoordinateplane.pdf




http://www.k-5mathteachingresources.com/support-files/division-strategy-partial-quotients3.pdf

http://www.k-5mathteachingresources.com/support-files/division-strategy-partition-the-dividend.pdf

http://www.k-5mathteachingresources.com/support-files/division-strategy-multiplying-up.pdf





http://www.k-5mathteachingresources.com/support-files/base-10-pictures-with-decimals.pdf










MAFS.5.NF.1.1

8-1 8-2

Fraction Time Fractions with Pattern Blocks Fraction Action: 4 Fraction Action: 5 Fraction Action: 9


cpalms.org Using Models to Add Fractions Making S'mores Fractions Jigsaw

k-5mathteachingresources.com Creating Equivalent Fractions to Add Unlike Fractions Creating Equivalent Fractions to Subtract Unlike Fractions




MAFS.5.NF.1.2

8-3 8-4 8-6

Royal Rugs Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Do These Add Up? Estimating Using Benchmark Fractions

k-5mathteachingresources.com Subtracting Mixed Numbers (Unlike Denominators)

Addition Word Problems with Fractions




MAFS.5.NF.2.3

9-7A Area Tiles Gr. 5 Daily Dose of Fractions & Decimals

cpalms.org Picture This! Fractions as Division

k-5mathteachingresources.com Relating Fractions to Division

www.engageny.org Grade 5 Module 4

grade5commoncoremath.wikispaces.hcpss.org 5.NF.3 5.NF.B.3 Lesson Dividing it Up.doc






http://www.k-5mathteachingresources.com/support-files/creating-equivalent-fractions-to-add-unlike-fractions.pdf

http://www.k-5mathteachingresources.com/support-files/creating-equivalent-fractions-to-subtract-unlike-fractions.pdf





http://www.k-5mathteachingresources.com/support-files/subtracting-mixed-numbers-with-unlike-denominators.pdf

http://www.k-5mathteachingresources.com/support-files/fractionwordproblem1.pdf




http://www.k-5mathteachingresources.com/support-files/relating-fractions-to-division-problems.pdf

http://www.engageny.org/sites/default/files/resource/attachments/math-g5-m4-full-module.pdf


https://grade6commoncoremath.wikispaces.hcpss.org/Grade+5+Numbers+and+Operations+-+Fractions



Formative Assessment Strategies

Mathematics K-5

Name Description Additional Information

A & D Statements

A & D Statements analyze a set of “fact or fiction” statements. First, students may choose to agree or disagree with a statement or identify whether they need more information. Students are asked to describe their thinking about why they agree, disagree, or are unsure. In the second part, students describe what they can do to investigate the statement by testing their ideas, researching what is already known, or using other means of inquiry.

http://www.mathsolutions.com/documents/How_to_Get_Students_Talking.pdf

Statement How can I find out? 9/16 is larger than 5/8. __agree __disagree __not sure __it depends on My thoughts:

Agreement Circles

Agreement Circles provide a kinesthetic way to activate thinking and engage students in mathematical argumentation. Students stand in a circle as the teacher reads a statement. They face their peers still standing and match themselves up in small groups of opposing beliefs. Students discuss and defend their positions. After some students defend their answers, the teacher can ask if others have been swayed. If so, stand up. If not, what are your thoughts? Why did you disagree? After hearing those who disagree, does anyone who has agreed want to change their minds? This should be used when students have had some exposure to the content.

There 20 cups in a gallon. Agree or disagree? 2/3 equivalent to 4/6. Agree or disagree? A square is a rectangle. Agree or disagree? Additional Questioning: Has anyone been swayed into new thinking? What is your new thinking? Why do you disagree with what you have heard? Does anyone want to change their mind? What convinced you to change your mind? Use when students have had sufficient exposure to content.

http://formativeassessment.barrow.wikispaces.net/Agreement+Circles

Annotated Student Drawings

Annotated Student Drawings are student-made, labeled illustrations that visually represent and describe students’ thinking about mathematical concepts. Younger students may verbally describe and name parts of their drawings while the teacher annotates it for them.

