FINAL Grade 5 Mathematics Curriculum Map …public.volusia.k12.fl.us/mathematics/Documents/Grade 5...

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MATHEMATICS Curriculum Map

2012 - 2013

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Next Generation Sunshine State Standards

Mathematics Department ii Fifth Grade Curriculum Map Volusia County Schools December 2012

Common Core State Standards

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them. (MACC.K12.MP.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. (MACC.K12.MP.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. (MACC.K12.MP.3) A well-crafted argument/critique requires a thoughtful and logical progression of mathematically sound statements and supporting

evidence.

4. Model with mathematics. (MACC.K12.MP.4) Many everyday problems can be solved by modeling the situation with mathematics.

5. Use appropriate tools strategically. (MACC.K12.MP.5) Strategic choice and use of tools can increase reliability and precision of results, enhance arguments, and deepen mathematical

understanding.

6. Attend to precision. (MACC.K12.MP.6) Attending to precise detail increases reliability of mathematical results and minimizes miscommunication of mathematical

explanations.

7. Look for and make use of structure. (MACC.K12.MP.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. (MACC.K12.MP.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.

Mathematics Department iii Fifth Grade Curriculum Map Volusia County Schools December 2012

Next Generation Sunshine State Standards

Following a six-year cycle review and revision of K-12 Mathematics content standards, the Next Generation Sunshine State Standards (NGSSS) were adopted by the Florida State Board of Education in September 2007. The revision in the benchmark language offers greater specificity to indicate clearly what teachers should teach and student should be able to do. Support of these standards can be found at www.floridastandards.org.

Mathematics Grade 5 Program Overview

Big Idea 1: Develop an understanding of and fluency with division of whole numbers.

Big Idea 2: Develop an understanding of and fluency with addition and subtraction of fractions and decimals.

Big Idea 3: Describe three-dimensional shapes and analyze their properties, including volume and

surface area.

Supporting Idea: Algebra

Supporting Idea: Geometry and Measurement

Supporting Idea: Number and Operations

Supporting Idea: Data Analysis

Mathematics Department iv Fifth Grade Curriculum Map Volusia County Schools December 2012

COMPONENTS OF THE CURRICULUM MAP

Unit/Organizing Principle: the overarching organizational structure used to group content and concepts within the curriculum map

Pacing: the recommended time period within the year for instruction related to the essential questions to occur

Essential Questions: the overarching question(s) that will serve to guide instruction and push students to higher levels of thinking; essential questions should guide students to the heart of the content and should be in student -friendly language.

Measurement Topics: an organized grouping of learning targets – these will be evident as headings in (Pinnacle) Gradebook

Learning Targets/Skills: the content knowledge, processes and enabling skills that will ensure successful mastery of the essential questions (tied to Common Core State Standards and/or Next Generation Sunshine State Standards)

Benchmarks (Pinnacle): Benchmarks for the Next Generation Sunshine State Standards until the Common Core State Standards are implemented

Academic Language: the content vocabulary and other key terms and phrases with which students should be familiar and that support mastery of the learning targets/skills and essential questions

Suggested Activities and Resources: a listing of available, appropriate materials, strategies, lessons, textbooks, videos and other media sources that are aligned with the learning targets, skills and essential questions; developed to save teachers time when planning for instruction

Assessment: a list of required assessments as well as suggested assessments that are available to use as formative or summative assessments

Mathematics Department v Fifth Grade Curriculum Map Volusia County Schools December 2012

Teachers are required to administer each of the District Interim Assessments. The assessments will be made available through the Copy Center as they are developed; the Scantron answer sheets are available through Scantron Achievement Series. Following the administration of the District Interim Assessments and the scanning of the Scantron answer sheets data will be immediately available through Scantron Achievement Series.

Weeks Grade 5 Math Interim Assessments Testing Window Weeks 1-5 05 Math Interim Assmt Division September 17-20 Weeks 6-9 05 Math Interim Assmt Algebra October 15-18 Weeks 10-12 05 Math Interim Assmt Data Analysis November 5-9 Weeks 13-14 05 Math Interim Assmt Integers November 19-20 Weeks 15-18 05 Math Interim Assmt Decimals December 17-20 Weeks 19-22 05 Math Interim Assmt Fractions January 28-February 1 Weeks 23-26 05 Math Interim Assmt Measurement February 25-March 1 Weeks 27-31 05 Math Interim Assmt Geometry April 8-12

Mathematics Department 1 Fifth Grade Curriculum Map Volusia County Schools December 2012

UNIT/ORGANIZING PRINCIPLE: DIVISION PACING: Weeks 1 – 5

ESSENTIAL QUESTIONS: What is division? How do you determine if a solution is reasonable?

MEASUREMENT TOPICS

LEARNING TARGETS/SKILLS BENCHMARKS

(Pinnacle) ACADEMIC LANGUAGE

Division (T03)

NGSSS: Describe the process of finding quotients involving multi-digit dividends using models, place value, properties, and the relationship of division to multiplication.

Students will:

• describe and demonstrate the process of division using a variety of models (e.g.,

25 ÷ 5, 5 25 , 5

25 , partial quotients, repeated subtraction, equal sharing, place-

value, expanded notation).

NOTE: Partial quotients is an alternative method to long division using groupings of multiples of the divisor and then adding the partial quotients to find the answer. Example:

26 r 4 partial quotients

5 134

- 50 10 Help Box x5 84 - 50 10 1 X 5 = 5 5 X 5 = 25 34 10 X 5 = 50 - 25 5 20 X 5 = 100 9 30 X 5 = 150 - 5 1 4

• explain the inverse relationship between multiplication and division.

• use multiplication as a tool for checking quotients in division problems. • model understanding of the Distributive Property used in division problems (e.g.

639 ÷ 3 can be expressed as (600 + 30 + 9) ÷ 3 = (600 ÷ 3) + (30 ÷ 3) + (9 ÷ 3)).

NOTE: Students do not need to memorize the name of the property.

• model and apply the standard algorithm for division to solve real-world problems with 1- or 2-digit divisors and dividends up to 4 digits.

• describe one or more steps of the standard algorithm. • describe missing steps of a partially completed division problem.

FCAT 2.0 Sample Item:

T03.MA.5.A.1.1

compatible numbers decimal Distributive Property divide dividend divisor equal sharing estimate expanded notation fraction hundredths inverse operation multiple partial quotients place value quotient reasonable remainder repeated subtraction standard algorithm tenths

continued on next page


Division (T03)

NGSSS: Estimate quotients or calculate them mentally depending on the context and numbers involved.

Students will:

• demonstrate a thorough understanding of the process of division to solve real-world problems using estimation or mental math strategies such as finding compatible numbers by using the closest multiple of the divisor (see Topic 1 p. 2E), or decomposition by finding a close friendly number that will divide easily.


T03.MA.5.A.1.2

NGSSS: Interpret solutions to division situations, including those with remainders, depending on the context of the problem.

Students will:

• model and interpret solutions and remainders using real-world problems (e.g. , A school bus holds 25 students. Sixty students are going on a field trip to Mosquito Lagoon. How many buses will be needed?).


• solve division problems involving quotients with fraction and decimal (to

hundredths) remainders (e.g., 42 ÷ 8 = 5 1

4or 5.25).

NOTE: EnVisionMATH does not address remainders expressed as decimals and fractions.

T03.MA.5.A.1.3



Division (T03)

NGSSS: Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm, and checking the reasonableness of results.

Students will:

• demonstrate fluency of basic division facts. • use estimation to predict the relative size of answers, check the reasonableness of

an answer and defend the estimate. • divide multi-digit whole numbers fluently.

NOTE: Fluently means accurately and efficiently.


• solve real-world division problems involving money (up to four digits representing dollars and two zeros representing cents: e.g., $372.00 ÷ 24).

• apply up to two operations to solve problems where at least one is division.

T03.MA.5.A.1.4

NGSSS: Solve non-routine problems using various strategies including “solving a simpler problem” and “guess, check, and revise.”

