GRADE 5 MATHEMATICS CURRICULUM GUIDE · GRADE 5 MATHEMATICS CURRICULUM GUIDE Loudoun County Public Schools 2016-2017 ... consensus of Loudoun’s teachers concerning the implementation

GRADE 5 MATHEMATICS

CURRICULUM GUIDE

Loudoun County Public Schools 2016-2017

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

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

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

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

http://loudounvision.net/

INTRODUCTION TO LOUDOUN COUNTY’S MATHEMATICS CURRICULUM GUIDE

This CURRICULUM GUIDE is a merger of the Virginia Standards of Learning (SOL) and the Mathematics Achievement Standards for Loudoun County Public Schools. The CURRICULUM GUIDE includes

excerpts from documents published by the Virginia Department of Education. Other statements, such as suggestions on the incorporation of technology and essential questions, represent the professional

consensus of Loudoun’s teachers concerning the implementation of these standards. This CURRICULUM GUIDE is the lead document for planning, assessment, and curriculum work.

NAVIGATING THE LCPS MATHEMATICS CURRICULUM GUIDE

The Curriculum Guide is created to link different components of the guide to related information from the

Virginia Department of Education, resources created by Loudoun County Public Schools, as well as vetted outside resources. To navigate the curriculum guide, click on the hyperlink (if in MSWord, hold the [ctrl] button and left click with the mouse on the

hyperlink). It will direct you to either another resource within the curriculum guide, or to a website resource. If you’re directed to a resource within the curriculum guide, to “go back,” hold the [alt] key and press the left arrow button.

Mathematics Internet Safety Procedures 1. Teachers should review all Internet sites and links prior to using it in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site, checking for broken links, and paying attention to any inappropriate pop-ups or solicitation of information. 2. Teachers should circulate throughout the classroom while students are on the internet checking to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their LCPS web pages. 4. Teachers should assure that the use of websites correlates with the objectives of the lesson and provide students with the appropriate challenge.

LCPS Grade 5 Mathematics Curriculum Guide 2016-2017

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

SOL Reporting Category 5th Grade SOL Number of Test Items (CAT)

NEW

Number of Items

Traditional

Number and Number Sense 5.1, 5.2a-b*, 5.3a-b 5 7

Computation and Estimation 5.4*, 5.5a-b*, 5.6*, 5.7* 9 13

Measurement and Geometry 5.8a-e, 5.9, 5.10, 5.11,

5.12a-b, 5.13a-b 8 12

Probability, Stats, Patterns,

Functions, & Algebra

5.14, 5.15, 5.16b-d, 5.17,

5.18a-d, 5.19 13 18

*Items measuring these SOL will be completed without the use of a calculator.

2016 – 2017 School Calendar

Starts Ends

First Quarter August 29 November 4

Second Quarter November 9 January 26

Third Quarter January 30 April 6

Fourth Quarter April 17 June 9

Quarter 1 Quarter 2 Quarter 3 Quarter 4

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


Grade 5 Nine Weeks Overview

1st Quarter 2nd Quarter 3rd Quarter 4th Quarter

Unit 1-Classroom Routines: “The First 20 Days Classroom Routines” NUMBER TALKS 5.4 Problem Solving (whole numbers) Unit 2-Whole Number Operations & Applications 5.4 Single- and Multi-step Practical Problems Using Whole Number Operations 5.3 Prime/Composite, Odd/Even 5.18 Variables, Expressions, and Equations 5.8a Perimeter and Area (whole numbers) Unit 4-Comparing & Applying Rational Number Concepts 5.10 Elapsed Time Unit 3-Patterns & Properties 5.19 Distributive Property 5.7 Order of Operations 5.17 Relationships in Numerical and Geometric Patterns

Unit 1-Classroom Routines: NUMBER TALKS 5.4 Problem Solving 5.10 Elapsed Time 5.15 Graphs Unit 4-Comparing & Applying Rational Number Concepts 5.1 Decimal Place Value and Rounding 5.2 Fraction/Decimal Equivalents, Comparing, Ordering 5.14 Probability & Sample Space 5.17 Relationships in Numerical Patterns (see unit summary) Unit 5-Rational Number Operations & Measurement Applications 5.6 Adding and Subtracting Fractions in Single- and Multi-Step Problem Solving, Simplest Form

Unit 1-Classroom Routines: NUMBER TALKS 5.4 Problem Solving 5.10 Elapsed Time 5.15 Graphs Unit 5 (cont’d)-Rational Number Operations & Measurement Applications 5.5 Decimal Operations 5.8 Metric & Customary Measurement, Perimeter/Area/Volume with Fractions and Decimals 5.17 Relationships in Numerical Patterns (conversions--see unit summary) Unit 6-Classifying & Subdividing Plane Geometric Figures 5.11 Angles 5.12 Angles and Triangles 5.13 Plane Figures, Combining and Subdividing 5.9 Circles Unit 7-Data & Statistics 5.16 Mean, Median, Mode, Range

Unit 1-Classroom Routines: NUMBER TALKS 5.4 Problem Solving 5.10 Elapsed Time 5.15 Graphs Unit 7-Data & Statistics 5.15 Stem and Leaf, Line Graphs 5.16 Mean, Median, Mode, Range Review for SOL Assessment & Post SOL Topics

48 days 45 days 48 days 39 days


Grade 5 Scope & Sequence Quarter 1: 48 days

Days Unit Standard Content Strand Topic All year Unit 1-Classroom

Routines

“The First 20 Days Classroom Routines” and NUMBER TALKS, Problem Solving, Elapsed Time, Graphs

24 Unit 2-Whole Number Operations & Applications

5.4 Computation and Estimation

Whole Number Problem Solving

5.3 Number and Number Sense

Prime/Composite/Even/Odd

5.18 Patterns, Functions, and Algebra

Variables, Expressions, and Equations

5.8a Measurement Perimeter and Area with Whole Numbers

15 Unit 3-Patterns & Properties


Distributive Property


Order of Operations


Relationships in Numerical and Geometric Patterns

5 Unit 4-Comparing & Applying Rational Number Concepts

5.10

Measurement Elapsed Time

4 Assessment, Review, and Intervention


Quarter 2: 45 days

Days UNIT Standard Content Strand Topic All

year Unit 1-Classroom Routines

NUMBER TALKS, Problem Solving, Elapsed Time, Graphs

27

Unit 4-Comparing & Applying Rational Number

Concepts


Decimal Place Value and Rounding


Fraction/Decimal Equivalents, Comparing, Ordering

5.14 Probability and Statistics Probability and Sample Space


Relationships in Numerical Patterns

14 Unit 5-Rational Number Operations &

Measurement Applications


Adding and Subtracting Fractions in Single- and Multistep Problem Solving, Simplest Form



Quarter 3: 48 days


year

Unit 1-Classroom

Routines


25 Unit 5 (cont’d)-Rational Number

Operations & Measurement Applications


Decimal Operations

5.8 Measurement Metric and Customary Systems, Perimeter/Area/Volume with Fractions and Decimals


Relationships in Numerical Patterns (conversions—see unit summary)

15

Unit 6-Classifying & Subdividing

Plane Geometric Figures

5.11 Measurement Angles

5.12 Geometry Angles and Triangles

5.13 Geometry Plane Figures, Combining and Subdividing

5.9 Measurement Circles

5 Unit 7-Data & Statistics

5.16 Probability and Statistics Mean, Median, Mode, and Range



Quarter 4: 39 days


year

Unit 1-Classroom

Routines


11 Unit 7-Data & Statistics

5.16 Probability and Statistics Mean, Median, Mode, and Range (continued)

5.15 Probability and Statistics Stem and Leaf Plot, Line Graphs


SOL Tests

LCPS MATH Unit Summary Grade 5 2016-2017

Unit: 1 Quarters 1-4

Classroom Routines

VDOE Standards of Learning:

1st quarter: The First 20 Days Classroom Routines 5.4 The student will create and solve single-step and multistep practical problem involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

5.10 The student will determine the amount of elapsed time in hours and minutes within a 24-hour period.

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

Learning Targets:

I can create, estimate, and solve addition, subtraction, multiplication, and division problems that have two or more steps involved in order to find the answer.

I can determine the elapsed time between two events within a 24-hour period.

Big Ideas Essential Questions

Classroom routines (about 10 minutes each day)

can be used to introduce, support, and extend

topics throughout the yearly curriculum in order to

provide students with regular practice in important

mathematical ideas.

Whole number operations in the context of

practical problems (integrated in a variety of

mathematical topics throughout the year).

Apply knowledge of number and number sense to

investigate and solve practical problems

Elapsed time within a 24-hour period (possibly

spanning from a.m. to p.m.) with the goal of

becoming a daily routine.

Can you describe the structure of the story problem? (for example: a part plus a part equals a whole in addition; a whole minus a part equals a part in subtraction; multiplication is repeated addition; division is repeated subtraction or fair shares)

What are some strategies for solving multistep story problems?

What are two strategies for determining elapsed time?

Prerequisite Skills Vocabulary

VDOE Vertical Alignment document 3-6

4.4 d) solve single‐step and multistep add/sub/mult problems with whole numbers 4.9 determine elapsed time in hours/min within 12‐hour period

VDOE Vocabulary Word Wall Cards

addend subtrahend minuend divisor dividend quotient remainder difference product sum part whole elapsed time hour, minute, second analog/digital clock

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

http://www.doe.virginia.gov/instruction/mathematics/resources/vocab_cards/math_vocab_cards_5.pdf


Achievement Criteria How to Assess Achievement

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

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

interpret practical situations.” -2009 Mathematics Standards of Learning

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

Pre and Post Unit Assessments for each standard

can be found in PowerSchool Assessment (formerly Interactive Achievement)

Sample Math Tasks are available in VISION:

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

NCSM Great Tasks

(available in all LCPS Elementary Schools—click link)

Classroom Routines

1st quarter: The First 20 Days Classroom Routines NUMBER TALKS: Example: http://www.mathsolutions.com/videopage/videos/Final/Classroom_NumberTalk_Gr3.swf Number Talks sample flipcharts available on the Elementary Math Resources VISION site INVESTIGATIONS: Measurement Benchmarks Estimation and Number Sense Guess My Number PROBLEM SOLVING: Math Playground’s Thinking Blocks (problem solving) ELAPSED TIME:

Randomly, throughout the school day, announce, “Start time!” and have students record the time. Later, announce, “End time!” and have students compute the amount of time elapsed. Do this activity daily for several weeks, and periodically throughout the weeks following elapsed time instruction.

Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

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


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


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

http://www.mathplayground.com/thinkingblocks.html



Unit: 2 Quarter 1

Whole Number Operations & Applications


5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

5.3 The student will a) identify and describe the characteristics of prime and composite numbers; and b) identify and describe the characteristics of even and odd numbers.

5.18 The student will Investigate and describe the concept of variable; Write an open sentence to represent a given mathematical relationship, using a variable; model one-step linear equations in one variable, using addition and subtraction; and create a problem situation based on a given open sentence, using a single variable. 5.8a The student will a) Find area and perimeter in standard units of measure for grid areas only (Volume will be introduced in 3rd quarter).


Learning Targets:

I can create, estimate, and solve addition, subtraction, multiplication, and division problems that have two or more steps involved in order to find the answer.

I can demonstrate examples of prime, composite, even, and odd numbers using models, numbers, and words.

I can describe and write an open sentence (including a variable) to represent a mathematical relationship. I can then model solving an open sentence (limited to addition or subtraction) and create a problem situation based on a given open sentence.

The student will, given a problem situation, decide if the problem requires perimeter, area, and/or volume and estimate and then measure, using appropriate units, to solve the problem.


Whole number operations in context of prob solving

Model prime/composite and odd/even numbers

Area and perimeter with whole numbers

Modeling Equations (solving equations is a 6th gr SOL)

Interpreting mathematical situations and models by using symbols and variables to interpret patterns

Division can be represented by sharing (partitive model) or grouping (quotitive model). For example:

Sharing (partitive)—Mrs. Smith has 225 pencils and wants to share them with her class. There are 25 students in her class. How many pencils will each student get?

Grouping (quotitive)—Mrs. Gomez has 288 pencils that come in packs (groups) of 12. How many packs of pencils does Mrs. Gomez have?

Partial products and partial quotients are strategies that allow for students to engage in number sense while using computation and the distributive property:(8 x 57 = 8 x (50 + 7) = (8 x 50) + (8 x 7) =400 + 56= 456)

How can you demonstrate, explain, and justify at least two ways to show a number is even or odd?

What is a prime number? a composite number?

How do prime and composite numbers compare and contrast?

What are strategies for estimating the sum, difference, product, or quotient of two numbers?

What is a variable? a variable expression?

What is an open sentence and what are its parts?

How do you express a word problem using an open sentence?

How are perimeter and area different?

Why is area expressed in square units?

Where would you use area and perimeter in your everyday life?



VDOE Vertical Alignment document 3-6

4.4 d) solve single‐step and multistep add/sub/mult problems with whole numbers 4.5 a) determine common multiples/ factors 4.16 a) recognize/demonstrate meaning of equality in equation 4.3 a) read/write/represent/ID decimals through thousandths; b) round to whole, tenth, hundredth; c) compare/order; d) write decimal and fraction equiv from a model 4.6 a) estimate/measure weight/mass, describe results in U.S. Cust/metric units; b) ID equiv measurements between units within U.S. Cust system and between units within metric system

VDOE Vocabulary Word Wall Cards

prime composite even odd term expression algebraic expression whole number more than balance equation less than factor inverse operation open sentence symbol twice area variable perimeter rounding standard form word form square units expanded form addend subtrahend minuend dividend quotient remainder divisor product sum difference partitive (sharing) quotitive (grouping)





Click here for a brief audio PowerPoint slide

with more information about the Process Goals





NCSM Great Tasks









Differentiation Resources

Have students enter large numbers in a calculator or a voice-supported word processing program that translates the number into words.

Have students use visual cues and/or mnemonic devices to help them remember place value order.

Have students write large numbers in a sand tray.

Have students color-code the different periods of the number line.

Have students work in groups to participate in a mock bank, using large-denomination play money.

Have students work in pairs to check each other when writing and reading large numbers.

Have students solve story problems using pictures, numbers and words.