Represent 747 by drawing rods and cubes. Represent 3x2=2x3 by drawing arrays. Describe the meaning of 5.60.

http://formativeassessment.barrow.wikispaces.net/Annotated+Student+Drawings










Formative Assessment Strategies/Mathematics K-5 (continued)


Card Sorts

Card Sorts is a sorting activity in which students group a set of cards with pictures or words according to certain characteristics or category. Students sort the cards based on their preexisting ideas about the concepts, objects, or processes on the cards. As students sort the cards, they discuss their reasons for placing each card into a designated group. This activity promotes discussion and active thinking.

http://teachingmathrocks.blogspot.com/2012/09/vocabulary-card-sort.html

Commit and Toss

Commit and Toss is a technique used to anonymously and quickly assess student understanding on a topic. Students are given a question. They are asked to answer it and explain their thinking. They write this on a piece of paper. The paper is crumpled into a ball. Once the teacher gives the signal, they toss, pass, or place the ball in a basket. Students take turns reading their "caught" response. Once all ideas have been made public and discussed, engage students in a class discussion to decide which ideas they believe are the most plausible and to provide justification for the thinking.

Stephanie eats 5 apple slices during lunch. When she gets home from school she eats more. Which statement(s) below indicates the number of apple slices Stephanie may have eaten during the day?

a. She eats 5 apple slices. b. She eats 5 apple slices at least. c. She eats more than 5 apple slices. d. She eats no more than 5 apple slices. e. I cannot tell how many apple slices were eaten.

Explain your thinking. Describe the reason for the answer(s) you selected.

Concept Card Mapping

Concept Card Mapping is a variation on concept mapping. Students are given cards with the concepts written on them. They move the cards around and arrange them as a connected web of knowledge. This strategy visually displays relationships between concepts.






Concept Cartoons

Concept Cartoons are cartoon drawings that visually depict children or adults sharing their ideas about common everyday mathematics. Students decide which character in the cartoon they agree with most and why. This formative is designed to engage and motivate students to uncover their own ideas and encourage mathematical argumentation. Concept Cartoons are most often used at the beginning of a new concept or skill. These are designed to probe students’ thinking about everyday situations they encounter that involve the use of math. Not all cartoons have one “right answer.” Students should be given ample time for ideas to simmer and stew to increase cognitive engagement.

www.pixton.com (comic strip maker)

Four corners

Four Corners is a kinesthetic strategy. The four corners of the classroom are labeled: Strongly Agree, Agree, Disagree and Strongly Disagree. Initially, the teacher presents a math-focused statement to students and asks them to go to the corner that best aligns with their thinking. Students then pair up to defend their thinking with evidence. The teacher circulates and records student comments. Next, the teacher facilitates a whole group discussion. Students defend their thinking and listen to others’ thinking before returning to their desks to record their new understanding.

A decimal is a fraction. http://debbiedespirt.suite101.com/four-corners-activities-a170020

http://wvde.state.wv.us/teach21/FourCorners.html

Frayer Model

Frayer Model graphically organizes prior knowledge about a concept into an operational definition, characteristics, examples, and non-examples. It provides students with the opportunity to clarify a concept or mathematical term and communicate their understanding. For formative assessment purposes, they can be used to determine students’ prior knowledge about a concept or mathematical term before planning the lesson. Barriers that can hinder learning may be uncovered with this assessment. This will then in turn help guide the teacher for beneficial instruction.

Frayer ModelDefinition in your own words Facts/characteristics

Examples NonexamplesQuadrilateral

A quadrilateral is a shape with 4 sides.

•4 sides• may or may not be of equal length• sides may or may not be parallel

• square• rectangle• trapezoid• rhombus

• circle• triangle• pentagon• dodecahedron

Agree

Disagree Strongly Disagree

Strongly Agree

http://www.pixton.com/

http://debbiedespirt.suite101.com/four-corners-activities-a170020

http://debbiedespirt.suite101.com/four-corners-activities-a170020

http://wvde.state.wv.us/teach21/FourCorners.html




Friendly Talk Probes

Friendly Talk Probes is a strategy that involves a selected response section followed by justification. The probe is set in a real-life scenario in which friends talk about a math-related concept or phenomenon. Students are asked to pick the person they most agree with and explain why. This can be used to engage students at any point during a unit. It can be used to access prior knowledge before the unit begins, or assess learning throughout and at the close of a unit.

http://www.sagepub.com/upm-data/37758_chap_1_tobey.pdf

Human Scatterplots

Human Scatterplot is a quick, visual way for teacher and students to get an immediate classroom snapshot of students’ thinking and the level of confidence students have in their ideas. Teachers develop a selective response question with up to four answer choices. Label one side of the room with the answer choices. Label the adjacent wall with a range of low confidence to high confidence. Students read the question and position themselves in the room according to their answer choice and degree of confidence in their answer.