Students will:

• solve non-routine problems using various strategies including, but not limited to, making an educated guess, checking and revising, solving a simpler problem, drawing diagrams, looking for patterns, and using models.

• make sense of problems and persevere in solving them by applying problem solving strategies to solve multi-step problems.

FCAT 2.0 Sample Item: NOTE: When modeling with mathematics the student uses a variety of strategies

to apply the math they have learned.

T03.MA.5.A.6.5

CCSS: 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.

MACC.K12.MP.1 MACC.K12.MP.2 MACC.K12.MP.3 MACC.K12.MP.4 MACC.K12.MP.5 MACC.K12.MP.6 MACC.K12.MP.7 MACC.K12.MP.8


Suggested Activities and Resources Assessment

enVisionMATH Student Edition Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7; Reteaching Sets: A-G p 22 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7; Reteaching Sets: A-F p 54-55 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8; Reteaching Sets: A-F p 78-79

enVisionMATH Ready-Made Centers Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5 Topic 3: Lessons 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

enVision Math Problem of the Day Topic 1: Lessons 1-2, 1-3, 1-4, 1-5 Topic 2: Lessons 2-1, 2-2, 2-3, 2-5 Topic 3: Lessons 3-3, 3-4, 3-5, 3-7, 3-8

envisionMath Daily Assessment and Reteaching Workbook Topic 1: Lessons 1-1, 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Topic 2: Lessons 2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

enVisionMATH Teacher Resource Masters pp. 73-78 Basic Timed Facts (T.E.pp 20C & 20D)

Everglades K-12: Grade 5 pp. 24-49 Chapter 1: Division of Whole Numbers

Safari Montage

http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=29696&location=local Division/Prime Factorization/Multiples

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# Click on Algorithms in Everyday Mathematics, then select a grade and select an operation to see videos on various algorithms. http://aaamath.com www.ixl.com www.pearsonsuccessnet.com http://illuminations.nctm.org/ www.evergladesk12.com www.rosley.cumbria.sch.uk/Division%20strategies.pdf (examples of division using partial quotients) https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# - For video lesson, click on Algorithm Handbook Animations and choose one of the Division: Partial Quotient Models.

Required Summative

05 Math Interim Assmt Division

Optional Formatives

Florida Benchmarks Assessment Workbook

Topic 1 Florida Test Topic 2 Florida Test Topic 3 Florida Test

(Cover Pages and Answer Keys are available for each topic test through Copy Center/DOD.)

Math Focus Formatives

05 Math Focus Formative Division Form A-Optional Online

(Available through Scantron/Achievement Series.)

For additional formative assessment strategies, see pages 38-47 in the

Fifth Grade Mathematics Curriculum Map.

Intervention/Remediation An intervention/remediation resource guide

can be found on page 48 of the Fifth Grade Mathematics Curriculum Map.

Enrichment (Math Extension Activities organized by each topic are available through

Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: ALGEBRA PACING: Weeks 6 – 9

ESSENTIAL QUESTIONS: How do you use order of operations and basic properties in order to solve algebraic equations?

MEASUREMENT TOPICS



Expressions and Equations

(T01)

NGSSS: Use the properties of equality to solve numerical and real-world situations.

Students will:

• reason abstractly and quantitatively to demonstrate knowledge of how to apply properties of equality (addition, subtraction, multiplication, and division).

NOTE: Equalities will involve no more than two operations.

Examples of balanced equations (equality):

1) 5 + 2 = 7 3(5 + 2) = 3 • 7 2) 12 = 15 – 3 12 ÷ 4 = (15 – 3) ÷ 4 When the same operation is performed on both sides of an equation, the equation remains balanced.

Another example of equality:

If the scale is balanced, what is the weight of one rectangle?

• solve equations with up to two variables by substituting a quantity for one of the variables in the equation.

NOTE: When a two variable equation is used, the value of one variable must be provided (e.g. If c = 6, solve for y in the following equation: 4c + y = 28).

• translate a written description or graphic into an expression or equation (using a variable for the unknown number).


T01.MA.5.A.4.1 Associative Property base number Commutative Property Distributive Property Equality Property of Addition Equality Property of Division Equality Property of Multiplication Equality Property of Subtraction exponent expression growing pattern order of operations parentheses power variable




(T01)

NGSSS: Use the order of operations to simplify expressions, which include exponents and parentheses.

Students will:

• follow steps in the order of operations to simplify expressions which include exponents and parentheses.

Steps:

1. Perform calculations inside parentheses or other grouping symbols. 2. Do calculations involving exponents. 3. Complete all multiplication/division as it appears from left to right. 4. Complete all addition/subtraction as it appears from left to right.

Example: 48 ÷ ( 20 – 8 ) + 2 x 3³

48 ÷ 12 + 2 x 33

48 ÷ 12 + 2 x 27 4 + 54 58

T01.MA.5.A.6.2

Division (T03)


Students will:

• make sense of and persevere in solving non-routine problems using various strategies (e.g., drawing diagrams, making tables or lists, looking for patterns, using models, estimating, solving a simpler problem, and/or make an educated guess, check, and revise).

• reason abstractly and quantitatively to extend growing patterns.

FCAT 2.0 Sample Item: NOTE: Practice with growing patterns can be found in the enVisionMATH Diagnostic & Intervention System. Go to Booklet F: Numeration, Patterns, and Relationships in Grades 4-6. Page F25 Geometric Growth Patterns.

NOTE: When modeling with mathematics the student uses a variety of strategies to apply the math they have learned.

T03.MA.5.A.6.5












Note: Exponents should be limited to 2 or 3.



enVisionMATH Student Edition Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7; Reteaching Sets: A-C, E, F p 102-103

enVisionMATH Ready-Made Centers

Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6

enVision Math Problem of the Day Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7

envisionMath Daily Assessment and Reteaching Workbook

Topic 4: Lessons 4-1, 4-2, 4-3, 4-4, 4-5, 4-6, 4-7

Everglades K-12: Grade 5 pp. 104-144 Chapter 4: Algebra pp. 152-155 Chapter 6: Order of Operations

Safari Montage

http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=21311&location=local “Variables, Expressions, and Equations, Order of Operations http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=20298&location=local (Algebraic Thinking)

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://aaamath.com www.ixl.com www.pearsonsuccessnet.com http://illuminations.nctm.org/ http://www.coolmath4kids.com/ http://www.homeschoolmath.net/teaching/equations-1.php (balance as a model of an equation) http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games)

Required Summative

05 Math Interim Assmt Algebra

Optional Formatives


Topic 4 Florida Test (Cover Pages and Answer Keys are available

for each topic test through Copy Center/DOD.)


05 Math Focus Formative Algebra Form A-Optional Online

05 Math Focus Formative Algebra Form B-Optional Online







Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: DATA ANALYSIS PACING: Weeks 10 – 12

ESSENTIAL QUESTIONS: How will ordered pairs help you determine location on a coordinate plane?

MEASUREMENT TOPICS



Ordered Pairs (T08)

NGSSS: Identify and plot ordered pairs on the first quadrant of the coordinate plane.

Students will:

• 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.

NOTE: The first quadrant includes only positive numbers.

• locate a point equidistant from two other points in the first quadrant of the coordinate plane.


• look for and make sense of structure when describing the horizontal and vertical movements (translations) necessary to get from one point to another on a coordinate plane.

• explain the relationship between the x-axis and the y-axis including the understanding that in a set of ordered pairs the first number represents the coordinate on the x-axis and the second number represents the coordinate on the y-axis (x, y).

T08.MA.5.G.5.1 bar graph conclusion continuous data coordinate grid coordinate plane coordinates decreasing discrete data double bar graph equidistant frequency table graph horizontal increasing intervals line graph line plot midpoint ordered pairs origin pictograph plot point prediction quadrant scale survey translation trend Venn diagram vertical x and y coordinates x – axis y – axis



Data Analysis (T02)

NGSSS: Construct and describe a graph showing continuous data, such as a graph of a quantity that changes over time.