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

ELL Model Performance Indicators

(click to link)

Investigations: Building on Numbers You Know (whole # operations) Mathematical Thinking at Grade 5: Investigation 1: Exploring Numbers and Number Relationships Measurement Benchmarks Investigation 1: Measures of Length and Distance Investigation 2: Measures of Weight and Liquid Volume Containers and Cubes Investigation 1: The Packaging Factory Investigation 2: Packing Problems Investigation 3: Measuring the Space in Our Classroom ESS Lessons: 5.4—Take a Trip 5.3—Sieve of Eratosthenes: An Ancient Algorithm 5.3—Partners and Leftovers 5.18—Variables and Open Sentences 5.8—Rolling Rectangles Learn Zillion: Multi-step word problems Find all the factor pairs of a number using area models Find all factor pairs using a rainbow factor line Find all factor pairs of a number using a t-chart Determine if a number is prime or composite using area models Algebraic expressions Brain Pop Prime Numbers Other: Illuminations: Factor Game Algebra Balance scales (NLVM) Math Literature Connections (click link) Hands-on Equations Book 1 (and Hands-on Equations Whiteboard software) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://www.doe.virginia.gov/testing/sol/scope_sequence/mathematics_2009/index.php

http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-4.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-3a.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-3b.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-18abcd.pdf

http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-8ab.pdf

http://learnzillion.com/lessonsets/352-solving-multistep-word-problems

http://learnzillion.com/lessons/780-find-all-the-factor-pairs-of-a-number-using-area-models

http://learnzillion.com/lessons/782-find-all-factor-pairs-using-a-rainbow-factor-line

http://learnzillion.com/lessons/785-find-all-factor-pairs-of-a-number-using-a-tchart

http://learnzillion.com/lessons/786-determine-if-a-number-is-prime-or-composite-using-area-models

http://learnzillion.com/lessons/786-determine-if-a-number-is-prime-or-composite-using-area-models

http://learnzillion.com/lessons/465-read-and-write-an-algebraic-expression-containing-a-variable

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

http://illuminations.nctm.org/ActivityDetail.aspx?ID=12

http://nlvm.usu.edu/en/nav/frames_asid_201_g_4_t_2.html?open=instructions



Unit: 3 Quarter 1

Patterns & Properties


5.19 The student will investigate and recognize the distributive property of multiplication over addition.

5.7 The student will evaluate whole number numerical expressions, using the order of operations limited to parenthesis, addition, subtraction, multiplication, and division.

5.17 The student will describe the relationship found in a number pattern and express the relationship.


Learning Targets:

I can recognize the distributive property of multiplication over addition, identify examples of the property, and model the property using pictures, numbers, and words.

I can simplify expressions with more than two operations using the order of operations and explain each step.

I can describe the mathematical relationships found in patterns using symbols.


Modeling and identifying the distributive property Partial products and partial quotients are strategies that allow for students to engage in number sense while using computation and reinforce the distributive property: (ie: 8 x 57 = 8 x (50 + 7) = (8 x 50) + (8 x 7) = 400 + 56 = 456) Order of operations (without exponents) **note that after parenthesis, multiplication/division is solved left to right, then addition/subtraction is also solved left to right. Input/output (function) table Using patterning as a problem solving tool Patterns represented and modeled in a variety of ways including numeric, geometric, and algebraic formats.

How does the distributive property relate to multiplication and addition?

Why would you use the distributive property?

How could the distributive property be used in computation strategies for whole numbers?

What is the order of operations?

Why is there a specific order of operations?

When would you use the order of operations?

How does the order of operations simplify an expression?

How can you use algebraic symbols to represent change in a pattern?

What are the connections between a pattern or function and the words, table, and symbols that represent it? How does an input/output table work?


VDOE Vertical Alignment document 3-6 4.16 b) investigate/ describe associative property for addition/multiplication 4.15 recognize/create/extend numerical/geometric patterns

VDOE Vocabulary Word Wall Cards distribute equality distributive property pattern function parentheses multiplication division addition subtraction function table evaluate input/output table relationship expression algebraic symbol equation sequence operation order of operations













NCSM Great Tasks



Have students follow the order of operations when solving multistep word problems.

Guess My Rule: Have students take turns giving the teacher a number to “input” on an input-output T-table. Using a predetermined rule, write the appropriate “output” number in the table. Next, provide an input number and ask a student who thinks he/she knows the rule being followed to determine the output—but do not allow the student to say the rule aloud. The student will prove that he/she knows the rule by being able to give the correct output. When most of the students seem to know the rule, have the students state the rule to the rest of the class.

Create a Venn diagram to explain the difference between a repeating pattern and a growing pattern.

How does the distributive property work with the problem 3 × 43? Use pictures and symbols.

Show how the distributive property works with variable expressions. Ask students how to write “3 times n + 1.” Lead them to see that this is written 3 × (n + 1). Ask students to represent this with their base-10 blocks, using a rod for n and a unit for one. Have them also represent this with symbols to help them see the connection between concrete and symbolic representations.



(click to link)

Investigations: Patterns of Change: Investigation 1: Number patterns in changing shapes ESS Lessons: 5.19—Exploring the Distributive Property 5.7—Order Out of Chaos 5.17—Pick Your Pattern Learn Zillion: Find the rule for a function machine using a vertical table (and 9 other lessons) Input Output Brain Pop Intro to Krypto Illuminations Krypto Game Distributive Property Order of Operations Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)









http://learnzillion.com/lessons/790-find-the-rule-for-a-function-machine-using-a-vertical-table

http://learnzillion.com/lessons/790-find-the-rule-for-a-function-machine-using-a-vertical-table

http://learnzillion.com/lessons/1190-identify-function-properties

http://www.brainpop.com/games/primarykrypto/

http://illuminations.nctm.org/ActivityDetail.aspx?ID=173

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

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



Unit: 4 Quarter 2

Comparing & Applying Rational Number Concepts


5.10 The student will determine an amount of elapsed time in hours and minutes within a 24- hour period.

5.1 The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth.

5.2 The student will a) recognize and name fractions in their equivalent decimal form and vice versa; and b) compare and order fractions and decimals in a given set from least to greatest and greatest to least

5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space.

5.17 The student will describe the relationship found in a number pattern and express the relationship. *in the context of equivalent fraction tables and skip counting.


Learning Targets:

I can determine the elapsed time between two events within a 24-hour period.

I can round decimal numbers expressed through thousandths to the nearest whole number, tenth, or hundredth, and represent my thinking using symbols, pictures, numbers, and words.

I can recognize and name fractions in their equivalent decimal form and compare and order fractions and decimals using models and multiple strategies.

I can make predictions and determine the probability of an outcome by using tools (spinners, number cubes, etc.) and models (sample space, number line, tree diagram, chart, etc.).


Elapsed time in the context of fractions

Decimal place value, rounding decimals using a variety of strategies including number lines

Fraction/Decimal equivalents, Comparing, Ordering

Representing probability with fractions and sample spaces, including tree diagrams

Investigate and develop an understanding of number sense by modeling numbers, using different representations such as physical materials, diagrams, mathematical symbols, and word names

Apply knowledge of number and number sense to investigate and solve practical problems

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

Patterns can be utilized as a strategy for finding equivalent fractions (equivalent fraction table):

3 = 3 I 6 I 9 I 12 I 15 (skip count by 3’s) 4 4 I 8 I 12 I 16 I 20 (skip count by 4’s)

What are two strategies for determining elapsed time?

Can you explain and justify various strategies for rounding decimal numbers?

How can you compare fractions that have the same denominator? Same numerator?

How can you compare fractions using a landmark number such as ½ or 1?

Why would you use estimation with rational numbers?

How can the same quantity be represented as both a fraction and a decimal?

How do you create and solve a practical problem using estimation of decimals and/or fractions?

How do you know that a fraction is in simplest form?

What are some strategies for adding and subtracting fractions with unlike denominators?

What are strategies for adding and subtracting mixed numbers and improper fractions?

What strategies are used to determine the sample space for an experiment?



VDOE Vertical Alignment document 3-6 4.9 determine elapsed time in hours/min within 12‐hour period 4.1 a) ID orally/in writing place value for each digit in a whole number through millions; b) compare two whole numbers through millions w/symbols; c) round whole numbers through millions to nearest 10/100/1,000/10,000/100,000 4.2 a) compare and order fractions/mixed numbers; b) represent equivalent fractions; c)ID division statement that represents a fraction 4.13 a) predict the likelihood of simple event; b) represent probability as a number between 0 and 1

VDOE Vocabulary Word Wall Cards elapsed time probability hour, minute, second tree diagram analog/digital clock equally likely place value likely fraction unlikely numerator certain denominator uncertain simplest form/simplify sample space multiple outcome lowest terms decimal reduce decimal point greatest common factor base ten unit least common denominator tenth hundredth thousandth rational numbers improper fraction mixed number factor least greatest










NCSM Great Tasks



Have students create elapsed time situations using television guides from newspapers and magazines. Have students trade problems to solve.

Allow students to continue to use the demonstration clocks as they use the timeline strategies.

Focus on computing elapsed time only in minutes. Then, focus on computing elapsed time in hours. Incorporate both hours and minutes once students are proficient in both separately.

Tape a decimal or fraction to the back of each student. Then have them ask the other students yes or no questions to try to figure out their number.

Investigations: Name that Portion Between Never and Always Measurement Benchmarks Investigation 3: It’s About Time ESS Lessons: 5.10—What Time is it? 5.1—Decimal Round-Up/Round-Down 5.2—Order Up! 5.14—It’s in the Bag













Use a variety of models (area, set, linear) to represent fractions and decimals.

Have students look at recipes and convert the fractions used into decimals.

Students can make connections to science by using both decimals and fractions to measure things.

Have students create their own lesson to share with small groups of third or fourth graders. Have students develop a lesson plan as well as an activity sheet with a probability situation. Use a rubric to grade students on their performance.

Draw a number line on the board that starts with 0 and goes to 1. Label a few points on the line. Above the 0, write “impossible.” Above the 1, write “certain.” Give students strips of paper with situations on them. (You will see a dinosaur as you walk home today. It will get dark tonight. It will rain tomorrow.) Have them read their paper to the class and then place it where they feel it should go on the number line. Include situations that will fall at different locations on the line.

Intervention Ideas


ELL Model Performance Indicators (click to link)

Learn Zillion: 5.10 Identifying the start time, change of time, and end time in real-world elapsed time problems (and 5 subsequent lessons) 5.1 Round decimals to the nearest whole number using a number line (and 3 subsequent lessons) 5.2 Convert decimals to fractions to the tenths place using number lines (and three more lessons) Convert fractions into decimals to the tenths place (and 2 more lessons) Compare Decimals Using Fractions 5.14 Find the probability of a compound event by creating a tree diagram Brain Pop: Fractions to decimals Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)

http://learnzillion.com/lessons/575-identifying-the-start-time-chane-of-time-and-end-time-in-realworld-elapsed-time-problems



http://learnzillion.com/lessons/431-round-decimals-to-the-nearest-whole-number-using-a-number-line

http://learnzillion.com/lessons/431-round-decimals-to-the-nearest-whole-number-using-a-number-line

http://learnzillion.com/lessons/1424-convert-decimals-to-fractions-to-the-tenths-place-using-number-lines

http://learnzillion.com/lessons/1424-convert-decimals-to-fractions-to-the-tenths-place-using-number-lines

http://learnzillion.com/lessons/336-convert-fractions-into-decimals-to-the-tenths-place

http://learnzillion.com/lessons/336-convert-fractions-into-decimals-to-the-tenths-place

http://learnzillion.com/lessons/562-compare-decimals-using-fractions

http://learnzillion.com/lessons/1861-find-the-probability-of-a-compound-event-by-creating-a-tree-diagram

http://learnzillion.com/lessons/1861-find-the-probability-of-a-compound-event-by-creating-a-tree-diagram

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



Unit: 5 Quarters 2-3

Rational Number Operations & Measurement Applications


5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

5.5 The student will a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit) b) create and solve practical problems involving decimals.

5.8 The student will a) find perimeter, area, and volume in standard units of measure c) identify equivalent measurements within the metric system d) estimate and then measure to solve problems, using U.S. Customary and metric units. e) choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units.

5.17 The student will describe the relationship found in a number pattern and express the relationship. *see Big Ideas for connection to measurement


Learning Targets:

I can develop strategies and use them to compute the sum or difference of fractions and mixed numbers in practical single and multi-step problems.

I can investigate, create, and solve single and multi-step problems involving decimal operations (addition, subtraction, multiplication, and division; decimals through thousandths and divisors with only one nonzero digit).

The student will, given a problem situation, decide if the problem requires perimeter, area, and/or volume and estimate and then measure, using appropriate units, to solve the problem.

I can describe the mathematical relationships found in patterns using symbols.


Number and operation sense and application to practical problems

Adding and subtracting fractions in the context of practical problems

Adding, subtracting, multiplying and dividing decimals

Measuring in the metric and customary systems, finding equivalent measures within the metric system

Perimeter /Area (rectangles, squares, right triangles)/Volume

Using fractions and decimals in the context of measurement situations

Conversions within systems of measurement can be modeled using a double number line, for example:

What strategies are used to estimate and compute addition and subtraction of fractions?

How are least common multiple and least common denominator important when adding and subtracting fractions?

How do you know if a fraction is in simplest form?

How can you use estimation strategies for the sum, difference, product, or quotient of two numbers?

What is the meaning of mathematical operations and how do these operations relate to one another when creating and solving single-step and multistep word problems?

How is multiplication and division of whole numbers and decimals alike and different?


How can the distributive property help with computation involving decimals?

How might the distributive property help find perimeter? * 2 ( L + W ) *

Why are equivalent measures within the metric system useful? When is it appropriate to convert from one unit to measure to another?

What are three examples of objects measured by each unit of measure in both the U.S. Customary and metric systems?

What are the connections between a pattern or function and the words, table, and symbols that represent it?

How can numerical or algebraic symbols to represent change in a pattern?


VDOE Vertical Alignment document 3-6 4.5 d) solve single‐/multistep practical problems involving add/sub fractions and decimals 4.6 a) estimate/measure weight/mass, describe results in U.S. Cust/metric units; b) ID equiv measurements between units Within U.S. Cust system and between units Within metric system 4.15 recognize/create/extend numerical/geometric patterns

VDOE Vocabulary Word Wall Cards estimate measure weight mass customary measurement metric system length width volume feet inches yards meter liter gram gallon pint quart cup miles ounce pound






Pre and Post Unit Assessments for each standard can be found in PowerSchool Assessment

(formerly Interactive Achievement)

Sample Math Tasks are available in VISION: Search: LCPS-Math: K-12 Math Tasks

Enrollment key: MATH

NCSM Great Tasks (available in all LCPS Elementary Schools—click link)









Bring in catalogs, sale flyers, and menus. Have the students use calculators to figure out the cost of dinner for their family. Have them choose gifts for their friends and family, given a budget of $75.00.

Have students complete all activities with a partner, taking turns being the recorder and measurer.

Focus on just one system at a time: first measure only in metric units, next, measure only in U.S. Customary units.



Investigations: Measurement Benchmarks Investigation 1: Measures of Length and Distance Investigation 2: Measures of Weight and Liquid Volume Name that Portion Fractions Investigation 2: 1-9 Decimals Investigation 3: 1-8 ESS Lessons: 5.5—Party Time 5.6—Enough Room? 5.8—Rolling Rectangles 5.8—Measurement Mania 5.17—Pick Your Pattern Learn Zillion: Improper and Mixed Numbers Add and Subtract Unlike Denominators Multiplying and Dividing Decimals Adding and Subtracting Decimals with Number Line Other: Math Playground’s Thinking Blocks (problem solving) Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)





http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-8cde.pdf


http://learnzillion.com/lessons/86-write-improper-fractions-as-mixed-numbers

http://learnzillion.com/lessons/121-add-and-subtract-fractions-with-unlike-denominators

http://learnzillion.com/lessons/555-multiply-decimals-to-the-hundredths-by-using-fractions

http://learnzillion.com/lessons/548-add-decimals-using-a-number-line

http://www.mathplayground.com/thinkingblocks.html



Unit: 6 Quarter 3

Classifying & Subdividing Plane Geometric Figures


5.11 The student will measure right, acute, obtuse, and straight angles.

5.12 The student will classify a) angles as right, acute, obtuse, or straight; and b) triangles as right, acute, obtuse, equilateral, scalene, or isosceles.

5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will a) develop definitions of these plane figures; and b) investigate and describe the results of combining and subdividing plane figures.