I Used to Think… But Now I Know…

I Used to Think…But Now I Know is a self-assessment and reflection exercise that helps students recognize if and how their thinking has changed at the end of a sequence of instruction. An additional column can be added to include…And This Is How I Learned It to help students reflect on what part of their learning experiences helped them change or further develop their ideas.

I USED TO THINK… BUT NOW I KNOW…

AND THIS IS HOW I LEARNED IT






Justified List

Justified List begins with a statement about an object, process, concept or skill. Examples and non-examples for the statement are listed. Students check off the items on the list that are examples of the statement and provide a justification explaining the rule or reasons for their selections. This can be done individually or in small group. Small groups can share their lists with the whole class for discussion and feedback. Pictures or manipulatives can be used for English-language learners.

Example 1

Put an X next to the examples that represent 734.

___700+30+4 ___7 tens 3 hundreds 4 ones ___730 tens 4 ones ___7 hundreds 3 tens 4ones ___734 ones ___seven hundred thirty-four ___seventy-four ___ 400+70+3

Explain your thinking. What “rule” or reasoning did you use to decide which objects digit is another way to state that number.

Example 2

K-W-L Variations

K-W-L is a general technique in which students describe what they Know about a topic, what they Want to know about a topic, and what they have Learned about the topic. It provides an opportunity for students to become engaged with a topic, particularly when asked what they want to know. K-W-L provides a self-assessment and reflection at the end, when students are asked to think about what they have learned. The three phrases of K-W-L help students see the connections between what they already know, what they would like to find out, and what they learned as a result.

K-This what I already KNOW

W-This is what I WANT to find out

L-This is what I LEARNED

Learning Goals Inventory (LGI)

Learning Goals Inventory (LGI) is a set of questions that relate to an identified learning goal in a unit of instruction. Students are asked to “inventory” the learning goal by accessing prior knowledge. This requires them to think about what they already know in relation to the learning goal statement as well as when and how they may have learned about it. The LGI can be given back to students at the end of the instructional unit as a self-assessment and reflection of their learning.

What do you think the learning goal is about?

List any concepts or ideas you are familiar with related to this learning goal.

List any terminology you know of that relates to this goal.

List any experiences you have had that may have helped you learn about the ideas in this learning goal.




Look Back

Look Back is a recount of what students learned over a given instructional period of time. It provides students with an opportunity to look back and summarize their learning. Asking the students “how they learned it” helps them think about their own learning. The information can be used to differentiate instruction for individual learners, based on their descriptions of what helped them learn.

What I Learned How I Learned it

Muddiest Point

Muddiest Point is a quick-monitoring technique in which students are asked to take a few minutes to jot down what the most difficult or confusing part of a lesson was for them. The information gathered is then to be used for instructional feedback to address student difficulties.

Scenario: Students have been learning about the attributes of three-dimensional shapes. Teacher states, “I want you to think about the muddiest point for you so far when it comes to three-dimensional shapes. Jot it down on this notecard. I will use the information you give to me to think about ways to help you better understand three-dimensional shapes in tomorrow’s lesson.”

Odd One Out

Odd One Out combines similar items/terminology and challenges students to choose which item/term in the group does not belong. Students are asked to justify their reasoning for selecting the item that does not fit with the others. Odd One Out provides an opportunity for students to access scientific knowledge while analyzing relationships between items in a group.

Show students three figures and ask: Which is the odd one out?

Explain your thinking. Ask students to choose a different odd one out and explain their thinking.

Partner Speaks

Partner Speaks provides students with an opportunity to talk through an idea or question with another student before sharing with a larger group. When ideas are shared with the larger group, pairs speak from the perspective of their partner’s ideas. This encourages careful listening and consideration of another’s ideas.

Today we are going to explore different ways to add three-digit numbers together.

What different kinds of strategies can you use to add 395+525?

Turn to your partner and take turns discussing your strategies. Listen carefully and be prepared to share your partner’s ideas.