Students will:

• attend to precision when choosing a title, label, scale and interval for a graph. • determine and create appropriate graphs for given data.

NOTE: Discrete data (finite) is counted and can only take certain values. Possible representations of discrete data may include, but are not limited to,:

� the number of students in a class (you can't have half a student) � the number of problems on a test � weekly total of money in a bank account � bar graphs, pictographs, line plots, frequency tables, and/or Venn diagrams

Continuous data (infinite) is measured and can take an unlimited number of values within a range. Possible representations of continuous data may include, but are not limited to:

� infinite measurable data (time, weight, mass, height, depth, length, speed) � measuring plant growth which can be represented with decimals such as 2.7

in. or 2.78 in. or 2.7843893 in. to show increments between the data points (limited by the measurement tool)

� measuring the burning of a candle; the time and length are both continuous measurements

� includes measurements such as seconds (part of a minute) and ounces (part of a pound)

� line graphs and frequency tables � the line on the graph represents data that can be between the points (when

measured the 1st week the data showed 3 in., when measured the 3rd week

the data showed 5 in. The line between the two points on the graph represent the continuous growth that took place between the 1

st and 3

rd week)

T02.MA.5.A.4.2

NGSSS: Construct and analyze line graphs and double bar graphs.

Students will:

• look for and make sense of structure when analyzing and comparing information from line graphs and from double bar graphs.

• identify, interpret, or describe a line graph that shows a quantity that changes over time.

• predict if a line graph shows data that is increasing or decreasing. • attend to precision when determining appropriate scales for a given set of data and

identifying the different parts of a graph. • make and state conclusions and predictions verbally and in writing based on the data

in a graph.

T02.MA.5.S.7.1



Data Analysis (T02)

NGSSS: Differentiate between continuous and discrete data, and determine ways to represent those using graphs and diagrams.

Students will:

• attend to precision when identifying, explaining and comparing continuous data and discrete data.

NOTE: See details of discrete and continuous data on previous page.

• look for and make sense of structure to categorize whether a set of data is discrete or continuous and support with evidence

• identify the appropriate graph to represent a set of either continuous or discrete data. • represent continuous and discrete data with graphs.


T02.MA.5.S.7.2










Look for and express regularity in repeated

reasoning.




enVisionMATH Student Edition Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7; Reteaching Sets: A-G p 358


Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6

enVision Math Problem of the Day Topic 4: Lessons 15-3, 15-4, 15-5, 15-6, 15-7


Topic 4: Lessons 15-1, 15-2, 15-3, 15-4, 15-5, 15-6, 15-7

Everglades K-12: Grade 5 pp. 180-199 Chapter 7: Data Analysis

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm Math blackline masters. www.ixl.com https://www.everydaymathonline.com/free_resources_main.html?frnologin=1# www.pearsonsuccessnet.com http://www.k-5mathteachingresources.com/ www.aaamath.com http://illuminations.nctm.org/ http://www.coolmath4kids.com/ http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) http://www.mathsisfun.com/data/pictographs.html (Shows different types of graphs, describes the type of data they represent and provides questions that go with the graph)

Required Summative

05 Math Interim Assmt Data Analysis

Optional Formatives


Topic 15 Florida Test (Cover Pages and Answer Keys are

available for each topic test through Copy Center/DOD.)


05 Math Focus Formative Data Analysis Form A-Optional Online







Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: INTEGERS PACING: Weeks 13 – 14 ESSENTIAL QUESTIONS: When do you use integers?

MEASUREMENT TOPICS



Integers (T04)

NGSSS: Describe real-world situations using positive and negative numbers.

Students will:

• demonstrate knowledge and understanding of integers (the set of positive and negative numbers).

• explain the location of a positive or negative number as the distance from zero on a number line.

• attend to precision when applying and solving real-world problems using positive and negative integers (e.g., owing money - My allowance is $4. Mom loans me $3 to buy a $7 book. I owe Mom $3; therefore, I have -3 dollars).

NOTE: Other appropriate real-world situations may include, but are not limited to, measuring elevations, above and below sea level, riding elevators up and down, temperature, ascending and descending mountains, and football yardage.

NOTE: In fifth grade this does not include adding and subtracting positive and negative numbers. It does include recognizing the distance between the numbers in relation to the amount above and below (less than and greater than) zero.


T04.MA.5.A.6.3 absolute value ascend compare descend decrease elevations equal to (=) greater than (>) greater than or equal to (≥) increase inequality integer less than (<) less than or equal to (≤) negative number number line not equal (≠) positive number sea level



Integers (T04)

NGSSS: Compare, order, and graph integers, including integers shown on a number line.

Students will:

• identify and graph integers (the set of positive and negative numbers) on a number line.

NOTE: Graph means to plot integers on a number line.

Graph -3 on the number line.

• explain that numbers are larger or increase when moving to the right on a number line and smaller or decrease when moving to the left on a number line.

• compare integers using inequalities ( >, <, ≥, ≤, ≠ ).

NOTE: Numbers may range between -500 and 500.

• order integers from a set of given data.


T04.MA.5.A.6.4














enVisionMATH Student Edition Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5; Reteaching Sets: A-D p 378-379


Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

enVision Math Problem of the Day Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5


Topic 4: Lessons 16-1, 16-2, 16-3, 16-4, 16-5

Everglades K-12: Grade 5 pp. 156-178 Chapter 6: Number and Operations

Safari Montage

http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=19637&location=local (Introduction to Integers – Chapter 1 and Chapter 2)

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.ixl.com www.pearsonsuccessnet.com www.aaamath.com http://illuminations.nctm.org/ http://www.coolmath4kids.com/

Required Summative

05 Math Interim Assmt Integers

Optional Formatives


Topic 16 Florida Test (Cover Pages and Answer Keys are

available for each topic test through Copy Center/DOD.)


05 Math Focus Formative Integers Form A-Optional Online

05 Math Focus Formative Integers Form B-Optional Online







Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: DECIMALS PACING: Weeks 15 – 18

ESSENTIAL QUESTIONS: How do prime factorization and the use of multiples relate to fractions?

MEASUREMENT TOPICS



Prime and Composite Numbers

(T06)

NGSSS: Determine the prime factorization of numbers.

Students will:

• model the use of factor trees to determine the prime factorization of numbers.

Example:

• attend to precision when expressing composite numbers as the product of prime factors (e.g., 36 = 2² • 3²). NOTE: If the base number is 2 or 3, the exponents are to be limited to 3, 4, or 5. If the base number is greater than 3, the exponent is to be limited to 2 (second power).

T06.MA.5.A.2.4 Associative Property base number benchmark fractions common factors Commutative Property composite decimal denominator difference Distributive Property divisible equivalent estimate exponents factor factor tree fraction greatest common factor (GCF) hundredths Identity Property least common denominator (LCD) least common multiple (LCM) like denominator numerator place value power prime prime factorization simplest form sum tenths thousandths unlike denominator whole number

NGSSS: Identify and relate prime and composite numbers, factors, and multiples within the context of fractions.

Students will:

• identify and explain prime and composite numbers to 100 (center activity using the Sieve of Eratosthenes activity (p.166 Topic 7); available to print at http://www.pedagonet.com/quickies/Eratosthenes.pdf).

• relate prime and composite numbers to finding common multiples (denominators), finding equivalent fractions and simplifying fractions.

• look for and express regularity in repeated reasoning when determining the greatest common factor (GCF) and least common multiple (LCM).

NOTE: When modeling with mathematics the student uses a variety of strategies they have learned.

T06.MA.5.A.6.1



Addition and Subtraction of Decimals

(T05)

NGSSS: Represent addition and subtraction of decimals and fractions with like and unlike denominators using models, place value, or properties.

Students will:

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

e.g. Place Value Charts

NOTE: Click on link (http://www.k-5mathteachingresources.com/5th-grade-

number-activities.html) and scroll down to 5th Grade Number Activities: Number

and Operations in Base Ten for a variety of hands on decimal centers for students.