5.9 The student will identify and describe the diameter, radius, chord, and circumference of a circle.


Learning Targets:

I can use a protractor or angle ruler to measure an angle in degrees and solve for a missing angle using addition or subtraction.

I can sort angles by their measures (acute, right, obtuse, or straight) and classify triangles by their characteristics (acute, right, obtuse, equilateral, scalene, or isosceles.

I can identify plane figures based on their definitions and describe how shapes change when they are combined with other shapes or divided into smaller parts.

I can identify and describe the relationship between the measures of the parts of a circle (radius, diameter, chord, and circumference).


Measuring and classifying angles

Classifying triangles

Properties of plane figures

Combining and subdividing plane figures

Parts of circles

Developing knowledge about how geometric figures relate to each other and beginning to use mathematical reasoning to analyze and justify properties and relationships among figures.

Discovering geometric relationships by constructing, drawing, measuring, comparing, and classifying geometric figures.

Visualizing, drawing, and comparing figures help to develop an understanding of the relationships and to develop spatial sense.

What are the measures (in degrees) of acute, right, obtuse and straight angles?

What tools are used to measure and draw acute, right, obtuse and straight angles?

What processes are used to measure and draw angles?

How are triangles classified by the size of their largest angle?

How are triangles classified by length of side?

What is a plane figure? What are the characteristics of a plane figure?

What are the definitions of plane figures?

What happens when plane figures are subdivided or combined?

What is the chord, diameter, and radius of a circle?

What is the relationship between the radius of a circle and its diameter?

What is the relationship between the radius of a circle and its circumference?



VDOE Vertical Alignment document 3-6 4.10 a) ID/describe representations of points/lines/line segments/rays/angles; b) ID representations of lines illustrating parallelism/perpendicularity 4.12 a) define polygon; b) ID polygons with 10 or fewer sides 4.11 a) investigate congruence of plane figures after transformations; b) recognize images of figures from transformations

VDOE Vocabulary Word Wall Cards point congruent vertex similar plane figures classify line line segment right triangle ray acute triangle polygon obtuse triangle quadrilateral equilateral triangle parallelogram isosceles triangle rectangle scalene triangle rhombus angle square circle trapezoid acute angle obtuse right angle subdivide obtuse angle combine straight angle straight edge diameter radius chord circumference protractor parallel perimeter area straight edge angle ruler










NCSM Great Tasks










Have students work individually or in groups on a project to construct scale models of their homes, while others may choose to compare the angles of triangles in different sized structures. Have all of the students present their projects to the rest of the class.

Use manipulatives including sets of fractals, pattern blocks, pinwheel tiling, platonic solids and more. Using such resources encourage your students to come to the front of the classroom and visually and physically engage with the stimuli on the interactive whiteboard.

Use string and/or geoboards to create the circle and parts of a circle.

Using the hands of a clock and a protractor, have students find the angle of the following times: 1:00, 2:00, 3:00, 4:00, 5:00, and 6:00. Is there a pattern?

When introducing types of triangles, focus on one parameter at a time. Have students identify triangles based on only angles first, then only on sides. Once students are comfortable with each, lead students to categorize triangles by both sides and angles.



(click to link)

Investigations: Picturing Polygons

ESS Lessons: 5.11—Angles Are Everywhere 5.12—Triangle Sort 5.13—All Cracked Up 5.9—Human Circles Learn Zillion: Circumference Perimeter Area and Perimeter Brain Pop: Angles Similar Figures Circles Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)






http://learnzillion.com/lessons/818-find-the-circumference-of-a-circle

http://learnzillion.com/lessons/1165-find-the-perimeter-of-a-polygon-in-real-world-problems

http://learnzillion.com/lessons/344-find-the-area-of-a-rectangle-using-side-lengths

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

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



Unit: 7 Quarter 3 - 4

Data & Statistics


5.15 The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots and line graphs.

5.16 The student will a) describe mean, median, and mode as measures of center b) describe mean as fair share c) find the mean, median, mode, and range of a set of data d) describe the range of a set of data as a measure of variation


Learning Targets:

I can interpret data organized in line graphs and stem-and-leaf plots and answer experimental questions quantitatively.

I can calculate measures of center (mean, median, mode) and range and describe them as measures of center and variation.


Further develop and investigate data collection strategies.

Collecting and organizing data into meaningful representations based on issues related to practical experiences.

Identifying and justifying comparisons in data representations and communicating the interpretation of data.

Recognizing data analysis methods as powerful means for decision making.

Demonstrating mean as a fair share visually with manipulatives.

Using mean, median, mode, and range in the context of other characteristics of the data in order to best describe the results.

How does data collected help determine the type of representation used?

What are the measures of center and what do they measure in the data set?

How does range measure variation in data?

How can you model mean as a “fair share”?

Can you determine the mean of a set a data represented in a stem-and-leaf plot? Median? Mode? Range?


VDOE Vertical Alignment document 3-6 4.14 collect/organize/display/interpret data from a variety of graphs

VDOE Vocabulary Word Wall Cards stem-and-leaf plot measures of center line graph mean as a fair share line plot mode bar graph median variation range data collect organize display interpret representation













NCSM Great Tasks



Have students work individually or in groups of two or three to collect data on topics of their choice (e.g., favorite sandwich choice, favorite fast food restaurant, favorite ice cream flavor, favorite after school activity). Have them first organize the data they collect by using tally tables or charts. Then, have them create appropriate bar graphs to display the organized data. Instruct them to write two or more questions that can be answered by reading the graphs.

Challenge students to find different types of graphs (e.g., bar, line, circle or pie) in magazines, newspapers and various other publications. Have them create a poster or display of the graphs they find and write an explanation of the use of each one under it.

Provide pairs of students with graphs from newspapers, magazines, and textbooks for them to use in discussing the various ways such information is displayed and the advantages of each.

Allow students to draw pictures instead of writing in their journals to summarize this activity.

Use large sized graph paper.



Investigations: Patterns of Change Investigation 2: Motion Stories, Graphs, and Tables Investigation 3: Computer Trips on Two Tracks Data, Kids, Cats, and Ads Investigation 1: Balancing Act Investigation 2: Examining Cats ESS Lessons: 5.15—Mystery Data 5.16—What Does It Mean? Learn Zillion: Mean Range Math Literature Connections (click link) Additional resources (including FLIPCHARTS based on VDOE ESS lessons) may be found on the Elementary Math Resources VISION site: http://loudounvision.net/ Search: Math—Elementary Resources Enrollment key: MATH (all caps)







http://www.doe.virginia.gov/testing/solsearch/sol/math/5/mess_5-16abcd.pdf

http://learnzillion.com/lessons/534-find-the-mean-of-a-data-set

http://learnzillion.com/lessons/535-use-and-find-the-range-of-a-data-set

http://learnzillion.com/lessons/535-use-and-find-the-range-of-a-data-set


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

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

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

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

to maintain a productive math community.

Goals:

Build a classroom community of learners

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

reasoning, connections, and representation).

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

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

Mini Lesson Key Ideas Essential Understandings

Anchor Charts/Supports Resources Teacher Notes

Day 1 Management: Classroom Procedures/ Community Guidelines

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

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

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

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

*Brainstorm the list with the students

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

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

Mathematicians can utilize math tools to help them solve problems.

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

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

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



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

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

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

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

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

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

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

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

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

- Talk bubbles or Talk move sticks

Introduce talk moves

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

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

- Revoicing (also called verify and clarify)

- Repeat - Agree/Disagree and why?

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



Day 5 Collaboration (Game) VA Process Goal: Communication

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

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

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

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

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

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

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

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

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

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



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

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

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

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

Chart paper Calendar / Daily Schedule

Consider connecting this discussion to everyday events in their life.

Day 8 Representing Thinking VA Process Goals: Representation, Communication

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

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

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

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

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

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



Day 9 Recording & Reflecting in Math

VA Process Goal: Communication

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

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

Example of Game Recording Sheet:

Introduce a Recording Sheet as a student tool.

Day 10 Academic Language of Math VA Process Goal: Communication

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

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

Post examples of key vocabulary terms with visual examples.

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

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

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





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

Mathematicians use a variety of strategies to build vocabulary.

Students will utilize a tool to reinforce their math vocabulary.

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

Student math journal VDOE Math Vocabulary Cards Frayer Model

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

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

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

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

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

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



Day 13 Connections VA Process Goals: Connections, Communication

Mathematicians make and recognize connections among mathematical ideas.

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

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

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

Day 14 Justification VA Process Goals: Reasoning, Representation

Mathematicians verify their thinking by showing it multiple ways.

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

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

Justify means: explain, defend,

describe, prove, give reasons, show

you understand, validate…

Using verbal explanation first can help facilitate written justification.



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

Mathematicians choose from a variety of strategies to solve problems.

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

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

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

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

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

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

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

Develop and post a problem solving protocol.

Post the protocol in the classroom for student reference.

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

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



Day 17 Rubric Familiarization VA Process Goals: Reasoning, Connections

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

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

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

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

Mathematicians modify their work as needed.

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

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

Sample Rubric:

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

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



Day 19 Collaboration (Task) VA Process Goal: Communication

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

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

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

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

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

Day 20

Process Goals

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

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

-2009 Mathematics Standards of Learning

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

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

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

Mathematics Standards of Learning Curriculum Framework 2009: Grade 5

VDOE Technical Assistance Document

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

Virginia Mathematics Standards of Learning

Curriculum Framework 2009 Introduction

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

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


5.1

The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth.

UNDERSTANDING THE STANDARD (Background Information for Instructor Use Only)

ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

The structure of the Base-10 number system is

based upon a simple pattern of tens in which each

place is ten times the value of the place to its

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

relationship.

A decimal point separates the whole number

places from the places less than one. Place values

extend infinitely in two directions from a decimal

point. A number containing a decimal point is

called a decimal number or simply a decimal.

To read decimals,

– read the whole number to the left of the

decimal point, if there is one;

– read the decimal point as “and”;

– read the digits to the right of the decimal

point just as you would read a whole

number; and

– say the name of the place value of the digit in

the smallest place.

Decimals may be written in a variety of forms:

– Standard: 23.456

– Written: Twenty-three and four hundred fifty-

six thousandths

– Expanded: (2 10) + (3 1) + (4 0.1) +

(5 0.01) + (6 0.001)

To help students identify the ten-to-one place

value relationship for decimals through

thousandths, use Base-10 manipulatives, such as

place value mats/charts, decimal squares, Base-10

blocks, and money.

All students should

Understand that decimals are rounded in a

way that is similar to the way whole numbers

are rounded.

Understand that decimal numbers can be

rounded to estimate when exact numbers are

not needed for the situation at hand.

The student will use problem solving, mathematical

communication, mathematical reasoning, connections, and

representations to

Round decimal numbers to the nearest whole number,

tenth, or hundredth.


5.1

The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth.



Decimals can be rounded to the nearest whole

number, tenth or hundredth in situations when

exact numbers are not needed.

Strategies for rounding decimal numbers to the

nearest whole number, tenth and hundredth are as

follows:

– Look one place to the right of the digit to

which you wish to round.

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

rounding place as it is, and change the

digits to the right of the rounding place to

zero.

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

the rounding place and change the digits to

the right of the rounding place to zero.

Create a number line that shows the decimal that

is to be rounded.

The position of the decimal will help children

conceptualize the number’s placement relative for

rounding. An example is to round 5.747 to the

nearest hundredth:

5.74 5.747 5.75


5.2

The student will

a) recognize and name fractions in their equivalent decimal form and vice versa; and

b) compare and order fractions and decimals in a given set from least to greatest and greatest to least.



Students should recognize, name, and focus on

finding equivalent decimals of familiar fractions

such as halves, fourths, fifths, eighths, and tenths.

Students should be able to determine equivalent

relationships between decimals and fractions with

denominators up to 12.

Students should have experience with fractions

such as1

8, whose decimal representation is a

terminating decimal (e. g., 1

8= 0.125) and with

fractions such as 2

9, whose decimal

representation does not end but continues to

repeat (e. g., 2

9= 0.222…). The repeating

decimal can be written with ellipses (three dots)

as in 0.222… or denoted with a bar above the

digits that repeat as in 0 .2 .

To help students compare the value of two

decimals through thousandths, use manipulatives,

such as place value mats/charts, 10-by-10 grids,

decimal squares, Base-10 blocks, meter sticks,

number lines, and money.

All students should

Understand the relationship between

fractions and their decimal form and vice

versa.

Understand that fractions and decimals can

be compared and ordered from least to

greatest and greatest to least.



representations to

Represent fractions (halves, fourths, fifths, eighths, tenths,

and twelfths) in their equivalent decimal form and vice

versa.

Recognize and name equivalent relationships between

decimals and fractions with denominators up to 12.

Compare and order from least to greatest and greatest to

least a given set of no more than five numbers written as

decimals, fractions, and mixed numbers with denominators

of 12 or less.


A procedure for comparing two decimals by

examining may include the following:

– Line up the decimal numbers at their decimal

points.

– Beginning at the left, find the first place value

where the digits are different.

– Compare the digits in this place value to

determine which number is greater (or

which is less).

– Use the appropriate symbol > or < or the

words greater than or less than to compare

the numbers in the order in which they are

presented.

– If both numbers are the same, use the symbol

= or words equal to.

Two numbers can be compared by examining

place value and/or using a number line.

Decimals and fractions represent the same

relationships; however, they are presented in two

different formats. Decimal numbers are another

way of writing fractions. Base-10 models (e.g.,

10-by-10 grids, meter sticks, number lines,

decimal squares, money) concretely relate

fractions to decimals and vice versa.


5.3

The student will

a) identify and describe the characteristics of prime and composite numbers; and

b) identify and describe the characteristics of even and odd numbers.



A prime number is a natural number that has

exactly two different factors, one and the number

itself.

A composite number is a natural number that has

more than two different factors.

The number 1 is neither prime nor composite

because it has only one factor, itself.

The prime factorization of a number is a

representation of the number as the product of its

prime factors. For example, the prime

factorization of 18 is 2 3 3.

Prime factorization concepts can be developed by

using factor trees.

Prime or composite numbers can be represented

by rectangular models or rectangular arrays on

grid paper. A prime number can be represented by

only one rectangular array (e.g., 7 can be

represented by a 7 1 and a 1 x 7). A composite

number can always be represented by more than

two rectangular arrays (e.g., 9 can be represented

by a 9 1, a 1 x 9, or a 3 3).

Divisibility rules are useful tools in identifying

prime and composite numbers.

Students should use manipulatives (e.g., Base-10

blocks, cubes, tiles, hundreds board, etc.) to

explore and categorize numbers into groups of

odd or even.

All students should

Understand and use the unique characteristics

of certain sets of numbers, including prime,

composite, even, and odd numbers.



representations to

Identify prime numbers less than or equal to 100.

Identify composite numbers less than or equal to 100.

Explain orally and in writing why a number is prime or

composite.

Identify which numbers are even or odd.

Explain and demonstrate with manipulatives, pictorial

representations, oral language, or written language why a

number is even or odd.


5.3

The student will

a) identify and describe the characteristics of prime and composite numbers; and

b) identify and describe the characteristics of even and odd numbers.



Students should use rules to categorize numbers

into groups of odd or even. Rules can include:

– An odd number does not have 2 as a factor or

is not divisible by 2.

– The sum of two even numbers is even.