A Picture Tells a Thousand Words

A Picture Tells a Thousand Words, students are digitally photographed during a mathematical investigation using manipulatives or other materials. They are given the photograph and asked to describe what they were doing and learning in the photo. Students write their description under the photograph. The images can be used to spark student discussions, explore new directions in inquiry, and probe their thinking as it relates to the moment the photograph was snapped. By asking students to annotate a photo that shows the engaged in a mathematics activity or investigation helps them activate their thinking about the mathematics, connect important concepts and procedures to the experience shown in the picture and reflect on their learning. Teachers can better understand what students are gaining from the learning experience and adjust as needed.

Question Generating

Question Generating is a technique that switches roles from the teacher as the question generator to the student as the question generator. The ability to formulate good questions about a topic can indicate the extent to which a student understands ideas that underlie the topic. This technique can be used any time during instruction. Students can exchange or answer their own questions, revealing further information about the students’ ideas related to the topic.

Question Generating Stems:

Why does___?

Why do you think___?

Does anyone have a different way to explain___?

How can you prove___?

What would happen if___?

Is___always true?

How can we find out if___?

Sticky Bars

Sticky Bars is a technique that helps students recognize the range of ideas that students have about a topic. Students are presented with a short answer or multiple-choice question. The answer is anonymously recorded on a Post-it note and given to the teacher. The notes are arranged on the wall or whiteboard as a bar graph representing the different student responses. Students then discuss the data and what they think the class needs to do in order to come to a common understanding.

http://www.google.com/imgres?q=kids+doing+math&sa=X&rls=com.microsoft:en-us:IE-SearchBox&biw=1366&bih=587&tbm=isch&tbnid=v-nI7qB0PdzrrM:&imgrefurl=http://www.sandi.net/domain/5358&docid=sPLPyfbptwU_1M&imgurl=http://www.sandi.net/cms/lib/CA01001235/Centricity/Domain/5358/pattern_block_kids.jpg&w=300&h=225&ei=4-upUabmM5DM9gTNkoE4&zoom=1&iact=hc&vpx=309&vpy=289&dur=592&hovh=180&hovw=240&tx=72&ty=88&page=2&tbnh=147&tbnw=196&start=21&ndsp=26&ved=1t:429,r:23,s:0,i:237




Thinking Log

Thinking Logs is a strategy that informs the teacher of the learning successes and challenges of individual students. Students choose the thinking stem that would best describe their thinking at that moment. Provide a few minutes for students to write down their thoughts using the stem. The information can be used to provide interventions for individuals or groups of students as well as match students with peers who may be able to provide learning support.

I was successful in…

I got stuck…

I figured out…

I got confused when…so I…

I think I need to redo…

I need to rethink…

I first thought…but now I realize…

I will understand this better if I…

The hardest part of this was…

I figured it out because…

I really feel good about the way…

Think-Pair-Share

Think-Pair-Share is a technique that combines thinking with communication. The teacher poses a question and gives individual students time to think about the question. Students then pair up with a partner to discuss their ideas. After pairs discuss, students share their ideas in a small-group or whole-class discussion. (Kagan)

NOTE: Varying student pairs ensures diverse peer interactions.

Three-Minute Pause

Three-Minute Pause provides a break during a block of instruction in order to provide time for students to summarize, clarify, and reflect on their understanding through discussion with a partner or small group. When three minutes are up, students stop talking and direct their attention once again to the teacher, video, lesson, or reading they are engaged in, and the lesson resumes. Anything left unresolved is recorded after the time runs out and saved for the final three-minute pause at the end.

Traffic Light Cards/Cups/Dots

Traffic Light Cards/Cups/Dots is a monitoring strategy that can be used at any time during instruction to help teachers gauge student understanding. The colors indicate whether students have full, partial, or minimal understanding. Students are given three different-colored cards, cups, or dots to display as a form of self-assessment revealing their level of understanding about the concept or skill they are learning.




Two-Minute Paper

Two-Minute Paper is a quick way to collect feedback from students about their learning at the end of an activity, field trip, lecture, video, or other type of learning experience. Teacher writes two questions on the board or on a chart to which students respond in two minutes. Responses are analyzed and results are shared with students the following day.

What was the most important thing you learned today?

What did you learn today that you didn’t know before?

What important question remains unanswered for you?

What would help you learn better tomorrow?

Two Stars and a Wish

Two Stars and a Wish is a way to balance positive and corrective feedback. The first sentence describes two positive commendations for the student’s work. The second sentence provides one recommendation for revision. This strategy could be used teacher-to-student or student-to-student.