• represent addition and subtraction of decimals using the associative or distributive properties through the thousandths place.

NOTE: Decimals may also be used in the context of money.

T05.MA.5.A.2.1



Addition and Subtraction of Decimals

(T05)

NGSSS: Add and subtract fractions and decimals fluently, and verify the reasonableness of results, including in problem situations.

Students will:

• add and subtract decimals fluently (accurately and efficiently using a variety of strategies with proper alignment of place value.

NOTE: Decimals may also be used in the context of money. Consider using this You Tube video on adding and subtracting decimals (includes real-world problem solving practice).

• solve real-world problems involving decimals.


• verify the reasonableness of the solution using estimation strategies.

T05.MA.5.A.2.2

NGSSS: Make reasonable estimates of fraction and decimal sums and differences, and use techniques for rounding.

Students will:

• use estimation strategies such as rounding, benchmark numbers, or number lines, to predict the relative size of answers when adding or subtracting decimals.

T05.MA.5.A.2.3











reasoning.




enVisionMATH Student Edition Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10; Reteaching Sets: A-J p 156 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-11; Reteaching Sets: A-E p 194 Topic 8: Lessons 8-1, 8-2; Reteaching Sets: A-B p 218

enVisionMATH Ready-Made Centers Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Topic 8: Lessons 8-1, 8-2

enVision Math Problem of the Day Topic 6: Lessons 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5 Topic 8: Lessons 8-1, 8-2

envisionMath Daily Assessment and Reteaching Workbook Topic 6: Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6-9, 6-10 Topic 7: Lessons 7-1, 7-2, 7-3, 7-4, 7-5, 7-11 Topic 8: Lessons 8-1, 8-2

Everglades K-12: Grade 5 pp. 55-56 Modeling Addition and Subtraction of Decimals pp. 146-151 Chapter 6: Primes, Composites, Factors, Multiples, and Fractions

Safari Montage http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=29696&location=local&chapterskeyindex=52831&play=1 (Chapter 6: Prime Factorization)

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://www.adaptedmind.com/Fifth-Grade-Math-Worksheets-And-Exercises.html www.ixl.com www.pearsonsuccessnet.com www.aaamath.com http://illuminations.nctm.org/ http://www.coolmath4kids.com/ www.factorsamurai.com (free ipad app on prime factorization) http://www.mathgoodies.com/games/ (math games including prime factorization) http://www.internet4classrooms.com/grade_level_help/prime_factorization_math_fifth_5th_grade.htm (prime factorization videos, games and resources) http://lrt.ednet.ns.ca/PD/BLM/table_of_contents.htm Collection of blackline masters for all math concepts.

Required Summative

05 Math Interim Assmt Decimals

Optional Formatives


Topic 6 Florida Test Topic 7 Florida Test

(Cover Pages and Answer Keys are available for each topic test through Copy

Center/DOD.)

Math Focus Formatives 05 Math Focus Formative MA.5.A.2.1

05 Math Focus Formative MA.5.A.2.2 & MA.5.A.2.3


(Online and scan versions available through Scantron/Achievement Series.)






Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: FRACTIONS PACING: Week 19 – 22

ESSENTIAL QUESTIONS: How do you add and subtract fractions and mixed numbers with like and unlike denominators? How and why do you estimate the sums and differences of fractions?

MEASUREMENT TOPICS



Addition and Subtraction of

Fractions (T07)


Students will:

• review equivalent fractions using fraction bars, models and graphics. • simplify a fraction into lowest terms. • find the Least Common Denominator (LCD) in a set of fractions using various

strategies (e.g., manipulatives, listing of multiples, prime factorization).

Example: Find the LCD of 12

5 and 8

3 .

Step 1: Write the product of prime factors for each denominator.

12 = 2 • 2 • 3 = 22 • 3¹

8 = 2 • 2 • 2 = 23

Step 2: Sort the prime factors according to the same bases. 2

2 and 2

3 AND

3¹

Step 3: Choose the base with the highest exponent.

For 22 and 2

3 , choose 2

3 because the highest exponent is 3.

For 3¹ , choose 3¹ because the highest (and only) exponent is 1.

Step 4: Multiply the factors with the highest exponent for each base together. 2

3 • 3¹

8 • 3 = 24 (Therefore the LCD is 24.)

• represent addition and subtraction of fractions with like and unlike denominators using concrete and graphical models.

NOTE: Concrete models include, but are not limited to, fraction strips, fraction circles, pattern blocks, Geoboards, and other tangible objects. Graphical models include, but are not limited to, pictures of base-ten blocks and drawings.

• use the commutative and associative properties when adding fractions (up to 3 addends).

• model addition and subtraction of mixed numbers with like and unlike denominators, with and without regrouping.

• model addition and subtraction of fractions greater than one with like and unlike denominators.


T07.MA.5.A.2.1 benchmark fractions common denominator denominator equivalent dozen estimate fraction greater than

one ( �

� )

(formerly called improper fractions) least common denominator (LCD) mixed number number lines numerator reasonableness simplest form





Fractions (T07)


Students will:

• attend to precision when adding and subtracting common fractions and mixed numbers fluently (accurately and efficiently) using like and unlike denominators, with and without regrouping.

• attend to precision when adding or subtracting real-world problems involving fractions and mixed numbers.

• use estimation to verify the reasonableness of answers.

NOTE: Appropriate denominators include 1-12, 14, 15, 16, 18, 21, 24, 25, 32, 35, 36, 45, 75, or any multiple of 10 through 100.

T07.MA.5.A.2.2


Students will:

• use estimation strategies such as rounding, benchmark fractions, or number lines to predict the relative size of answers when adding or subtracting fractions.

NOTE: Benchmark fractions are common fractions that you can judge other numbers against such as 0,

2

1 , and 1.

T07.MA.5.A.2.3











reasoning.




enVisionMATH Student Edition Topic 7: Lessons 7-6, 7-7, 7-8, 7-9, 7-10; Reteaching Sets: F-J p 196 Topic 8: Lessons 8-3, 8-4, 8-5, 8-6, 8-7; Reteaching Sets: C-F p 218 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6; Reteaching Sets: A-F p 240

enVisionMATH Ready-Made Centers Topic 7: Lessons 7-6, 7-7, 7-8, 7-9, 7-10 Topic 8: Lessons 8-3, 8-4, 8-5, 8-6 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

enVision Math Problem of the Day Topic 7: Lessons 7-6, 7-7, 7-8, 7-9, 7-10 Topic 8: Lessons 8-3, 8-4, 8-5, 8-6 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

envisionMath Daily Assessment and Reteaching Workbook Topic 7: Lessons 7-6, 7-7, 7-8, 7-9, 7-10 Topic 8: Lessons 8-3, 8-4, 8-5, 8-6, 8-7 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

Everglades K-12: Grade 5 pp. 52-84 Chapter 2: Addition and Subtraction of Fractions

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.ixl.com www.aaamath.com www.pearsonsuccessnet.com http://illuminations.nctm.org/ www.abcya.com/fraction_tiles.htm http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) http://www.visualfractions.com/Games.htm (visual fractions games) http://www.softschools.com/math/fractions/ (fraction games, worksheets and quizzes

Required Summative

05 Math Interim Assmt Fractions

Optional Formatives

Florida Benchmarks Assessment

Workbook Topic 7 Florida Test (if not already given)



Center/DOD.)

Math Focus Formatives 05 Math Focus Formative MA.5.A.2.1





Intervention/Remediation An intervention/remediation resource guide can be found on page 48 of the



Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: MEASUREMENT PACING: Weeks 23 – 26

ESSENTIAL QUESTIONS: How do you determine the appropriate tool and unit when measuring? How do you measure accurately (precisely) to the nearest unit of measure?

MEASUREMENT TOPICS



Measurement (T13)

NGSSS: Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurement.