– The sum of two odd numbers is even.

– The sum of an even and an odd is odd.

– Even numbers have an even number or zero in

the ones place.

– Odd numbers have an odd number in the ones

place.

– An even number has 2 as a factor or is

divisible by 2.


5.4

The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication,

and division with and without remainders of whole numbers.



An example of an approach to solving problems

is Polya’s four-step plan:

– Understand: Retell the problem; read it twice;

take notes; study the charts or diagrams;

look up words and symbols that are new.

– Plan: Decide what operation(s) to use and

what sequence of steps to use to solve the

problem.

– Solve: Follow the plan and work accurately.

If the first attempt doesn’t work, try

another plan.

– Look back: Does the answer make sense?

Estimation gives a rough idea of an amount.

Strategies such as front-end, rounding, and mental

computation may be used to estimate addition,

subtraction, multiplication, and division of whole

numbers.

Examples of problems to be solved by using

estimation strategies are encountered in shopping

for groceries, buying school supplies, budgeting

allowance, and sharing the cost of a pizza or the

prize money from a contest.

Estimation can be used to check the

reasonableness of the results.

All students should

Understand the meaning of mathematical

operations and how these operations relate to

one another when creating and solving

single-step and multistep word problems.



representations to

Select appropriate methods and tools from among paper

and pencil, estimation, mental computation, and

calculators according to the context and nature of the

computation in order to compute with whole numbers.

Create single-step and multistep problems involving the

operations of addition, subtraction, multiplication, and

division with and without remainders of whole numbers,

using practical situations.

Estimate the sum, difference, product, and quotient of

whole number computations.

Solve single-step and multistep problems involving

addition, subtraction, multiplication, and division with

and without remainders of whole numbers, using paper

and pencil, mental computation, and calculators in which

– sums, differences, and products will not exceed five

digits;

– multipliers will not exceed two digits;

– divisors will not exceed two digits; or

– dividends will not exceed four digits.

Use two or more operational steps to solve a multistep

problem. Operations can be the same or different.


5.5

The student will

a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with

only one nonzero digit); and

b) create and solve single-step and multistep practical problems involving decimals.



Addition and subtraction of decimals may be

investigated using a variety of models (e.g., 10-by-10

grids, number lines, money).

Decimal computation uses similar procedures as

those developed for whole number computation and

applies them to decimal place values, giving careful

attention to the placement of the decimal point in the

solution.

Multiplication of decimals follows the same

procedure as multiplication of whole numbers. The

only difference is that a decimal point must be

correctly placed in the product giving careful

attention to the placement of the decimal point in the

solution.

The product of decimals is dependent upon the two

factors being multiplied.

In cases where an exact product is not required, the

product of decimals can be estimated using strategies

for multiplying whole numbers, such as front-end

and compatible numbers, or rounding. In each case,

the student needs to determine where to place the

decimal point to ensure that the product is

reasonable.

Division is the operation of making equal groups or

shares. When the original amount and the number of

shares are known, divide to find the size of each

share. When the original amount and the size of each

share are known, divide to find the number of shares.

Both situations may be modeled with Base-10

manipulatives.

All students should

Use similar procedures as those developed for

whole number computation and apply them to

decimal place values, giving careful attention to

the placement of the decimal point in the

solution.

Select appropriate methods and tools from

among paper and pencil, estimation, mental

computation, and calculators according to the

context and nature of the computation in order to

compute with decimal numbers.

Understand the various meanings of division and

its effect on whole numbers.

Understand various representations of division,

i.e.,

dividend divisor = quotient

quotient

divisor dividend

dividend

divisor = quotient.


communication, mathematical reasoning,

connections, and representations to

Determine an appropriate method of calculation to

find the sum, difference, product, and quotient of

two numbers expressed as decimals through

thousandths, selecting from among paper and

pencil, estimation, mental computation, and

calculators.

Estimate to find the number that is closest to the

sum, difference, and product of two numbers

expressed as decimals through thousandths.

Find the sum, difference, and product of two

numbers expressed as decimals through

thousandths, using paper and pencil, estimation,

mental computation, and calculators.

Determine the quotient, given a dividend expressed

as a decimal through thousandths and a single-digit

divisor. For example, 5.4 divided by 2 and 2.4

divided by 5.

Use estimation to check the reasonableness of a

sum, difference, product, and quotient.

Create and solve single-step and multistep

problems.

A multistep problem needs to incorporate two or

more operational steps (operations can be the same

or different).


5.5

The student will

a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with

only one nonzero digit); and




The fair-share concept of decimal division can be

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

Division with decimals is performed the same way as

division of whole numbers. The only difference is the

placement of the decimal point in the quotient.

The quotient can be estimated, given a dividend

expressed as a decimal through thousandths (and no

adding of zeros to the dividend during the division

process) and a single-digit divisor.

Estimation can be used to check the reasonableness

of a quotient.

Division is the inverse of multiplication; therefore,

multiplication and division are inverse operations.

Terms used in division are dividend, divisor, and

quotient.

dividend divisor = quotient

quotient

divisor ) dividend

There are a variety of algorithms for division such as

repeated multiplication and subtraction. Experience

with these algorithms may enhance understanding of

the traditional long division algorithm.

A multistep problem needs to incorporate no more

than two operational steps (operations can be the

same or different).


5.6

The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed

numbers and express answers in simplest form.



A fraction can be expressed in simplest form

(simplest equivalent fraction) by dividing the

numerator and denominator by their greatest

common factor.

When the numerator and denominator have no

common factors other than 1, then the fraction is

in simplest form.

Fractions having like denominators means the

same as fractions having common denominators.

Equivalent fractions name the same amount. To

find equivalent fractions, multiply or divide the

numerator and denominator by the same nonzero

number.

Addition and subtraction with fractions and

mixed numbers can be modeled using a variety of

concrete materials and pictorial representations as

well as paper and pencil.

To add, subtract, and compare fractions and

mixed numbers, it often helps to find the least

common denominator. The least common

denominator (LCD) of two or more fractions is

the least common multiple (LCM) of the

denominators.

To add or subtract with fractions having the same

or like denominators, add or subtract the

numerators and write in simplest form.

All students should

Develop and use strategies to estimate and

compute addition and subtraction of

fractions.

Understand the concept of least common

multiple and least common denominator as

they are important when adding and

subtracting fractions.

Understand that a fraction is in simplest form

when its numerator and denominator have no

common factors other than 1. The numerator

can be greater than the denominator.



representations to

Solve single-step and multistep practical problems

involving addition and subtraction with fractions having

like and unlike denominators. Denominators in the

problems should be limited to 12 or less (e.g., 1

5 +

1

4 ) and

answers should be expressed in simplest form.

Solve single-step and multistep practical problems

involving addition and subtraction with mixed numbers

having like and unlike denominators, with and without

regrouping. Denominators in the problems should be

limited to 12 or less, and answers should be expressed in

simplest form.

Use estimation to check the reasonableness of a sum or

difference.


5.6

The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed

numbers and express answers in simplest form.



To add or subtract with fractions that do not have

the same denominator, first find equivalent

fractions with the least common denominator.

Then add or subtract and write the answer in

simplest form.

A mixed number has two parts: a whole number

and a fraction. The value of a mixed number is

the sum of its two parts.

To add or subtract with mixed numbers, students

may use a number line, draw a picture, rewrite

fractions with like denominators, or rewrite mixed

numbers as fractions.


5.7

The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition,

subtraction, multiplication, and division.



An expression, like a phrase, has no equal sign.

Expressions are simplified by using the order of

operations.

The order of operations defines the computation

order to follow in simplifying an expression.

The order of operations is as follows:

– First, complete all operations within grouping

symbols. If there are grouping symbols

within other grouping symbols, do the

innermost operation first.

– Second, evaluate all exponential expressions.

– Third, multiply and/or divide in order from

left to right.

– Fourth, add and/or subtract in order from left

to right.

All students should

Understand that the order of operations

describes the order to use to simplify

expressions containing more than one

operation.



representations to

Simplify expressions by using the order of operations in a

demonstrated step-by-step approach.

Find the value of numerical expressions, using the order of

operations.

Given an expression involving more than one operation,

describe which operation is completed first, which is

second, etc.


5.8

The student will

a) find perimeter, area, and volume in standard units of measure;

b) differentiate among perimeter, area, and volume and identify whether the application of the concept of perimeter, area, or

volume is appropriate for a given situation;

c) identify equivalent measurements within the metric system;

d) estimate and then measure to solve problems, using U.S. Customary and metric units; and

e) choose an appropriate unit of measure for a given situation involving measurement using U.S. Customary and metric units.



Perimeter is the distance around an object. It is a

measure of length. Area is the number of square

units needed to cover a surface. Volume is a

measure of capacity and is measured in cubic

units.

To find the perimeter of any polygon, add the

lengths of the sides.

Students should label the perimeter, area, and

volume with the appropriate unit of linear, square,

or cubic measure.

Area is the number of square units needed to

cover a surface or figure.

Students should investigate, using manipulatives,

to discover the formulas for the area of a square,

rectangle, and right triangle; and volume of a

rectangular solid.

– Area of a rectangle = Length Width

– Area of a square = Side Side

– Area of a right triangle = 1

2 Base Height

– Volume of a rectangular solid = Length x

Width x Height

Length is the distance along a line or figure from

one point to another.

All students should

Understand the concepts of perimeter, area,

and volume.

Understand and use appropriate units of

measure for perimeter, area, and volume.

Understand the difference between using

perimeter, area, and volume in a given

situation.

Understand how to select a measuring device

and unit of measure to solve problems

involving measurement.



representations to

Determine the perimeter of a polygon, with or without

diagrams, when

– the lengths of all sides of a polygon that is not a

rectangle or a square are given;

– the length and width of a rectangle are given; or

– the length of a side of a square is given.

Estimate and determine the perimeter of a polygon, and

area of a square, rectangle, and right triangle following the

parameters listed above, using only whole number

measurements given in metric or U.S. Customary units,

and record the solution with the appropriate unit of

measure (e.g., 24 square inches).

Estimate and determine the area of a square, with or

without diagrams, when the length of a side is given.

Estimate and determine the area of a rectangle, with or

without diagrams, when the length and width are given.

Estimate and determine the area of a right triangle, with or

without diagrams, when the base and the height are given.

Differentiate among the concepts of area, perimeter, and

volume.

Develop a procedure for finding volume using

manipulatives (e.g., cubes).


5.8

The student will









U.S. Customary units for measurement of length

include inches, feet, yards, and miles. Appropriate

measuring devices include rulers, yardsticks, and

tape measures. Metric units for measurement of

length include millimeters, centimeters, meters,

and kilometers. Appropriate measuring devices

include centimeter ruler, meter stick, and tape

measure.

When measuring with U.S. Customary units,

students should be able to measure to the nearest

part of an inch (1

2 ,

1

4 ,

1

8 ), foot, or yard.

Weight and mass are different. Mass is the

amount of matter in an object. Weight is

determined by the pull of gravity on the mass of

an object. The mass of an object remains the same

regardless of its location. The weight that an

object changes is dependent on the gravitational

pull at its location. In everyday life, most people

are actually interested in determining an object’s

mass, although they use the term weight (e.g.,

“How much does it weigh?” versus “What is its

mass?”).

Appropriate measuring devices to measure mass

in U.S. Customary units (ounces, pounds) and

metric units (grams, kilograms) are balances.

Determine volume in standard units.

Describe practical situations where area, perimeter, and

volume are appropriate measures to use, and justify their

choices orally or in writing.

Identify whether the application of the concept of

perimeter, area, or volume is appropriate for a given

situation.

Identify equivalent measurements within the metric system

for the following:

– length: millimeters, centimeters, meters, and

kilometers;

– mass: grams and kilograms;

– liquid volume: milliliters, and liters.

Solve problems involving measurement by selecting an

appropriate measuring device and a U.S. Customary or

metric unit of measure for the following:


5.8

The student will









U.S. Customary units to measure liquid volume

(capacity) include cups, pints, quarts, and gallons.

Metric units to measure liquid volume (capacity)

include milliliters and liters.

Temperature is measured using a thermometer.

The U.S. Customary unit of measure is degrees

Fahrenheit; the metric unit of measure is degrees

Celsius.

Practical experience measuring familiar objects

helps students establish benchmarks and

facilitates students’ ability to use the units of

measure to make estimates.

– length: part of an inch (1

2 ,

1

4 ,

1

8 ), inches, feet, yards,

millimeters, centimeters, meters, and kilometers;

– weight: ounces, pounds, and tons;

– mass: grams and kilograms;

– liquid volume: cups, pints, quarts, gallons, milliliters,

and liters;

– area: square units; and

– temperature: Celsius and Fahrenheit units.

– Water freezes at 0C and 32F.

– Water boils at 100C and 212F.

– Normal body temperature is about 37C and

98.6F.


5.9

The student will identify and describe the diameter, radius, chord, and circumference of a circle.



A circle is a set of points on a flat surface (plane)

with every point equidistant from a given point

called the center.

A chord is a line segment connecting any two

points on a circle. Students will benefit from

understanding that a chord goes from one side of

the circle to the other, but does not need to pass

through the center.

A diameter is a chord that goes through the center

of a circle. The diameter is two times the radius.

A radius is a segment from the center of a circle

to any point on the circle. Two radii end-to-end

form a diameter of a circle.

Circumference is the distance around or perimeter

of a circle. The circumference is about 3 times

larger than the diameter of a circle.

All students should

Understand that a chord is a line segment that

extends between any two unique points of a

circle.

Understand that a diameter is also a special

chord that goes through the center of a circle.

Understand the relationship between the

measures of diameter and radius and the

relationship between the measures of radius

and circumference.

Understand that a radius is a line segment

that extends between the center and the

circumference of the circle.

Understand that the circumference is the

distance around the circle. Perimeter is the

measure of the circumference.



representations to

Identify and describe the diameter, radius, chord, and

circumference of a circle.

Describe the relationship between

– diameter and radius;

– diameter and chord;

– radius and circumference; and

– diameter and circumference.

The length of the diameter of a circle is twice the length of

the radius.


5.10

The student will determine an amount of elapsed time in hours and minutes within a 24-hour period.



Elapsed time is the amount of time that has

passed between two given times.

Elapsed time can be found by counting on from

the beginning time to the finishing time.

– Count the number of whole hours between

the beginning time and the finishing time.

– Count the remaining minutes.

– Add the hours and minutes. For example, to

find the elapsed time between 10:15

a.m. and 1:25 p.m., count on as follows:

from 10:15 a.m. to 1:15 p.m., count 3

hours;

from 1:15 p.m. to 1:25 p.m., count 10

minutes; and then

add 3 hours to 10 minutes to find the total

elapsed time of 3 hours and 10 minutes.

All students should

Understand that elapsed time can be found by

counting on from the beginning time to the

finishing time.



representations to

Determine elapsed time in hours and minutes within a 24-

hour period.


5.11

The student will measure right, acute, obtuse, and straight angles.

UNDERSTANDING THE STANDARD

(Background Information for Instructor Use Only) ESSENTIAL UNDERSTANDINGS ESSENTIAL KNOWLEDGE AND SKILLS

Angles are measured in degrees. There are up to

360 degrees in an angle. A degree is 1

360 of a

complete rotation of a full circle. There are 360

degrees in a circle.

To measure the number of degrees in an angle,

use a protractor or an angle ruler.