Two-Thirds Testing

Two-Thirds Testing provides an opportunity for students to take an ungraded “practice test” two thirds of the way through a unit. It helps to identify areas of difficulty or misunderstanding through an instructional unit so that interventions and support can be provided to help them learn and be prepared for a final summative assessment. Working on the test through discussions with a partner or in a small group further develops and solidifies conceptual understanding.




What Are You Doing and Why?

What Are You Doing and Why? is a short, simple monitoring strategy to determine if students understand the purpose of the activity or how it will help them learn. At any point in an activity the teacher gets the students’ attention and asks “What are you doing and why are you doing it?” Responses can be shared with the class, discussed between partners, or recorded in writing as a One-Minute Paper to be passed in to the teacher. The data are analyzed by the teacher to determine if the class understands the purpose of the activity they are involved in.

Scenario: Students are decomposing a fraction into the sum of two or more of its parts.

Teacher stops students in their tracks and asks,

“What are you do and why are you doing it?”

Whiteboarding

Whiteboarding is a technique used in small groups to encourage students to pool their individual thinking and come to a group consensus on an idea that is shared with the teacher and the whole class. Students work collaboratively around the whiteboard during class discussion to communicate their ideas to their peers and the teacher.

http://www.educationworld.com/a_lesson/02/lp251-01.shtml

3-2-1

3-2-1 is a technique that provides a structured way for students to reflect upon their learning. Students respond in writing to three reflective prompts. This technique allows students to identify and share their successes, challenges, and questions for future learning. Teachers have the flexibility to select reflective prompts that will provide them with the most relevant information for data-driven decision making.

Sample 1 3 – Three key ideas I will remember

2 – Two things I am still struggling with

1 – One thing that will help me tomorrow Sample 2





Intervention/Remediation Guide

Resource Location Description Intervention Lessons (Student and Teacher pages)

Math Diagnosis and Intervention System

Use for pre-requisite skills or remediation. For grades K-2, the lessons consist of a teacher-directed activity followed by problems. In grades 3-5, the student will first answer a series of questions that guide him or her to the correct answer of a given problem, followed by additional, but similar problems.

Meeting Individual Needs Planning section of each Topic in the enVision Math Teacher’s Edition

Provides topic-specific considerations and activities for differentiated instruction of ELL, ESE, Below-Level and Advanced students.

Differentiated Instruction Close/Assess and Differentiate step of each Lesson in the enVision Math Teacher’s Edition

Provides lesson-specific activities for differentiated instruction for Intervention, On-Level and Advanced levels.

Error Intervention Guided Practice step of each Lesson in the enVision Math Teacher’s Edition

Provides on-the-spot suggestions for corrective instruction.

ELL Companion Lesson Florida Interactive Lesson Support for English Language Learners

Includes short hands-on lessons designed to provide support for teachers and their ELL students, useful for struggling students as well


GLOSSARY OF TERMS

Definitions for the framework of the curriculum map components are defined below.

Pacing: the recommended timeline determined by teacher committee for initial delivery of instruction in preparation for State Assessments Domain: the broadest organizational structure used to group content and concepts within the curriculum map Cluster: a sub-structure of related standards; standards from different clusters may sometimes be closely related because mathematics is a connected subject Standard: a definition of what students should understand and be able to do Learning Targets/Skills: the content knowledge, processes, and behaviors students should exhibit for mastery of the standards Hints: additional information that serves to further clarify the expectations of the learning targets/skills to assist with instructional decision-making processes Vocabulary: the content vocabulary and other key terms and phrases that support mastery of the learning targets and skills; for teacher and student use alike

Standards for Mathematical Practice: processes and proficiencies that teachers should seek to purposefully develop in students

Resource Alignment: a listing of available, high quality and appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets and skills; recommendations are not intended to limit lesson development

Common Addition and Subtraction, Multiplication and Division Situations: a comprehensive display of possible addition and subtraction, multiplication and division problem solving situations that involve an unknown number in varied locations within an equation

Formative Assessment Strategies: a collection of assessment strategies/techniques to help teachers discover student thinking, determine student understanding, and design learning opportunities that will deepen student mastery of standards

Intervention/Remediation Guide: a description of resources available within the adopted mathematics textbook resource (enVision MATH) that provides differentiated support for struggling learners—ESE, ELL, and General Education students alike

2015 Fifth Grade MATHEMATICS - Mr. Smith's...

Documents

Transcript of 2015 Fifth Grade MATHEMATICS - Mr. Smith's...