Students will:

• select and use appropriate units of measurement. • select and use appropriate tools strategically for:

� weight/mass (down to the nearest ounce and milligram) � capacity/volume (down to the nearest ounce and milliliter) � length (down to the nearest

16

1 inch and millimeter)

� area (base/height instead of length/width) � temperature (be familiar with reading both Celsius and Fahrenheit) � time (down to the nearest minute) including elapsed time

NOTE: Tools may include, but are not limited to, scales, rulers, yardsticks, tape measures, meter sticks, measuring cups, analog and digital clocks, and thermometers.

• determine when to use an approximate measure or a more precise measure in real-world contexts.

• recognize and explain precision of measurement (measuring to the nearest 1

4

inch is more precise than measuring to the nearest 1

2inch;

1

2inch is more precise than

1

4foot).


• solve real-world problems involving measurement. • defend solutions.

T13.MA.5.G.5.3 accurate balance Celsius customary units degrees elapsed time Fahrenheit foot gallons gram hours inch liter mass meter meter stick metric units mile milligram milliliter millimeter minutes ounces pint pounds precise quart ruler scale seconds thermometer tons yard yard stick



Measurement (T13)

NGSSS: Compare, contrast, and convert units of measure within the same dimension (length, mass, or time) to solve problems.

Students will:

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

• convert within the customary system with up to two conversions using the Grade 5 FCAT 2.0 Mathematics Reference Sheet found on page 49 in the Grade 5 Mathematics Curriculum Map.


• convert within the metric system with up to two conversions using the Grade 5 FCAT 2.0 Mathematics Reference Sheet found on page 49 in the Grade 5 Mathematics Curriculum Map.

• determine elapsed time to the nearest minute using analog and digital clocks.


• attend to precision when applying knowledge of length, weight, mass, calendars and elapsed time to solve problems.

T13.MA.5.G.5.2










Look for and express regularity in

repeated reasoning.




enVisionMATH Student Edition Topic 7: Lessons 10-1, 10-2, 10-3, 10-4, 10-5; Reteaching Sets: A-D p 256-257 Topic 8: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6; Reteaching Sets: A-E p 274-275

enVisionMATH Ready-Made Centers Topic 7: Lessons 10-1, 10-2, 10-3, 10-4, 10-5 Topic 8: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

enVision Math Problem of the Day Topic 7: Lessons 10-2, 10-3, 10-4, 10-5 Topic 8: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

envisionMath Daily Assessment and Reteaching Workbook Topic 7: Lessons 10-1, 10-2, 10-3, 10-4, 10-5 Topic 8: Lessons 11-1, 11-2, 11-3, 11-4, 11-5, 11-6

Everglades K-12: Grade 5 pp. 131-134 Measurement Problems with Approximations and Precision

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.ixl.com www.pearsonsuccessnet.com www.aaamath.com http://illuminations.nctm.org/ http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.mathplayground.com (shapes, geometry) http://bbc.co.uk/schools/ks2bitesize/maths/shape_space (interactive math site - 2-D shapes, 3-D shapes, angles, measures, symmetry, time)

Required Summative

05 Math Interim Assmt Measurement

Optional Formatives




Center/DOD.)

Math Focus Formatives 05 Math Focus Formative MA.5.G.5.2 05 Math Focus Formative MA.5.G.5.3







Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: GEOMETRY PACING: Week 27 – 31

ESSENTIAL QUESTIONS:

How can you compare and contrast polygons and polyhedra? How does knowing the area of a rectangle help derive area formulas you don’t know? What do the surface area and volume of a 3-dimensional shape represent and how can each be found?

MEASUREMENT TOPICS



2-Dimensional Figures and

3-Dimensional Solids (T09)

NGSSS: Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces.

Students will:

• use appropriate geometric vocabulary to describe 2-dimensional figures and 3-dimensional solids (polyhedra).

NOTE: Polyhedra (prisms and pyramids) are 3-dimensional solids in which all surfaces are polygons.

• determine the types of faces (e.g., rectangle, triangle) and the number of edges, faces, bases, and vertices in polyhedra.

• compose/decompose solids such as cereal boxes (from a net to a solid and vice versa).

• reason abstractly and quantitatively to identify and name the 3-dimensional solid formed by a net, based on the number of faces and types of faces.

• reason abstractly and quantitatively to identify the net formed by a 3-dimensional solid, based on the number of faces and types of faces.

• identify different views of a composite solid composed of cubes. • look for and make use of structure to determine the number of cubes needed to

build a composite solid.

NOTE: A composite solid is a 3-dimensional shape formed by combining geometric solids to build a new shape (assessment will be limited to composite solids formed by cubes only).

T09.MA.5.G.3.1 2-dimensional figures 3-dimensional solids area area of base (B) base (b) cube cubic unit edges faces height (h) length (l) net parallelogram perimeter polygon polyhedron prisms pyramid rectangle right angle solid square unit surface areas.(S.A.) trapezoid triangle vertex/vertices volume (V) width (w)



Area Formulas (T10)

NGSSS: Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle.

Students will:

• look for and make sense of structure when exploring the area of a rectangle based on the number of squares it takes to fill or cover the inside of a rectangle (A = bh).

• justify why the formula for finding the area of a parallelogram is the same as a rectangle (A = bh).

NOTE: Cutting off a right triangle from one side of a rectangle and translating it to the other side of the shape forms a parallelogram with the same area as the original rectangle.

• derive and apply the area formula of a triangle (A = ½bh) from the area formula of a rectangle.

NOTE: Cutting a rectangle in half diagonally (joining nonadjacent vertices of a polygon) gives two triangles, each with half the area of the original rectangle.

• derive and apply the area formula for an isosceles trapezoid from the area formula of a rectangle (A = ½ h(b1 + b2) or A = h(b1 + b2) ÷ 2).

NOTE: An isosceles trapezoid is a trapezoid with two equal sides. Cutting off a right triangle from one side of a rectangle and reflecting, rotating, and translating it to the other side of the shape forms a trapezoid with the same area as the original rectangle.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 49) should be used consistently for finding area AFTER the students understand the relationship that exists between the area of a rectangle and the areas of a parallelogram, triangle, and trapezoid.

T10.MA.5.G.5.4



Surface Area (T12)

NGSSS: Describe, define, and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools.

Students will:

• describe and define surface area using nets and solids of rectangular prisms and cubes.

• model and choose appropriate strategies and tools for determining surface area. • calculate surface area of rectangular prisms and cubes (S.A. = 2bh + 2bw + 2hw)

using appropriate tools. • label appropriate units of measure for surface area.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 49) should be used consistently AFTER the students have explored and developed the concept of surface area.

T12.MA.5.G.3.2

Volume (T11)

NGSSS: Describe, define, and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools.

Students will:

• describe and define volume of rectangular prisms and cubes. • model and choose appropriate strategies and tools for determining volume. • calculate volume of rectangular prisms and cubes (V = bwh or V = Bh) using

appropriate tools. • label appropriate units of measure for volume.

NOTE: The Grade 5 FCAT 2.0 Mathematics Reference Sheet (page 49) should be used consistently AFTER the students have explored and developed the concept of volume.