A right angle measures exactly 90°.

An acute angle measures less than 90°.

An obtuse angle measures greater than 90° but

less than 180°.

A straight angle measures exactly 180°.

Before measuring an angle, students should first

compare it to a right angle to determine whether

the measure of the angle is less than or greater

than 90°.

Students should understand how to work with a

protractor or angle ruler as well as available

computer software to measure and draw angles

and triangles.

All students should

Understand how to measure acute, right,

obtuse, and straight angles.



representations to

Identify the appropriate tools (e.g., protractor and

straightedge or angle ruler as well as available software)

used to measure and draw angles and triangles.

Measure right, acute, straight, and obtuse angles, using

appropriate tools, and identify their measures in degrees.

Recognize angle measure as additive. When an angle is

decomposed into nonoverlapping parts, the angle measure

of the whole is the sum of the angle measures of the parts.†

Solve addition and subtraction problems to find unknown

angle measures on a diagram in practical and mathematical

problems, (e.g., by using an equation with a symbol for the

unknown angle measure).†

†Revised March

2011


5.12

The student will classify

a) angles as right, acute, obtuse, or straight; and

b) triangles as right, acute, obtuse, equilateral, scalene, or isosceles.



A right angle measures exactly 90.

An acute angle measures greater than 0 but less

than 90.

An obtuse angle measures greater than 90 but

less than 180.

A straight angle forms an angle that measures

exactly 180°.

A right triangle has one right angle.

An obtuse triangle has one obtuse angle.

An acute triangle has three acute angles (or no

angle measuring 90 or greater).

A scalene triangle has no congruent sides.

An isosceles triangle has two congruent sides.

To facilitate the exploration of relationships, ask

students whether a right triangle can have an

obtuse angle. Why or why not? Can an obtuse

triangle have more than one obtuse angle? Why or

why not? What type of angles are the two angles

other than the right angle in a right triangle? What

type of angles are the two angles other than the

obtuse angle in an obtuse triangle?

All students should

Understand that angles can be classified as

right, acute, obtuse, or straight according to

their measures.

Understand that a triangle can be classified as

either right, acute, or obtuse according to the

measure of its largest angle.

Understand that a triangle can be classified as

equilateral, scalene, or isosceles according to

the number of sides with equal length.



representations to

Classify angles as right, acute, straight, or obtuse.

Classify triangles as right, acute, or obtuse.

Classify triangles as equilateral, scalene, or isosceles.


5.13

The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and

b) investigate and describe the results of combining and subdividing plane figures.



A triangle is a polygon with three sides. Triangles

may be classified according to the measure of

their angles, i.e., right, acute, or obtuse. Triangles

may also be classified according to the measure of

their sides, i.e., scalene (no sides congruent),

isosceles (at least two sides congruent) and

equilateral (all sides congruent).

A quadrilateral is a polygon with four sides.

A parallelogram is a quadrilateral in which both

pairs of opposite sides are parallel. Properties of a

parallelogram include the following:

– A diagonal (a segment that connects two

vertices of a polygon but is not a side)

divides the parallelogram into two

congruent triangles.

– The opposite sides of a parallelogram are

congruent.

– The opposite angles of a parallelogram are

congruent.

– The diagonals of a parallelogram bisect each

other. To bisect means to cut a geometric

figure into two congruent halves. A

bisector is a line segment, line, or plane

that divides a geometric figure into two

congruent halves. A sample of a bisected

parallelogram is below.

All students should

Understand that simple plane figures can be

combined to make more complicated figures

and that complicated figures can be

subdivided into simple plane figures.


communication, mathematical reasoning, connections and

representation to

Develop definitions for squares, rectangles, triangles,

parallelograms, rhombi, and trapezoids.

Investigate and describe the results of combining and

subdividing plane figures.


5.13

The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and

b) investigate and describe the results of combining and subdividing plane figures.



A rectangle is a parallelogram with four right

angles. Since a rectangle is a parallelogram, a

rectangle has the same properties as those of a

parallelogram.

A square is a rectangle with four congruent sides.

Since a square is a rectangle, a square has all the

properties of a rectangle and of a parallelogram.

A rhombus is a parallelogram with four congruent

sides. Opposite angles of a rhombus are

congruent. Since a rhombus is a parallelogram,

the rhombus has all the properties of a

parallelogram.

A trapezoid is a quadrilateral with exactly one

pair of parallel sides. The parallel sides are called

bases, and the nonparallel sides are called legs. If

the legs have the same length, then the trapezoid

is an isosceles trapezoid.

Two or more figures can be combined to form a

new figure. Students should be able to identify the

figures that have been combined.

The region of a polygon may be subdivided into

two or more regions that represent figures.

Students should understand how to divide the

region of a polygon into familiar figures.


5.14

The student will make predictions and determine the probability of an outcome by constructing a sample space.



Probability is the chance of an event occurring.

The probability of an event occurring is the ratio of

desired outcomes to the total number of possible

outcomes. If all the outcomes of an event are equally

likely to occur, the probability of the event =

number of favorable outcomes

total number of possible outcomes.

The probability of an event occurring is represented by a

ratio between 0 and 1. An event is “impossible” if it has

a probability of 0 (e.g., the probability that the month of

April will have 31 days). An event is “certain” if it has a

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

rise tomorrow morning).

When a probability experiment has very few trials, the

results can be misleading. The more times an experiment

is done, the closer the experimental probability comes to

the theoretical probability (e.g., a coin lands heads up

half of the time).

Students should have opportunities to describe in

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

unlikely, as likely as, equally likely, likely, and certain)

the degree of likelihood of an event occurring. Activities

should include practical examples.

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

things that can happen are called outcomes. For

example, there are two equally likely outcomes when

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

can land tails up.

A sample space represents all possible outcomes of an

experiment. The sample space may be organized in a

list, chart, or tree diagram.

All students should

Understand that the basic concepts of

probability can be applied to make

predictions of outcomes of simple

experiments.

Understand that a sample space represents all

possible outcomes of an experiment.




Construct a sample space, using a tree diagram to

identify all possible outcomes of a single event.

Construct a sample space, using a list or chart to

represent all possible outcomes of a single event.

Predict and determine the probability of an outcome

by constructing a sample space. The sample space

will have a total of 24 or less possible outcomes.


5.14

The student will make predictions and determine the probability of an outcome by constructing a sample space.



Tree diagrams show all possible outcomes in a sample

space. The Fundamental Counting Principle describes

how to find the number of outcomes when there are

multiple choices. For example, how many different

outfit combinations can you make from 2 shirts (red and

blue) and 3 pants (black, white, khaki)? The sample

space displayed in a tree diagram would show that there

are 2 3 = 6 (Fundamental Counting Principle) outfit

combinations: red-black; red-white; red-khaki; blue-

black; blue-white; blue-khaki.

A spinner with eight equal-sized sections is equally

likely to land on any one of the sections, three of which

are red, three green, and two yellow. Have students write

a problem statement involving probability, such as,

“What is the probability that the spinner will land on

green?”


5.15

The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots

and line graphs.



The emphasis in all work with statistics should be

on the analysis and the communication of the

analysis, rather than on a single correct answer.

Data analysis should include opportunities to

describe the data, recognize patterns or trends,

and make predictions.

Statistical investigations should be active, with

students formulating questions about something

in their environment and finding quantitative

ways to answer the questions.

Investigations can be brief class surveys or more

extended projects taking many days.

Through experiences displaying data in a variety

of graphical representations, students learn to

select an appropriate representation.

Line graphs are used to show how two continuous

variables are related. Line graphs may be used to

show how one variable changes over time. If one

variable is not continuous, then a broken line is

used. By looking at a line graph, it can be

determined whether the variable is increasing,

decreasing, or staying the same over time.

– The values along the horizontal axis represent

continuous data on a given variable,

usually some measure of time (e.g., time in

years, months, or days). The data presented

on a line graph is referred to as

“continuous data” because it represents

data collected over a continuous period of

time.

All students should

Understand how to interpret collected and

organized data.

Understand that stem-and-leaf plots list data

in a meaningful array. It helps in finding

median, modes, minimum and maximum

values, and ranges.

Understand that line graphs show changes

over time.



representations to

Formulate the question that will guide the data collection.

Collect data, using observations (e.g., weather),

measurement (e.g., shoe sizes), surveys (e.g., hours

watching television), or experiments (e.g., plant growth).

Organize the data into a chart, table, stem-and-leaf plots,

and line graphs.

Display data in line graphs and stem-and-leaf plots.

Construct line graphs, labeling the vertical axis with equal

whole number, decimal, or fractional increments and the

horizontal axis with continuous data commonly related to

time (e.g., hours, days, months, years, and age). Line

graphs will have no more than six identified points along a

continuum for continuous data (e.g., the decades: 1950s,

1960s, 1970s, 1980s, 1990s, and 2000s).

Construct a stem-and-leaf plot to organize and display

data, where the stem is listed in ascending order and the

leaves are in ascending order, with or without commas

between leaves.

Title the given graph or identify the title.

Interpret the data in a variety of forms (e.g., orally or in

written form).


– The values along the vertical axis are the

scale and represent the frequency with

which those values occur in the data set.

The values should represent equal

increments of multiples of whole numbers,

fractions, or decimals depending upon the

data being collected. The scale should

extend one increment above the greatest

recorded piece of data.

– Each axis should be labeled and the graph

should have a title.

– A line graph tells whether something has

increased, decreased, or stayed the same

with the passage of time. Statements

representing an analysis and interpretation

of the characteristics of the data in the

graph should be included (e.g., trends of

increase and/or decrease, and least and

greatest). A broken line is used if the data

collected is not continuous data (such as

test scores); a solid line is used if the data

is continuous (such as height of a plant).

Stem-and-leaf plots allow the exact values of data

to be listed in a meaningful array. Data covering a

range of 25 numbers are best displayed in a stem-

and-leaf plot and are utilized to organize

numerical data from least to greatest, using the

digits of the greatest to group data.

– The data is organized from least to greatest.

– Each value should be separated into a stem

and a leaf [e.g., two-digit numbers are

separated into stems (tens) and leaves

(ones)].

– The stems are listed vertically from least to

greatest with a line to their right. The

leaves are listed horizontally, also from

least to greatest, and can be separated by

spaces or commas. Every value is recorded

regardless of the number of repeats.


5.15

The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots

and line graphs.



– A key is often included to explain how to

read the plot.


5.16

The student will

a) describe mean, median, and mode as measures of center;

b) describe mean as fair share;

c) find the mean, median, mode, and range of a set of data; and

d) describe the range of a set of data as a measure of variation.



Statistics is the science of conducting studies to

collect, organize, summarize, analyze, and draw

conclusions from data.

A measure of center is a value at the center or

middle of a data set. Mean, median, and mode

are measures of center.

The mean, median, and mode are three of the

various ways that data can be analyzed.

Mean represents a fair share concept of the data.

Dividing the data constitutes a fair share. This is

done by equally dividing the data points. This

should be demonstrated visually and with

manipulatives. The arithmetic way is to add all of

the data points then divide by the number of data

points to determine the average or mean.

The median is the piece of data that lies in the

middle of the set of data arranged in order.

The mode is the piece of data that occurs most

frequently in the data set. There may be one, more

than one, or no mode in a data set. Students

should order the data from least to greatest so

they can better find the mode.

The range is the spread of a set of data. The range

of a set of data is the difference between the

greatest and least values in the data set. It is

determined by subtracting the least number in the

data set from the greatest number in the data set.

An example is ordering test scores from least to

greatest: 73, 77, 84, 87, 89, 91, 94. The greatest

All students should

Understand that mean, median, and mode are

described as measures of center.

Understand that mean, median, and mode are

three of the various ways that data can be

described or summarized.

Understand that mean as fair share is

described as equally dividing the data set or

the data set has already been divided equally.

Understand how to find the mean, median,

and mode of a set of data as measures of

center.

Understand values in the context of other

characteristics of the data in order to best

describe the results.



representations to

Describe and find the mean of a group of numbers

representing data from a given context as a measure of

center.

Describe and find the median of a group of numbers


center.

Describe and find the mode of a group of numbers


center.

Describe mean as fair share.

Describe and find the range of a group of numbers


variation.

Describe the impact on measures of center when a single

value of a data set is added, removed, or changed.†

†Revised March 2011


5.16

The student will







score in the data set is 94 and the least score is 73,

so the least score is subtracted from the greatest

score or 94 - 73 = 21. The range of these test

scores is 21.

Students need to learn more than how to identify

the mean, median, mode, and range of a set of

data. They need to build an understanding of what

the number tells them about the data, and they

need to see those values in the context of other

characteristics of the data in order to best describe

the results.


5.17

The student will describe the relationship found in a number pattern and express the relationship.



There are an infinite number of patterns.

The simplest types of patterns are repeating

patterns. In such patterns, students need to

identify the basic unit of the pattern and repeat it.

Growing patterns are more difficult for students

to understand than repeating patterns because not

only must they determine what comes next, they

must also begin the process of generalization.

Students need experiences with growing patterns.

Sample numerical patterns are

6, 9, 12, 15, 18, ;

5, 7, 9, 11, 13, ;

1, 2, 4, 7, 11, 16, ;

2, 4, 8, 16, 32, ;

32, 30, 28, 26, 24…; and

1, 5, 25, 125, 625,.

An expression, like a phrase, has no equal sign.

When the pattern data are expressed in a T-

table, an expression can represent that data. An example is:

X Y

6 9

7 10

11 14

15 18

This example defines the relationship as x + 3.

Expressions are simplified by using the order of

operations.

A verbal quantitative expression involving one

operation can be represented by a variable

All students should

Understand that patterns and functions can be

represented in many ways and described

using words, tables, and symbols.

Understand the structure of a pattern and how

it grows or changes using concrete materials

and calculators.

Understand that mathematical relationships

exist in patterns.

Understand that an expression uses symbols

to define a relationship and shows how each

number in the list, after the first number, is

related to the preceding number.

Understand that expressions can be numerical

or variable or a combination of numbers and

variables.



representations to

Describe numerical and geometric patterns formed by

using concrete materials and calculators.

Describe the relationship found in patterns, using words,

tables, and symbols to express the relationship.


5.17

The student will describe the relationship found in a number pattern and express the relationship.



expression that describes what is going on.

Numbers are used when they are known;

variables are used when the numbers are

unknown. For example, “a full box of cookies and

four extra” can be represented by b + 4; “three

full boxes of cookies” by 3b; “a full box of

cookies shared among four” by b

4 .

A mathematical expression contains a variable or

a combination of variables, numbers, and/or

operation symbols and represents a mathematical

relationship. An expression cannot be solved.


5.18

The student will

a) investigate and describe the concept of variable;

b) write an open sentence to represent a given mathematical relationship, using a variable;

c) model one-step linear equations in one variable, using addition and subtraction; and

d) create a problem situation based on a given open sentence, using a single variable.



A variable is a symbol that can stand for an unknown

number or object.

A variable expression is like a phrase: as a phrase

does not have a verb, so an expression does not have

an equals sign (=).

A verbal expression involving one operation can be

represented by a variable expression that describes

what is going on. Numbers are used when they are

known; variables are used when the numbers are

unknown. For example, “a full box of cookies and

four extra” can be represented by b + 4; “three full

boxes of cookies” by 3b; “a full box of cookies

shared among four” by b

4 .