T11.MA.5.G.3.2











reasoning.




enVisionMATH Student Edition Topic 12: Lessons 12-2, 12-3, 12-4, 12-5, 12-6, 12-7; Reteaching Sets: B-E p 294-295 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5; Reteaching Sets: A-D p 312-313 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6; Reteaching Sets: A-F p 334-335

enVisionMATH Ready-Made Centers Topic 12: Lessons 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

enVision Math Problem of the Day Topic 12: Lessons 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

envisionMath Daily Assessment and Reteaching Workbook Topic 12: Lessons 12-2, 12-3, 12-4, 12-5, 12-6, 12-7 Topic 13: Lessons 13-1, 13-2, 13-3, 13-4, 13-5 Topic 14: Lessons 14-1, 14-2, 14-3, 14-4, 14-5, 14-6

Everglades K-12: Grade 5 pp. 86-99 Chapter 3: 3-Dimensional Shapes: Volume and Surface Area pp. 135-139 Chapter 5: Derive and Apply Area Formulas

Safari Montage http://vsod.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=33061&location=local (area of rectangle, parallelogram, and triangle) http://safari4.volusia.k12.fl.us/SAFARI/montage/play.php?keyindex=51311&location=local&chapterskeyindex=122406&play=1 (area of geometric shapes, surface area, and volume)

Internet www.fi.uu.nl/toepassingen/02015/toepassing_wisweb.en.html - The Freudenthal Institute for Science and Mathematics Education (FIsme) is a research institute of Utrecht Universiteit, faculty of Science. “Building houses with side views” a great interactive site on perspective. CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx www.ixl.com www.pearsonsuccessnet.com www.aaamath.com http://illuminations.nctm.org/ http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.mathplayground.com (shapes, geometry) http://bbc.co.uk/schools/ks2bitesize/maths/shape_space (interactive math site- 3-D shapes) http://www.coolmath.com/reference/areas.html (site for area of geometric shapes and where the formula comes from) http://www.studyzone.org/testprep/math4/d/formareal.cfm (formulas for area of geometric shapes including a link to practice finding area)

Required Summative

05 Math Interim Assmt Geometry

Optional Formatives

Florida Benchmarks Assessment

Workbook Topic 12 Florida Test Topic 13 Florida Test Topic 14 Florida Test


Center/DOD.)

Math Focus Formatives 05 Math Focus Formative MA.5.G.3.1 05 Math Focus Formative MA.5.G.3.2 05 Math Focus Formative MA.5.G.5.4




Intervention/Remediation An intervention/remediation resource guide can be found on page 48 of the



Copy Center/DOD)


UNIT/ORGANIZING PRINCIPLE: EXTENSION OF DIVISION PACING: Week 32 – 34

ESSENTIAL QUESTIONS: What is division? How do you determine if a solution is reasonable?

MEASUREMENT TOPICS



Division (T03)

NGSSS: Describe the process of finding quotients involving multi-digit dividends using models, place value, properties, and the relationship of division to multiplication.

Students will:

• describe and demonstrate the process of division using a variety of models (e.g.,

25 ÷ 5, 5 25 , 5

25 , partial quotients, repeated subtraction, equal sharing, place-

value, expanded notation).

NOTE: Partial quotients is an alternative method to long division using groupings of multiples of the divisor and then adding the partial quotients to find the answer.

Example:

26 r 4 partial quotients

5 134

- 50 10 Help Box x5 84 - 50 10 1 X 5 = 5 5 X 5 = 25 34 10 X 5 = 50 - 25 5 20 X 5 = 100 9 30 X 5 = 150 - 5 1 4

• explain the inverse relationship between multiplication and division.

• use multiplication as a tool for checking quotients in division problems. • model understanding of the Distributive Property used in division problems (e.g.

639 ÷ 3 can be expressed as (600 + 30 + 9) ÷ 3 = (600 ÷ 3) + (30 ÷ 3) + (9 ÷ 3)).

NOTE: Students do not need to memorize the name of the property.


• describe one or more steps of the standard algorithm. • describe missing steps of a partially completed division problem.

T03.MA.5.A.1.1

compatible numbers decimal Distributive Property divide dividend divisor equal sharing estimate expanded notation fraction hundredths inverse operation multiple partial quotients place value quotient reasonable remainder repeated subtraction standard algorithm tenths



Division (T03)

NGSSS: Estimate quotients or calculate them mentally depending on the context and numbers involved.

Students will:

• demonstrate a thorough understanding of the process of division to solve real-world problems using estimation or mental math strategies such as finding compatible numbers by using the closest multiple of the divisor (see Topic 1 p. 2E), or decomposition by finding a close friendly number that will divide easily.

T03.MA.5.A.1.2

NGSSS: Interpret solutions to division situations, including those with remainders, depending on the context of the problem.

Students will:

• model and interpret solutions and remainders using real-world problems (e.g. , A school bus holds 25 students. Sixty students are going on a field trip to Mosquito Lagoon. How many buses will be needed?).

• solve division problems involving quotients with fraction and decimal (to

hundredths) remainders (e.g., 42 ÷ 8 = 5 1

4or 5.25).

NOTE: EnVisionMATH does not address remainders expressed as decimals and fractions.

T03.MA.5.A.1.3

NGSSS: Divide multi-digit whole numbers fluently, including solving real-world problems, demonstrating understanding of the standard algorithm, and checking the reasonableness of results.

Students will:

• demonstrate fluency of basic division facts. • use estimation to predict the relative size of answers, check the

reasonableness of an answer and defend the estimate. • divide multi-digit whole numbers fluently.

NOTE: Fluently means accurately and efficiently.


• solve real-world division problems involving money (up to four digits representing dollars and two zeros representing cents: e.g., $372.00 ÷ 24). apply up to two operations to solve problems where at least one is division.

T03.MA.5.A.1.4











reasoning.





* These materials may have been used in earlier units. They should be used now, as needed, to help

students reach mastery of these concepts.

Student Edition

Topic 1: Lessons 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 Reteaching Sets: A-G p 22-23 Topic 2: Lessons 2-2, 2-4, 2-5, 2-6 Reteaching Sets: A-F p 54-55 Topic 3: Lessons 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8 Reteaching Sets: A-F p 78-79

Daily Assessment and Reteaching workbook

Lesson: 1-2, 1-3, 1-4, 1-5, 1-6, 1-7 2-2, 2-4, 2-5, 2-6 3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8

Internet

CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://illuminations.nctm.org/ www.ixl.com www.pearsonsuccessnet.com http://aaamath.com http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.mathplayground.com


UNIT/ORGANIZING PRINCIPLE: Extension of ALGEBRA PACING: Weeks 35 – 36

ESSENTIAL QUESTIONS: How do you use order of operations and basic properties in order to solve algebraic equations?

MEASUREMENT TOPICS




(T01)

NGSSS: Use the properties of equality to solve numerical and real-world situations.

Students will:

• reason abstractly and quantitatively to demonstrate knowledge of how to apply properties of equality (addition, subtraction, multiplication, and division).

NOTE: Equalities will involve no more than two operations.

Examples of balanced equations (equality):

1) 5 + 2 = 7 3(5 + 2) = 3 • 7 2) 12 = 15 – 3 12 ÷ 4 = (15 – 3) ÷ 4 When the same operation is performed on both sides of an equation, the equation remains balanced.

Another example of equality:

If the scale is balanced, what is the weight of one rectangle?

• solve equations with up to two variables by substituting a quantity for one of the variables in the equation.

NOTE: When a two variable equation is used, the value of one variable must be provided (e.g. If c = 6, solve for y in the following equation: 4c + y = 28).

• translate a written description or graphic into an expression or equation (using a variable for the unknown number).

T01.MA.5.A.4.1 Associative Property base number Commutative Property Distributive Property Equality Property of Addition Equality Property of Division Equality Properly of Multiplication Equality Property of Subtraction exponent expression growing pattern order of operations parentheses power variable



NGSSS: Use the order of operations to simplify expressions, which include exponents and parentheses.

Students will:

• follow steps in the order of operations to simplify expressions which include exponents and parentheses.

Steps:

1. Perform calculations inside parentheses or other grouping symbols. 2. Do calculations involving exponents. 3. Complete all multiplication/division as it appears from left to right. 4. Complete all addition/subtraction as it appears from left to right.

Example: 48 ÷ ( 20 – 8 ) + 2 x 3³

48 ÷ 12 + 2 x 33

48 ÷ 12 + 2 x 27 4 + 54 58

T01.MA.5.A.6.2

Division (T03)


Students will:

• make sense of and persevere in solving non-routine problems using various strategies including: drawing diagrams, making tables or lists, looking for patterns, using models, estimating, solving a simpler problem, and/or make an educated guess, check, and revise.