An open sentence contains a variable and an equals

sign (=). For example, the sentence, “A full box of

cookies and four extra equal 24 cookies.” can be

written as b + 4 = 24, where b stands for the number

of cookies in one full box. “Three full boxes of

cookies equal 60 cookies.” can be written as 3b = 60.

Another example of an open sentence is b + 3 = 23

and represents the answer to the word problem,

“How many cookies are in a box if the box plus three

more equals 23 cookies, where b stands for the

number of cookies in the box?

All students should

Understand that a variable is a symbol that can

stand for an unknown number or object.

Understand that a variable expression is a

variable or combination of variables, numbers,

and symbols that represents a mathematical

relationship.

Understand that verbal expressions can be

translated to variable expressions.

Understand that an open sentence has a variable

and an equal sign (=).

Understand that problem situations can be

expressed as open sentences.




Describe the concept of a variable (presented as

boxes, letters, or other symbols) as a representation

of an unknown quantity.

Write an open sentence with addition, subtraction,

multiplication, or division, using a variable to

represent a missing number.

Model one-step linear equations using a variety of

concrete materials such as colored chips on an

equation mat or weights on a balance scale.

Create and write a word problem to match a given

open sentence with a single variable and one

operation.


5.18

The student will

a) investigate and describe the concept of variable;

b) write an open sentence to represent a given mathematical relationship, using a variable;

c) model one-step linear equations in one variable, using addition and subtraction; and

d) create a problem situation based on a given open sentence, using a single variable.



At this level, discuss how the symbol used to

represent multiplication can often be confused with

the variable x. Students can minimize this confusion

by using parentheses [e.g., 4(x) = 20 or 4x = 20] or a

small dot raised off the line to represent

multiplication [4 • x = 20].

By using story problems and numerical sentences,

students begin to explore forming equations and

representing quantities using variables.

An open sentence containing a variable is neither true

nor false until the variable is replaced with a number.


5.19

The student will investigate and recognize the distributive property of multiplication over addition.



The distributive property states that multiplying a

sum by a number gives the same result as

multiplying each addend by the number and then

adding the products (e.g.,

3(4 + 5) = 3 x 4 + 3 x 5,

5 x (3 + 7) = (5 x 3) + (5 x 7); or

(2 x 3) + (2 x 5) = 2 x (3 + 5).

The distributive property can be used to simplify

expressions (e.g., 9 x 23 = 9(20+3) =180+ 27 = 207;

or 5 x 19 = 5(10 + 9) = 50 + 45 = 95).

All students should

Understand that the distributive property

states that multiplying a sum by a number

gives the same result as multiplying each

addend by the number and then adding the

products.

Understand that using the distributive

property with whole numbers helps with

understanding mathematical relationships.

Understand when and why the distributive

property is used.



representations to

Investigate and recognize the distributive property of

whole numbers, limited to multiplication over addition

using diagrams and manipulatives.

Investigate and recognize an equation that represents the

distributive property, when given several whole number

equations, limited to multiplication over addition.

Loudoun County Public Schools Mathematics Office – Department of Curriculum and Instruction Grade 5

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


LP 5.1 SOL 5.1: The student, given a decimal through thousandths, will round to the nearest whole number, tenth, or hundredth. Learning Target: I can round decimal numbers expressed through thousandths to the nearest whole number, tenth, or hundredth, and represent my thinking using symbols, pictures, numbers, and words.

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

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

Advanced Proficient

I can compare and contrast the accuracy of rounding compared to other forms of estimations (compatible number, front-end estimation, etc.) and describe an example from real-life in which rounding would be appropriate.

Proficient

I can round decimal numbers expressed through thousandths to the nearest whole number, tenth, or hundredth, and represent my thinking using symbols, pictures, numbers, and words.

Intermediate

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

Beginner

I can round whole numbers to the nearest ten, hundred, thousand, ten thousand, and hundred thousand and recognize a model for rounding.


LP 5.2 SOL 5.2: The student will

a) recognize and name fractions in their equivalent decimal form and vice versa; and b) compare and order fractions and decimals in a given set from least to greatest and greatest to least.

Learning Target: I can recognize and name fractions in their equivalent decimal form and compare and order fractions and decimals using models

and multiple strategies.



Advanced Proficient

I can compare and contrast multiple strategies for comparing and ordering fractions and decimals and develop generalizations about my strategies.

Proficient

I can recognize and name fractions in their equivalent decimal form and compare and order fractions and

decimals using models and multiple strategies.

Intermediate

I can recognize and name fractions in their equivalent decimal form using models and compare fractions to fractions, decimals to decimals, and fractions to decimals.

Beginner

I can identify equivalent fractions and equivalent decimals and order a set of fractions and/or order a set of decimals.



a) identify and describe the characteristics of prime and composite numbers; and b) identify and describe the characteristics of even and odd numbers.

Learning Target: I can demonstrate examples of prime, composite, even, and odd numbers using models, numbers, and words.



Advanced Proficient

I can create examples and non-examples of prime, composite, even, and odd numbers and compare and contrast the rules for each category of numbers.

Proficient

I can demonstrate examples of prime, composite, even, and odd numbers using models, numbers, and words.

Intermediate

I can recognize and sort examples of prime, composite, odd, and even numbers.

Beginner

I can understand that numbers can be categorized into different groups based on rules.


LP 5.4 SOL 5.4: The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and

division with and without remainders of whole numbers. Learning Target: I can create, estimate, and solve addition, subtraction, multiplication, and division problems that have two or more steps involved in order to find the answer.



Advanced Proficient

I can create multi-step problems involving more than one operation and compare and contrast strategies used to solve problems.

Proficient

I can create, estimate, and solve addition, subtraction, multiplication, and division problems that have two or

more steps involved in order to find the answer.

Intermediate

I can estimate and solve addition, subtraction, multiplication, and division problems that can be solved in one step using one strategy.

Beginner

I can understand that different computation strategies will help me to estimate and solve problems.



a) find the sum, difference, product, and quotient of two numbers expressed as decimals through thousandths (divisors with only one nonzero digit); and

b) create and solve single-step and multistep practical problems involving decimals. Learning Target: I can investigate, create, and solve single and multi-step problems involving decimal operations (addition, subtraction,

multiplication, and division; decimals through thousandths and divisors with only one nonzero digit).



Advanced Proficient

I can compare and contrast strategies for solving multi-step problems as well as identify similarities and differences between whole number operations and decimal operations.

Proficient

I can investigate, create, and solve single and multi-step problems involving decimal operations (addition,

subtraction, multiplication, and division; decimals through thousandths and divisors with only one nonzero digit).

Intermediate

I can investigate and estimate problems involving decimal operations using decimal models (number lines, 10x10 grids, etc.).

Beginner

I can solve single and multi-step problems involving whole number operations.


LP 5.6 SOL 5.6: The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form. Learning Target: I can develop strategies and use them to compute the sum or difference of fractions and mixed numbers in practical single and

multi-step problems.



Advanced Proficient

I can create single and multi-step problems involving the sum and difference of fractions and compare and contrast my solution strategy with a classmate’s strategy.

Proficient

I can develop strategies and use them to compute the sum or difference of fractions and mixed numbers in

practical single and multi-step problems.

Intermediate

I can use a strategy to compute the sum or difference of fractions and mixed numbers.

Beginner

I can use models and strategies to identify equivalent fractions.


LP 5.7 SOL 5.7: The student will evaluate whole number numerical expressions, using the order of operations limited to parentheses, addition,

subtraction, multiplication, and division. Learning Target: I can simplify expressions with more than two operations using the order of operations and explain each step.



Advanced Proficient

I can create expressions with more than two operations and provide a proof using models and numbers.

Proficient

I can simplify expressions with more than two operations using the order of operations and explain each step.

Intermediate

I can simplify expressions with one or two inverse operations (limited to only addition/subtraction or multiplication/division).

Beginner

I can understand that expressions do not contain an equal sign and must be solved in a particular order.



a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume, and identify whether the application of the concept of perimeter, area, or volume is appropriate

for a given situation; c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using US Customary and metric units; and e) choose an appropriate unit of measure for a given situation involving measurement using US Customary and metric units.

Learning Target: The student will, given a problem situation, decide if the problem requires perimeter, area, and/or volume and estimate and then measure, using appropriate units, to solve the problem.



Advanced Proficient

I can make connections between the metric measures and the base 10 system of numeration.

Proficient

I can, given a problem situation, decide if the problem requires perimeter, area, and/or volume and estimate and then measure, using appropriate units and tools, to solve the problem.

Intermediate I will investigate volume of solids and areas of polygons, using manipulatives to develop formulas for area of each, and find perimeter as well.


Beginning I can identify equivalent measurements between units in the metric system; and estimate and then use US Customary and metric units to measure length, liquid volume, and mass, area and perimeter.

LP 5.9 SOL 5.9: The student will identify and describe the diameter, radius, chord, and circumference of a circle. Learning Target: I can identify and describe the relationship between the measures of the parts of a circle (radius, diameter, chord, and circumference).



Advanced Proficient

I can create a model of a circle when given clues about a circle without using formulas (for example: Draw a circle whose circumference is 18 centimeters and label each part of a circle with its measurement).

Proficient

I can identify and describe the relationship between the measures of the parts of a circle (radius, diameter, chord, and

circumference).

Intermediate

I can use strategies to measure parts of a circle in order to compare them to other parts.


Beginner

I can identify the parts of a circle when given a drawing or model.

LP 5.10 SOL 5.10: The student will determine an amount of elapsed time in hours and minutes within a 24-hour period. Learning Target: I can determine the elapsed time between two events within a 24-hour period.



Advanced Proficient

I can solve practical problems that use elapsed time, expressed in a variety of structures (ie: We arrived in New York City at 2:45 p.m. and the car ride lasted 5 hours and 47 minutes. What time did the car ride begin?).

Proficient I can determine the elapsed time between two events within a 24-hour period.

Intermediate I can “count on” from the beginning time to the finish time to find the elapsed time.


Beginning I can determine elapsed time in hours and minutes within a 12-hour period.

LP 5.11 SOL 5.11: The student will measure right, acute, obtuse, and straight angles. Learning Target: I can use a protractor or angle ruler to measure an angle in degrees and solve for a missing angle using addition or subtraction.



Advanced Proficient

I can create angles that fit given guidelines (ie: draw an angle that is 75 degrees) and find angles to measure in real life.

Proficient

I can use a protractor or angle ruler to measure an angle in degrees and solve for a missing angle using addition or

subtraction.

Intermediate

I can compare an angle to a right angle to estimate its measure and identify the angle as right, acute, obtuse, or straight.


Beginner

I can recognize that a protractor or angle ruler are tools to measure angels and that the unit for the measure is degrees.

LP 5.12 SOL 5.12: The student will classify

a) angles as right, acute, obtuse, or straight; and b) triangles as right, acute, obtuse, equilateral, scalene, or isosceles.

Learning Target: I can sort angles by their measures (acute, right, obtuse, or straight) and classify triangles by their characteristics (acute,

right, obtuse, equilateral, scalene, or isosceles.



Advanced Proficient

I can create angles and triangles that have certain characteristics (ie: draw an acute, equilateral triangle) and find examples of specific triangles in real life.

Proficient

I can sort angles by their measures (acute, right, obtuse, or straight) and classify triangles by their characteristics

(acute, right, obtuse, equilateral, scalene, or isosceles).


Intermediate

I can measure lengths of sides and measures of angles.

Beginner

I can sort angles and triangles by the way that they look.

LP 5.13 SOL 5.13: The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and b) investigate and describe the results of combining and subdividing plane figures.

Learning Target: I can identify plane figures based on their definitions and describe how shapes change when they are combined with other shapes or divided into smaller parts.



Advanced Proficient

I can compare and contrast shapes based on their characteristics, create new shapes given certain parameters (ie: create a parallelogram using rhombuses), and justify my work.

Proficient

I can identify plane figures based on their definitions and describe how shapes change when they are combined

with other shapes or divided into smaller parts.


Intermediate

I can match plane figures to their description. I can put shapes together to make new shapes.

Beginner

I can sort plane figures based on how they look.

LP 5.14 SOL 5.14: The student will make predictions and determine the probability of an outcome by constructing a sample space. Learning Target: I can make predictions and determine the probability of an outcome by using tools (spinners, number cubes, etc.) and models

(sample space, number line, tree diagram, chart, etc.).



Advanced Proficient

I can compare and contrast different tools and models to represent the probability of a simple event and create events that would fit positions on a number line from 0 to 1.

Proficient

I can make predictions and determine the probability of an outcome by using tools (spinners, number cubes, etc.) and models

(sample space, number line, tree diagram, chart, etc.).


Intermediate

I can conduct simple experiments, identify how many outcomes are possible, and organize my results.

Beginner

I can identify the probability of an event as impossible, less likely, equally likely, more likely, or certain and label a number line in equal parts to represent the probability (0=impossible, 1=certain).

LP 5.15 SOL 5.15: The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-leaf plots and line graphs. Learning Target: The student will interpret data organized in line graphs and stem-and-leaf plots and answer experimental questions quantitatively.



Advanced Proficient

I can justify a data display strategy.


Proficient

I can interpret data organized in line graphs and stem-and-leaf plots and answer experimental questions quantitatively.

Intermediate I can organize my data into tables, charts, line graphs, and stem-and-leaf plots.

Beginning Given a problem situation, I can formulate a question that will guide my data collection.


a) describe mean, median, and mode as measures of center; b) describe mean as fair share; c) find the mean, median, mode, and range of a set of data; and d) describe the range of a set of data as a measure of variation.

Learning Target: I can calculate measures of center and range and describe them as measures of center and variation.




Advanced Proficient

I can use the measures of center and variation to understand other characteristics of my data set.

Proficient I can calculate measures of center and range and describe them as measures of center and variation.

Intermediate I can explore the mean as a description of “equally dividing” and range as variation.

Beginning I can understand that mean, median, and mode are measures of center and describe the center or middle of a data set.

LP 5.17 SOL 5.17: The student will describe the relationship found in a number pattern and express the relationship. Learning Target: I can describe the mathematical relationships found in patterns using symbols.




Advanced Proficient

I can justify my representation of a mathematical relationship in symbols with manipulatives and words in an organized way.

Proficient I can describe the mathematical relationships found in patterns using words, numbers, and symbols.

Intermediate I can investigate the structure of patterns and how they grow or change, using concrete materials and calculators.

Beginning I can understand that patterns and functions can be represented with words, numbers, and symbols.


a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical relationship, using a variable; c) model one-step linear equations in one variable, using addition and subtraction; and d) create a problem situation based on a given open sentence, using a single variable.

Learning Target: I can describe and write an open sentence (including a variable) to represent a mathematical relationship. I can then model solving an open sentence (limited to addition or subtraction) and create a problem situation based on a given open sentence.




Advanced Proficient

I can compare and contrast a variety of models for solving open sentences and explain why a variable could have many solutions in an expression but one solution in an equation (at the 5th grade level).

Proficient

I can describe and write an open sentence (including a variable) to represent a mathematical relationship. I can then model solving an open sentence (limited to addition or subtraction) and create a problem situation based on a

given open sentence.

Intermediate

I can write an open sentence (including a variable) to represent a mathematical relationship. I can model solving an open sentence (limited to addition or subtraction).

Beginner

I can understand that a variable is a symbol that stands for an unknown number or object.