• reason abstractly and quantitatively to extend growing patterns.

NOTE: Practice with growing patterns can be found in the enVisionMATH Diagnostic & Intervention System. Go to Booklet F: Numeration, Patterns, and Relationships in Grades 4-6. Page F25 Geometric Growth Patterns.


T03.MA.5.A.6.5












Note: Exponents should be limited to 2 or 3.



* These materials may have been used in earlier units. They should be used now, as needed, to help students reach mastery of these concepts.

Student Edition

Topic 1: Lessons 1-5 Topic 3: Lessons 3-8 Reteaching Sets: E p 23 Reteaching Sets: F p 79 Topic 4: Lessons 4-4 Topic 5: Lessons 5-3 Reteaching Sets: D p 103 Reteaching Sets: C p 124 Topic 6: Lessons 6-2 Topic 7: Lessons 7-11 Reteaching Sets: B p 156 Reteaching Sets: K p 197 Topic 10: Lessons 10-5 Topic 11: Lessons 11-6 Reteaching Sets: E p 257 Reteaching Sets: F p 275 Topic 12: Lessons 12-7 Topic 13: Lessons 13-5 Reteaching Sets: E p 295 Reteaching Sets: D p 313 Topic 14: Lessons 14-6 Topic 16: Lessons 16-5 Reteaching Sets: F p 335 Reteaching Sets: E p 379


Lesson: 1-5, 3-8, 4-4, 5-3, 6-2, 7-11, 10-5, 11-6, 12-7, 13-5, 14-6, 16-5

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://illuminations.nctm.org/ www.ixl.com www.pearsonsuccessnet.com http://aaamath.com http://bbc.co.uk/schools/ks2bitesize/maths/shape_space (interactive math site)


UNIT/ORGANIZING PRINCIPLE: Extension of FRACTIONS PACING: Weeks 37 – 39

ESSENTIAL QUESTIONS: How do you add and subtract fractions and mixed numbers with like and unlike denominators? How and why do you estimate the sums and differences of fractions?

MEASUREMENT TOPICS




Fractions (T07)


Students will:

• review equivalent fractions using fraction bars, models and graphics. • simplify a fraction into lowest terms. • find the Least Common Denominator (LCD) in a set of fractions using various

strategies (e.g., manipulatives, listing of multiples, prime factorization).

Example: Find the LCD of 12

5 and 8

3 using prime factorization.

Step 1: Write the product of prime factors for each denominator.

12 = 2 • 2 • 3 = 22 • 3¹

8 = 2 • 2 • 2 = 23

Step 2: Sort the prime factors according to the same bases. 2

2 and 2

3 AND

3¹

Step 3: Choose the base with the highest exponent.

For 22 and 2

3 , choose 2

3 because the highest exponent is 3.

For 3¹ , choose 3¹ because the highest (and only) exponent is 1.

Step 4: Multiply the factors with the highest exponent for each base together. 2

3 • 3¹

8 • 3 = 24 (Therefore the LCD is 24.)

• represent addition and subtraction of fractions with like and unlike denominators using concrete and graphical models.

NOTE: Concrete models include, but are not limited to, fraction strips, fraction circles, pattern blocks, Geoboards, and other tangible objects. Graphical models include, but are not limited to, pictures of base-ten blocks and drawings.

• use the commutative and associative properties when adding fractions (up to 3 addends).

• model addition and subtraction of mixed numbers with like and unlike denominators, with and without regrouping.

• model addition and subtraction of fractions greater than one with like and unlike denominators.


T07.MA.5.A.2.1 benchmark fractions common denominator denominator equivalent dozen estimate

fraction greater than one ( �

� )

(formerly called improper fractions) Least Common Denominator (LCD) mixed number number lines numerator prime factorization reasonableness simplest form




Students will:

• attend to precision when adding and subtracting common fractions and mixed numbers fluently (accurately and efficiently) using like and unlike denominators, with and without regrouping.

• attend to precision when adding or subtracting real-world problems involving fractions and mixed numbers.

• use estimation to verify the reasonableness of answers.

NOTE: Appropriate denominators include 1-12, 14, 15, 16, 18, 21, 24, 25, 32, 35, 36, 45, 75, or any multiple of 10 through 100.

T07.MA.5.A.2.2


Students will:

• use estimation strategies such as rounding, benchmark fractions, or number lines to predict the relative size of answers when adding or subtracting fractions.

NOTE: Benchmark fractions are common fractions that you can judge other numbers against such as 0,

2

1 , and 1.

T07.MA.5.A.2.3











reasoning.




* These materials may have been used in earlier units. They should be used now, as needed, to help students reach mastery of these concepts.

Student Edition

Topic 7: Lessons 7-6, 7-7, 7-8, 7-9, 7-10 Reteaching Sets: F-J p 196 Topic 8: Lessons 8-2, 8-3, 8-4, 8-5, 8-6, 8-7 Reteaching Sets: B-F p 218 Topic 9: Lessons 9-1, 9-2, 9-3, 9-4, 9-5, 9-6 Reteaching Sets: A-F p 240


Lesson: 7-6, 7-7, 7-8, 7-9, 7-10 8-2, 8-3, 8-4, 8-5, 8-6, 8-7 9-1, 9-2, 9-3, 9-4, 9-5, 9-6

Internet CPALMS is a state wide project to build information systems and tools to support the implementation of the Next Generation Sunshine State Standards (NGSSS). http://www.floridastandards.org/homepage/index.aspx http://illuminations.nctm.org/ www.ixl.com www.pearsonsuccessnet.com http://aaamath.com http://www.internet4classrooms.com/skills-5th-mathbuilders.htm (choose a topic for fun math games) www.abcya.com/fraction_tiles.htm


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, examining what is already known, or using other means of mathematical inquiry.

• http://www.mathsolutions.com/documents/Ho

w_to_Get_Students_Talking.pdf • http://www.sagepub.com/upm-

data/37758_chap_1_tobey.pdf

• http://formativeassessment.barrow.wikispaces

.net/Agreement+Circles

Statement How can you 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 discussing and defending their mathematical ideas. Students stand in a circle as the teacher reads a statement. Students who agree with the statement step to the center of the circle. Those who disagree remain on the outside circle. Those on the inner circle face their peers on the outer circle and divide themselves into small groups who agree and disagree. Small groups then discuss to defend their thinking.

• Are there 20 cups in a gallon? Agree or disagree.

• Is 2/3 equivalent to 4/6? Additional Questioning: 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? Use when students have had some exposure to the content.

Annotated Student Drawings

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

• http://formativeassessment.barrow.wikispaces

.net/Annotated+Student+Drawings

• Represent the number 747 drawing rods and cubes.

• Represent 3x2=2x3 using arrays.


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, numbers, symbols, or words according to certain characteristics or category. Students sort the cards based on their preexisting ideas about the concepts or procedures. As students sort the cards they discuss their reasons or placing each card into a designated group. This activity promotes discussion and active thinking. Card sorts are best used in small groups to encourage students to share their thinking with their peers. Teacher circulates around the classroom listening to students hearing and seeing their levels of understanding. Make sure that the students explain their reasons for placing the card in one of the rows.

• http://teachingmathrocks.blogspot.com/2012/

09/vocabulary-card-sort.html

• Use with equivalent fractions • Place value (standard form, expanded

form, written form) • Measurement conversions • Fact families • Number to number word and drawing of

numbers

Commit and Toss

Commit and Toss is an anonymous technique used to get a quick read on the different ideas students have in the class. Students are given a question and 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 either 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. THIS IS A FUN, ENGAGING TECHNIQUE! BE CAREFUL NOT TO OVERUSE IT OR IT WILL LOSE ITS EFFECTIVENESS.

Stephanie stood with both feet on the bathroom scale. She recorded her weight. She lifted her left foot and stood on the scale with only one foot on it. Which best describes what happened to the reading on the scale? a. The weight shown on the scale increased. b. The weight shown on the scale decreased. c. The weight shown on the scale stayed the same. Explain your thinking. Describe the reason for the answer you selected.