LP 5.19 SOL 5.19: The student will investigate and recognize the distributive property of multiplication over addition. Learning Target: I can recognize the distributive property of multiplication over addition, identify examples of the property, and model the property using pictures, numbers, and words.



Advanced Proficient

I can create equations that demonstrate the properties (identity, commutative, associative, and distributive) and compare and contrast the properties.

Proficient

I can recognize the distributive property of multiplication over addition, identify examples of the property, and model

the property using pictures, numbers, and words.

Intermediate

I can match models and equations with the property that they demonstrate (identity, commutative, associative, and/or distributive).

Beginner

I understand that each side of an equation represents an equivalent value and that properties are true regardless of the numbers.

Grade 5 Math Intervention Ideas

Unit 2 – Whole Number Operations & Applications

Hands-On Standards Book Grades 3-4 Every Day Counts Partner Games

Number and Operations Lesson 13 Measurement Lessons 4-6

Game #1: Prime or Not? Game #2: Multiple Rally Game # 3: Target Products Game #10: Target Quotients Game #14: Factor Search Game #15: Divisibility Search

Hands-On Standards Book Grades 5-6

Number and Operations Lessons 9, 15 Algebra Lessons 5-8 Measurement Lesson 2

Unit 3 – Patterns & Properties


Algebra Lessons 2, 9


Algebra Lessons 3, 4, 9

Unit 4 – Comparing & Applying Rational Number Concepts


Number and Operations Lessons 15, 17-18, 21-23 Data Analysis and Probability Lessons 6-8

Game #1: Make One With Decimals Game #4: Get Them In Order Decimals Game #5: Make One With Fractions Game #6: Fraction/Decimal Concentration Game #9: From Here to There Decimals Game #13: Fraction/Decimal Match Up Game #16: Get Them In Order Fractions Game #12: Go For Zero With Decimals Game #17: Decimal Number Maker Game #18: From Here to There Fractions Game #19: Target Fractions


Number and Operations Lessons 1, 4-6

Unit 5 – Rational Number Operations & Measurement Applications


Number and Operations Lessons 20, 24 Measurement Lessons 3, 10-11

Game #12: Go For Zero With Decimals Game #20: Ready, Set, Fractions


Number and Operations Lessons 11-13, 17 Measurement Lessons 1, 4, 6

Unit 6 – Classifying & Subdividing Plane Geometric Figures


Geometry Lessons 3, 8


Geometry Lessons 1-4

Unit 7 – Data & Statistics


Data Analysis and Probability Lessons 1, 5


Data Analysis and Probability Lessons 1-3

Resources available in all LCPS Elementary Schools

Hands-On Standards books Every Day Counts Partner Games

NCSM Great Tasks K-5 (available in all LCPS Elementary Schools)

VA SOL Alignment

Kindergarten Math

Domino Addition and Subtraction

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; b) write the numeral to tell how many are in the set; and c) select the corresponding numeral from a given set of numerals.

Activity

SOL K.1 The student, given two sets, each containing 10 or fewer concrete objects, will identify and describe one set as having more, fewer, or the same number of members as the other set, using the concept of one-to-one correspondence.

Counting Sheep

Launch

SOL K.2 The student, given a set containing 15 or fewer concrete objects, will a) tell how many are in the set by counting the number of objects orally; d) write the numeral to tell how many are in the set; and e) select the corresponding numeral from a given set of numerals.

Activity SOL K.3 The student, given an ordered set of ten objects and/or

pictures, will indicate the ordinal position of each object, first through tenth, and the ordered position of each object.

How Big is Your Foot?

Launch & Activity

SOL K.10 The student will compare two objects or events, using direct comparisons or nonstandard units of measure, according to one or more of the following attributes: length (shorter, longer), height (taller, shorter), weight (heavier, lighter), temperature (hotter, colder). Examples of nonstandard units include foot length, hand span, new pencil, paper clip, and block.

1st Grade Math

Bunny Hip Hop

Launch

SOL 1.1 The student will a) count from 0 to 100 and write the corresponding numerals;

and b) group a collection of up to 100 objects into tens and ones and

write the corresponding numeral to develop an understanding of place value.

Activity

SOL 1.2 The student will count forward by ones, twos, fives, and tens to 100 and backward by ones from 30.

When does it Happen?

Launch & Activity

SOL 1.8 The student will tell time to the half-hour, using analog and digital clocks.

Ten is our Friend!

Launch

SOL 1.5 The student will recall basic addition facts with sums to 18 or less and the corresponding subtraction facts.

Activity SOL 1.6 The student will create and solve one-step story and picture

problems using basic addition facts with sums to 18 or less and the corresponding subtraction facts.

2nd Grade Math

Creative Cards

Launch & Activity

SOL 2.16 The student will identify, describe, compare, and contrast plane and solid geometric figures (circle/sphere, square/cube, and rectangle/rectangular prism).

Piggy Banks

Launch & Activity

SOL 2.10 The student will a) count and compare a collection of pennies, nickels, dimes, and

quarters whose total value is $2.00 or less; and b) correctly use the cent symbol (¢), dollar symbol ($), and

decimal point (.).

Show What You Know!

Launch

SOL 2.2 The student will a) identify the ordinal positions first through twentieth, using an

ordered set of objects; and b) write the ordinal numbers.

Activity

SOL 2.8 The student will create and solve one- and two-step addition and subtraction problems, using data from simple tables, picture graphs, and bar graphs.

SOL 2.9 The student will recognize and describe the related facts that represent and describe the inverse relationship between addition and subtraction.

Pies for Sale

Launch SOL 2.19 The student will analyze data displayed in picture graphs,

pictographs, and bar graphs.

Activity

SOL 2.17 The student will use data from experiments to construct picture graphs, pictographs, and bar graphs.

SOL 2.19 The student will analyze data displayed in picture graphs, pictographs, and bar graphs.

3rd Grade Math

Playful Puppies

Launch

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

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

surface in order to determine area.

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

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

for addition and multiplication.

Activity

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

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

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

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

surface in order to determine area.

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

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

for addition and multiplication.

Correcting the Calculator

Launch & Activity

SOL 3.1 The student will a) read and write six-digit numerals and identify the place value

and value of each digit; b) round whole numbers, 9,999 or less, to the nearest ten,

hundred, and thousand; and c) compare two whole numbers between 0 and 9,999, using

symbols (>, <, or =) and words (greater than, less than, or equal to).

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

Fraction Reactions

Launch & Activity

SOL 3.3 The student will a) name and write fractions (including mixed numbers)

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

fractions’ names; and c) compare fractions having like and unlike denominators, using

words and symbols (>, <, or =).

4th Grade Math

Bugs, Giraffes, Elephants, and More

Launch

SOL 4.2 The student will a) compare and order fractions and mixed numbers; b) represent equivalent fractions; and c) identify the division statement that represents a fraction.

SOL 4.7 The student will a) estimate and measure length, and describe the result in

both metric and U.S. Customary units; and b) identify equivalent measurements between units within

the U.S. Customary system (inches and feet; feet and yards; inches and yards; yards and miles) and between units within the metric system (millimeters and centimeters; centimeters and meters; and millimeters and meters).

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Activity

SOL 4.14 The student will collect, organize, display, and interpret data from a variety of graphs.

Does it Make Sense?

Launch

SOL 4.3 The student will a) read, write, represent, and identify decimals expressed

through thousandths; b) round decimals to the nearest whole number, tenth, and

hundredth; c) compare and order decimals; and

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

Activity

SOL 4.4 The student will a) estimate sums, differences, products, and quotients of whole

numbers; b) add, subtract, and multiply whole numbers; c) divide whole numbers, finding quotients with and without

remainders; and d) solve single-step and multistep addition, subtraction, and

multiplication problems with whole numbers.

The Bigger Half

Launch & Activity


Harry’s Hike

Launch


Activity

SOL 4.5 The student will a) determine common multiples and factors, including least

common multiple and greatest common factor; b) add and subtract fractions having like and unlike

denominators that are limited to 2, 3, 4, 5, 6, 8, 10, and 12, and simplify the resulting fractions, using common multiples and factors;

c) add and subtract with decimals; and d) solve single-step and multistep practical problems involving

addition and subtraction with fractions and with decimals.

5th Grade Math

Packed Parking

Launch

SOL 5.4 The student will create and solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without remainders of whole numbers.

Activity

SOL 5.5 The student will a) find the sum, difference, product, and quotient of two numbers

expressed as decimals through thousandths (divisors with only one nonzero digit); and


SOL 5.6 The student will solve single-step and multistep practical problems involving addition and subtraction with fractions and mixed numbers and express answers in simplest form.

Finding Fractions

Launch

SOL 5.2 The student will a) recognize and name fractions in their equivalent decimal form

and vice versa; and b) compare and order fractions and decimals in a given set from

least to greatest and greatest to least.

Activity

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Varying Volumes

Launch & Activity

SOL 5.8 The student will a) find perimeter, area, and volume in standard units of measure; b) differentiate among perimeter, area, and volume and identify

whether the application of the concept of perimeter, area, or volume is appropriate for a given situation;

c) identify equivalent measurements within the metric system; d) estimate and then measure to solve problems, using U.S.

Customary and metric units; and e) choose an appropriate unit of measure for a given situation

involving measurement using U.S. Customary and metric units.

SOL 5.13 The student, using plane figures (square, rectangle, triangle, parallelogram, rhombus, and trapezoid), will

a) develop definitions of these plane figures; and b) investigate and describe the results of combining and

subdividing plane figures.

Location, Location, Location

Launch

SOL 5.17 The student will describe the relationship found in a number pattern and express the relationship.

Activity

SOL 5.18 The student will a) investigate and describe the concept of variable; b) write an open sentence to represent a given mathematical

relationship, using a variable; c) model one-step linear equations in one variable, using addition

and subtraction; and d) create a problem situation based on a given open sentence,

using a single variable.

SOL 5.19 The student will investigate and recognize the distributive property of multiplication over addition.

Mathematics Literature Connections Organized by Curriculum Units

Grade K Math Literature Connections

Unit 2: Counting

One, Two, Skip a Few: First Number Rhymes by Roberta Arenson

98,99,100! Ready or Not, Here I come! by Marilyn Bums and Teddy Slater

Unit 3: Comparing Sets

20 Hungry Piggies: A Number Book by Trudy Harris

Ten Little Rubber Ducks by Eric Carle

Ten Little Caterpillars by Bill Martin Jr

Henry the Fourth by Stuart J. Murphy

One Monday Morning by Uri Shulevitz

The Napping House by Audrey Wood

Tally O’Malley by Stewart J. Murphy

So you want to be President? by Judith St. George

The Great Graph Contest by Loreen Leedy

Unit 4: Geometry & Sorting

Dave’s Down-to-Earth Rock Shop by Stuart J. Murphy

Unit 5: Shapes in Space

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 6: Geometry & Fractions

Give Me Half by Stuart J. Murphy

Full House by Dayle Ann Dodds

Unit 7: Measuring My World

Measuring Up by J.E. Osborne

Dumpling Soup by Jama Kim Rattigan

How Big is a Foot by Rolf Myller

Big and Little by Steven Jenkins

Time to… by Bruce McMillan

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

Telling Time with Big Mama Cat by D. Harper

Biggest, Strongest, Fastest by Steven Jenkins

Inch by Inch by Leo Lionni

Before and After: A Book of Nature Timescapes by Jan Thornhill

Unit 8: Skip Counting & Money

Arctic Fives Arrive by Elinor J. Pinczes

26 Letters and 99 Cents by Tana Hoban

Unit 9: Combining & Separating

More or Less by Stuart J. Murphy

Animals on Board by Stuart J. Murphy

A Quarter from the Tooth Fairy by Caren Holtzman

Grade 1 Math Literature Connections

Unit 2: Sorting, Ordering, & Patterns

Twizzlers Shapes and Patterns by Jerry Pallotta

Unit 3: Developing a Base Ten System

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

Is It Larger? Is It Smaller? By T. Hoban

One Hundred Hungry Ants by Elinor J. Pinczes

Ten Sly Piranhas: A Counting Story in Reverse by William Wise

How Many, How Many, How Many by Rick Walton

98, 99, 100! Ready or Not, Here I Come! By Marilyn Burns and Teddy Slater

Stay in Line by Teddy Slater


Three Pigs, One Wolf, and Seven Magic Shapes by Grace Maccarone

Flat Stanley by J. Brown

The Shapes We Eat by Simone T. Ribke

Give Me Half! By Stuart J. Murphy

Gator Pie by L. Mathews

Unit 5: Time & Fractions


Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Unit 6: Working With Data

Probably Pistachio by Stuart J. Murphy

So You Want to be President? By Judith St. George


Ready, Set, Hop! By Stuart J. Murphy

Bunches and Bunches of Bunnies by Mathews and Bassett

Unit 7: Combining & Separating

Rooster’s Off to See the World by Eric Carle

Round Trip by A. Jonas

Lemonade For Sale by Stuart J. Murphy


How Do You Measure Weight? by Thomas K. and Heather Adamson

The Greedy Triangle by Marilyn Burns


How Big is a Foot? by Rolf Myller


Biggest, Strongest, Fastest by Steven Jenkins



Best Bug Parade by Stuart J. Murphy

Me and the Measure of Things by J. Sweeney

Unit 9: Applying Place Value

Shoes, Shoes, Shoes by A. Morris

Unit 10: Whole Number Computation

Animals on Board by Stuart J. Murphy

Elevator Magic by Stuart J. Murphy

Ten Black Dots by Donald Crew

Rooster’s Off to See the World by Eric Carle


How High Can a Dinosaur Count? by V. Fisher


The Penny Pot by Stuart J. Murphy


Unit 2: Extending Place Value

The Crayon Counting Book by Pam Munoz

Underwater Counting: Even Numbers by Jerry Pallotta

Unit 3: Computational Fluency

Growing Patterns: Fibonacci Numbers in Nature by S.G. and R.P. Campbell

Mission: Addition by Loreen Leedy

Each Orange Had 8 Slices: A Counting Book by Paul Giganti


Unit 4: Applying Place Value to Computation/Problem Solving

Great Estimations by Bruce Goldstone

How Many Seeds in a Pumpkin? By Margaret McNamara and G. Brian Karas

How Many Feet? How Many Tails? A Book of Math Riddles by Marilyn Burns

Sam and the Lucky Money by K. Chinn

Balancing Act by Ellen Stoll Walsh

Betcha by Stuart J. Murphy

Unit 5: Probability & Data

Frog and Toad are Friends by A. Lobel

Polar Bear Math: Learning About Fractions from Klondike and Snow by Nagda and Bickel

Get Up and Go! By Stuart J. Murphy

Unit 6: Data & Problem Solving

So You Want to be President? By Judith St. George

Unit 7: Time & Temperature

Telling Time: How to Tell Time on Digital and Analog Clock by Jules Older


Why Mosquitoes Buzz in People’s Ears: A West African Tale by V. Aardema

The Grouchy Lady Bug by Eric Carle

Chimp Math: Learning About Time from a Baby Chimpanzee by Nagda and Bickel

What Time Is It? A Book of Math Riddles by Sheila Keenan


Eating Fractions by Bruce McMillan


Full House by Dayle Ann Dodds

The Patchwork Quilt by Valerie Flournoy



How Big is a Foot? By Rolf Myller



Biggest, Strongest, and Fastest by Steven Jenkins



Jelly Beans for Sale by Bruce McMillan

The Penny Pot by Stuart J. Murphy

The Coin Counting Book by Rosanne Lanczak Williams

Once Upon a Dime by Nancy Kelly Allen


Unit 2: Place Value

Many Is How Many? By Illa Pondendorf

A Light in the Attic (“How Many, How Much” and “Overdues”) by Shel Silverstein

Counting on Frank by Rod Clement

How Much Is a Million? by David M. Schwartz

If You Made a Million by David M. Schwartz

Moira’s Birthday by Robert Munsch

Something Good by Robert Munsch

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

Ten Black Dots by Donald Crews

Dealing with Addition Lynette Long

One Duck Stuck by Phyllis Root

One Gorilla by Atsuko Morozumi

A Three Hat Day by Laura Geringer

Unit 4: Money

Alexander, Who Used To Be Rich Last Sunday by Judith Viorst

Penny: The Forgotten Coin by Denise Brenna-Nelson

The Coin Counting Book by Rozanne Lanczak Williams

The Penny Pot by Stuart Murphy

Pigs Will Be Pigs: Fun With Math and Money by Amy Axelrod

Unit 5: Computation With Whole Numbers (multiplication/division)

Amanda Bean’s Amazing Dream by Cindy Neuschwander

A Remainder of One (*extension) by Elinor J. Pinczes

One Hundred Angry Ants by Elinor J. Pinczes

2 x 2 = Boo by Loreen Leedy

7 x 9 Trouble by Claudia Mills

Too Many Kangaroo Things to Do by Stuart Murphy

Divide and Ride by Stuart Murphy

Bananas Jacqueline Farmer

Centipede’s 100 Shoes by Tony Ross

Ten Times Better by Richard Michelson

Unit 6: Patterns & Data

Emma’s Christmas by Irene Trivias

The Doorbell Rang by Pat Hutchins

One Hundred Angry Ants by Elinor Pinczes

She Came Bringing Me That Little Baby Girl by Eloise Greenfield

Knots on a Counting Rope by Bill Martin Jr.