Concept Card Mapping

Concept Card Mapping is provides an opportunity for students to activate their prior knowledge, think about relationships between familiar concepts and make visual representation of connections in their own knowledge network. Students are given cards with the concepts written on them. They move the cards around and arrange them as a connected web of knowledge. They create linkages between the concept cards that describe the relationship between concepts.




Concept Cartoons

Concept Cartoons are cartoon drawings that visually depict children or adults sharing their ideas about common everyday math. 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 mathematics. Not all cartoons have one “right answer”. Allow students time to for ideas to simmer and stew to increase cognitive engagement.

• www.pixton.com (comic strip maker)

Four corners

Four Corners provides an opportunity for students to make their ideas public. By meeting “in the corner” with students with similar ideas, students can further discuss and clarify their own thinking with others before returning to their seats and engage in mathematical discussion with the class. Present a controversial text-based statement and have students go to the corner that best fits their opinion. Students then pair up to defend their opinion with text based evidence. The teacher circulates and records comments. Next, there can be a whole group discussion, where opinions are defended and/or students can return to their desks to write a brief defense of their opinion.

• http://debbiedespirt.suite101.com/four-

corners-activities-a170020

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

html

Corners are labeled: Strongly agree, agree, disagree and strongly disagree.

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




Friendly Talk Probes

Friendly Talk Probes are two-tiered questions that consist of a selected-response section followed by a justification. The probe is set in a real-life scenario in which “friends” talk about a mathematical concept. Students are asked to pick the person they most agree with and explain why. Distracters are based on commonly held ideas from the research on students’ misconceptions and common errors. The conversation between the characters draws students into the ideas almost as if they are participating in the conversation.

Human Scatterplots

Human Scatterplots 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. This formative can be used at the beginning of a lesson or sequence of instruction to bring out students initial ideas and motivate them to want to further explore and discover mathematical ideas. Label the wall (Y-axis) on one side of the room with the choices: for example, A, B, C (and D, if there are four responses). Label the adjacent wall (X-axis) with a range of low confidence to high confidence. Have students position themselves based on where they feel they fall on the graph. A paper version can be used instead of a human graph.

What’s the Substitute? When you substitute ½ for x in 4x and simplify the results, what is the correct answer?

A. 4 ½ B. 2 C. 8

Human Scatterplot for “What’s the Substitute?”

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 concept or skill. 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…




Justified List

Justified List begins with a statement or question about a mathematical concept or procedure. Multiple examples that fit or do not fit the statement are listed. Students choose the examples on the list that fit the statement or answer the question and provide a justification explaining their 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. You can also use pictures of manipulatives for English-language learners.

Ways to Make 734 All the numbers listed below are digits. Put an X next to the number that represents 734. ___ 700+30+4 ____7tens 3hundreds 4 ones ___730tens 4 ones ____7hundreds 3tens 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.

KWL Variations

K-W-L is a general technique in which students describe what the Know about a topic, Want to know about a topic, and Learned about the topic. It provides an opportunity for students to become engaged with a topic, particularly when asked what they would like to learn. K-W-L provides a self-assessment and reflection at the end, when students are asked to think about what they 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 area they feel they have prior knowledge about the learning goal. 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. A key principle of learning is that students must know what the learning target is. 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 facts, concepts or skills 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 also provides students with an opportunity to look back on 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 commonly used, 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 is used as instructional feedback to address student difficulties.

You have been learning about three dimensional shapes. What is the muddiest point for you so far when it comes to three dimensional shapes? 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 seemingly similar items and challenges students to choose which item in the group does not belong. Students are asked to justify their reasoning for selecting the number, symbol, representation, or mathematical term that does not fit with the others. Odd One Out can be used at the beginning of instruction to find out what students already know about a mathematic topic. It can also be used during the development of conceptual understanding to examine the reasoning students use in comparing and contrasting the items on the list. Teachers can use this strategy to examine how their students make connections among concepts.

Show students three objects. "Which is the odd one out?" "Describe properties that two share that the third does not." "Now choose a different object from the three and justify it as the odd one out."

Partner Speaks

Partner Speaks provides students with an opportunity to talk through a concept or problem solution with another student and receive feedback 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 changes the emphasis from student’s ideas to consider the ideas of his or her partner and encourages careful listening between student pairs. This can be used to promote deeper engagement with an idea, especially when there is a need to have students think through a new idea or difficult question.

Today we are going to explore different ways to add three-digit numbers together. What different kinds of strategies can you use to add 345+525? Turn to your partner and take turns discussing your strategies. Be sure to listen carefully, without interrupting, as your partner shares his/her thinking. Then the partner shares. When you are finished taking turns, each of you will need to be prepared to share one way your partner added the numbers with the rest of class.




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 generator of questions 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 at the beginning of instruction in a topic to find out what students already know about the topic. Teachers can have students 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 could we find out if___?

Sticky Bars

Sticky Bars help students recognize that there is often a range of ideas students in the class 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 passed in to the teacher. The teacher or a student arranges the notes 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.




Thinking Log

Thinking Logs help the teacher identify areas where the students are aware of their own learning successes or challenges. The information can be used to provide interventions for individual or groups of students as well as match students with peers who may provide learning support. Use impromptu moments during a learning experience or at the end of a lesson for students to record in their Thinking Logs. 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.

• 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 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)

This formative can be used during any stage of the mathematics assessment and instruction cycle. Using different pairing strategies to ensure that students have the opportunity to form pairs with students other than the ones who sit next to them in order to avoid having students always interact with the same group of peers.

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.

3-2-1

3-2-1 provides a structured way for students to reflect on their learning. Students respond in writing to three reflective prompts; providing six responses that describe what they learned from a lesson or instructional sequence. This technique scaffolds students’ reflections providing an opportunity to share their success in learning difficult or new concepts as well as recognize what was challenging for them. (Three key ideas I will remember; Two things I am still struggling with; One thing that will help me tomorrow)




Traffic Light Cards

Traffic Light Cards are a monitoring strategy that can be used at any time during instruction to help gauge student understanding. The colors indicate whether students have full, partial, or minimal understanding. Students are given three different-colored cards, asked to self-assess their understanding about the concept or skill they are learning, and hold up the card that best matches their understanding.

Traffic Light Cups

Traffic Light Cups are used during group work and student investigations to signal to the teacher when groups need help or feedback. Red, yellow, and green stackable party cups placed in the center of a group’s table or workstation represent whether the group is able to proceed without the need for teacher intervention or whether they need assistance.

Variations of Traffic Light Formatives

Traffic Light Dots

Traffic Light Dots provide a way for students to self-assess areas of their work. Small peel-off dots serve as traffic signal icons. Students place the dots in the margins of their work to indicate areas where they feel they were successful (green), areas where they aren’t sure about their work and would like feedback (yellow), and areas where they feel they didn’t understand or perform well on the task and need help (red).

Variations of Traffic Light Formatives

Two-Minute Paper

Two-Minute Paper is a quick and simple 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. Write two questions on the board or on a chart that you want students to respond to. Give students two minutes to write and then collect their papers. After their responses have been analyzed, share the results with students the next day, letting them know how you are going to use the feedback they shared with you.

• What was the most important thing you learned today?

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

• 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 used in “comments-only marking.” It is a way to balance positive comments with the need for improvement when providing students with feedback on their work. The first sentence describes two good features of the section of work that is commented on. The second sentence encourages revision or further improvement.

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 a “What are you doing and why are you doing it?” question. 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.

Whiteboarding

Whiteboarding is 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/lp25

1-01.shtml


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

FINAL Grade 5 Mathematics Curriculum Map …public.volusia.k12.fl.us/mathematics/Documents/Grade 5...

Documents

Transcript of FINAL Grade 5 Mathematics Curriculum Map …public.volusia.k12.fl.us/mathematics/Documents/Grade 5...