Berries, Nuts, and Seeds by Diane L. Burns

Lemonade for Sale by Stuart Murphy

Tiger Math: Learning to Graph from a Baby Tiger by Ann Whitehead Nagda

Grapes of Math by Greg Tang

The Quilting Bee by Gail Gibbons

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

Unit 7: Geometry

The Important Book by Margaret Wise Brown

Three Pigs, One Wolf, and Severn Magic Shapes by Grace Maccarone

Pablo’s Tree Pat Mora

If You Were a Polygon Marcie Aboff

It Looked Like Spilt Milk by Charles G. Shaw

Mummy Math by Cindy Neuschwander

Shape Up by David Adler

A Cloak for the Dreamer by Aileen Friedman

Unit 8: Fractions, Probability, & Measurement (length) / Unit 9: Computation With Fractions

Eating Fractions by Bruce McMillan

Seven Little Hippos by Mike Thaler

Shoes, Shoes, Shoes by Ann Morris

Biggest, Strongest, Fastest Steve Jenkins

The Wolf’s Chicken Stew Keiko Kasza

A Very Improbably Story: A Math Adventure by Edward Einhorn

The Thirteen Days of Halloween Carool Greene

The Doorbell Rang Pat Hutchins

Whole-y Cow, Fractions are Fun! by Taryn Souders

Apple Fractions by Jerry Pallotta

The Hershey’s Milk Chocolate Bar Fractions BookU by Jerry Pallotta

Fraction Action by Loreen Leedy

Unit 10: Elapsed Time and Temperature

Telling Time: How to Tell Time on Digital and Analog Clocks by Jules Older

What Time is it, Mr. Crocodile? By Judy Sierra

Chimp Math by Ann Whitehead Nagda

Unit 11: Measurement

Spaghetti and Meatballs for All by Marilyn Burns

Perimeter, Area, and Volume David A. Adler

Pastry School in Paris Cindy Neuschwander

Measuring Penny (length) by Loreen Leedy

Biggest, Strongest, Fastest by Steve Jenkins

Is a Blue Whale the Biggest Thing There Is? by Robert E. Wells

Polly’s Pen Pal by Stuart L. Murphy


Room for Ripley by Stuart Murphy


Unit 2: Number Sense: Whole Numbers

A Million Fish…More or Less by Patricia C. McKissack

Unit 3: Whole Number Operations & Applications (adding & subtracting)

Math Curse by Jon Scieszka and Lane Smith

The $1.00 Word Riddle Book by Marilyn Burns

Esio Trot by Roald Dahl

From Seashells to Smart Cards: Money and Currency (everyday economics) by Ernestine

Giesecke

Anno’s Magic Seeds by Mitsumasa Anno

Equal Shmequal by Virginia Kroll

Unit 4: Whole Number Operations & Applications (multiplication & division)

The King’s Chessboard by David Birch

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

Math Curse by Jon Scieszka and Lane Smith

Hottest, Coldest, Highest, Deepest by Steve Jenkins

In the Next Three Seconds…Predictions for the Millennium by Comp. Rowland Morgan

Ten Times Better by Richard Michelson

Two Ways to Count to Ten: A Liberian Folktale by Ruby Dee

A Remainder of One by Elinor J. Pinczes

Counting on Frank by Rod Clement

Unit 5: Data & Statistics


Unit 6: Number Sense: Rational Numbers

The Man Who Counted: A Collection of Mathematical Adventures by Malba Tahan

One Riddle, One Answer by Lauren Thompson

Icebergs and Glaciers by Seymour Simon

Tiger Math: Learning to Graph from a Baby Tiger by Ann W. Nagda and Cindy Bickel

Unit 7: Rational Number Operations

Jump, Kangaroo Jump (Math Start) by Stuart Murphy and Kevin O’Malley

Pizza Counting by Christina Dobson

Piece=Part=Portion by Gifford and Thaler

Fractions=Trouble! By Claudia Mills

Unit 8: Probability & Data Using Rational Numbers

Jumanji by Chris Van Allsburg

A Very Improbable Story by Edward Einhorn and Adam Gustavson

Pigs at Odds by Amy Axelrod and Sharon Nally

Unit 9: Patterns & Measurement

G is for Googol: A Math Alphabet Book by David M. Schwartz

How Much, How Many, How Far, How Heavy, How Long, How Tall Is 1000? by Helen

Nolan

Icebergs and Glaciers by Seymour Simon

If You Hopped Like a Frog by David M. Schwartz

Is a Blue Whale the Biggest Thing There Is? By Robert E. Wells

Biggest, Strongest, Fastest by Steve Jenkins

Unit 10: Plane Geometry & Transformations

Marvelous Math by Lee Bennett Hopkins

The Warlord’s Puzzle by Virginia Walton Pilegard

Shape Up! Fun with Triangles and Other Polygons by David Adler and Nancy Tobin

Spaghetti and Meatballs for All! by Marilyn Burns and Debbie Tilley

Chickens on the Move (Math Matters!) by Pamela Pollack


Unit 2

A Remainder of One by Elinor Pinczes

My Even Day by Doris Fisher

The Grapes of Math by Greg Tang

Math Appeal by Greg Tang

Among the Odds and Evens by Prescilla Turner


Unit 3

Germs Make Me Sick by Melvin Berger

Bats on Parade by Kathi Appelt

Unit 4

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Fraction Fun by David Adler

Unit 5

Measuring Penny by Loreen Leedy

Alexander Who Used to Be Rich Last Sunday by Judith Viorst

Counting On Frank by Rod Clements

How Long? How Wide? by Brian Cleary

Millions to Measure by David Schwartz

Fractions, Decimals, and Percents by David Adler

Unit 6

The Greedy Triangle by Marilyn Burns

Sir Cumference and the Dragon of Pi by Cindy Neuschwander

Unit 7

Chimp Math, Tiger Math, Polar Bear Math, and Cheetah Math (series) by Anne Nagda

A More Perfect Union by Betsy Maestro

Model Performance Indicator Information for Curriculum Guides

Embedded in the LCPS curriculum guides are sample Model Performance Indicator (MPI) tables (below).

These tables will be useful as you differentiate instruction for all of your learners, but they are especially

helpful for English Language Learners. Below are frequently asked questions about MPI.

What is a Model Performance Indicator (MPI)?

An MPI is a tool that can be used to show examples of how language is processed or produced within a

particular context, including the language with which students may engage during classroom instruction and

assessment.

Each MPI contains three main parts:

Language Function: The first part of an MPI, this shows how students are processing/producing

language at each level of language proficiency

Content Stem: This will remain consistent throughout an MPI strand and should reflect the knowledge

and skills of the state’s content standards

Support: The final part of an MPI, this highlights the differentiation that should be incorporated for

students at each language level by suggesting appropriate instructional supports for students at each

level of language proficiency

The samples provided also include an example context for language use that provides a brief descriptor of the

activity or task in which students would be engaged, while the inclusion of topic-related language helps to

support the emphasis on imbedding academic language instruction into our content-area teaching practices.

How can these sample MPIs help me?

Educators can use MPI strands in several ways:

to align students’ performance to levels of language development

as a tool for creating language objectives/targets that will help extend students’ level of language

proficiency

as a means for differentiating instruction that incorporates the language of the content area in a way that

meets the needs of students’ levels of language proficiency

An MPI strand helps illustrate the progression of language development from one proficiency level to the next

within a particular context. As these strands are examples, they represent one of many possibilities; therefore,

they can be transformed in order to be made more relevant to the individual classroom context.

Where can I get more information about WIDA, MPIs, etc.?

See My Learning Plan for several WIDA training modules

Introduction to the WIDA ELD Standards

Transforming the WIDA ELD Standards

Interpreting the WIDA ACCESS Score Report

The information above was adapted from the 2012 Amplification of the English Development Standards Kindergarten-Grade 12 resource guide and can be accessed at www.wida.us

http://www.wida.us/

SOL Strand and Bullet: 5.14 The student will make predictions and determine the probability of an outcome by constructing a sample space.

Example Context for Language Use: The student will work in small groups or with a partner to create a tree diagram, list, or chart to show all

possible outcomes of an event (e.g., ordering pizza with the following choices: 2 types of crust, 3 toppings, and 4 sides).

COGNITIVE FUNCTION: Students at all levels of English language proficiency will EVALUATE all possible outcomes of a simple event in a

sample space with 24 or less possible outcomes.

SP

EA

KIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify all possible

outcomes of a simple

event as a class using

photos or illustrations

Discuss all possible


event with a small group

using oral sentence

starters

Predict all possible


event with a partner using

a graphic organizer (e.g.,

tree diagram)

Explain all possible


event and the related

sample space to a partner

Defend outcome

predictions of a simple


sample space to a

partner

WR

ITIN

G

Create a sample space of

all possible outcomes of

a simple event using a

tree diagram, list, or chart

with a partner

Describe all possible


event in a tree diagram

using sentence starters

with a small group

Predict in a written list all

possible outcomes of a

simple event with a

partner

Explain in complete

sentences all possible

outcome predictions of a

simple event and the

related sample space in a

math journal

Defend in complete

sentence all outcome

predictions of a simple


sample space in a math

journal

TOPIC-RELATED LANGUAGE: Students at all levels of English language proficiency interact with grade level words and expressions

such as: predict, prediction, outcome, probability, possible, sample space, tree diagram, list, chart, certain, likely, equally likely, unlikely,

impossible, fraction, numerator, denominator, identify, discuss, predict, explain, defend, create, and describe.

SOL Strand and Bullet: 5.15 The student, given a problem situation, will collect, organize, and interpret data in a variety of forms, using stem-and-

leaf plots and line graphs.

Example Context for Language Use: Students will collect data on the daily temperature lows or highs for one month. Students will work in small

groups or with a partner to choose the best way to organize the data (e.g., stem-and-leaf plot or line graph). Students will represent the temperature

data on a stem-and-leaf plot and the temperature changes through time on a line graph.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will ANALYZE representations of data in various forms.

LIS

TE

NIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Follow oral directions to

represent data in various

forms (e.g., stem-and-

leaf plot, line graph)

using illustrated

examples in small groups

using L1 or L2


represent data in various

forms using illustrated

examples in small

groups

Identify the best

representation of data to

use for data gathered (e.g.,

stem-and-leaf plot, line

graph) based on teacher-

modeled simple oral

directions with a partner

Identify the best

representation of data to

use for data gathered

(e.g., stem-and-leaf plot,

line graph) based on

teacher-modeled multi-

step oral directions with a

partner

Recommend the best

representation for each

type of data gathered

(e.g., stem-and-leaf

plot, line graph) based

on oral discourse with a

partner

SP

EA

KIN

G

Verbally identify

characteristics of

representations of data


line graph) using

illustrated word banks in

small groups

Formulate questions

about the representation

of data using

illustrations and oral

sentence frames in small

groups

Verbally Formulate

questions about the

representation of data

using illustrated examples

with a partner

Explain the preferred

form for the


(e.g., stem-and-leaf plot

or line graph) to a partner

Present completed


to the class with a

partner

RE

AD

ING

Associate representations

of data with their name


line graph) using

illustrated text, labeled

examples, and illustrated

word banks in small

groups

Develop an

understanding of various

forms for representation

of data (e.g., stem-and-

leaf plot, line graph)

using illustrated text and

labeled examples in a

small group

Compare various forms of


using illustrated text with

a partner

Analyze various forms of



line graph) for accuracy

with a partner

Evaluate another

group’s representation

of data with a partner

Lev

el 6-R

each

ing

WR

ITIN

G

Write labels on


(e.g., titles on stem-and-

leaf plot or line graph)

using examples and

illustrated word banks in

small groups

Describe types of


using labeled examples

and written sentence

frames with a partner

Compare types of


using labeled examples

and written sentence

frames with a partner

Create a representation of

data (e.g., stem-and-leaf

plot, line graph) using

labeled examples

Explain findings from


in a math journal


such as: data, survey, problem situation, collect, organize, interpret, analyze, stem-and-leaf plot, line graph, identify, explain, formulate,

present, associate, develop, compare, analyze, evaluate, describe, create

SOL Strand and Bullet: 5.16 The student will





Example Context for Language Use: The student will work independently or with a partner to find the mean, median, mode and range of the ages

of his/her classmates.

COGNITIVE FUNCTION: Students at all levels of English language proficiency will EVALUATE measures of center and measure of variation

of gathered data.

LIS

TE

NIN

G

Level 1

Entering

Level 2

Emerging

Level 3

Developing

Level 4

Expanding

Level 5

Bridging

Lev

el 6-R

each

ing

Identify mean, median,

mode and range of

gathered data based on

online videos

(e.g., study jams or

Brainpop) in L1 or L2

Distinguish between

mean, median, mode

and range for gathered

data based on online

videos


Brainpop) in L1 or L2


find the mean, median,

mode and range of

gathered data using a

template with a partner

(e.g., record classmates’

ages and find measures of

center and variation)

Apply knowledge of

mean, median, mode and

range of gathered data to

check work with a

partner

Compare and contrast

the mean, median,

mode and range of

gathered data with

those of another

partnership

(e.g., “I got _____.

What did you get?”

SP

EA

KIN

G

Describe mean, median,

mode and range of

gathered data using

illustrated word banks

and following teacher

model

Describe the mean,

median, mode and range

of gathered data with a

partner using oral

sentence frames

Justify the mean, median,

mode and range of


graphic organizer with a

partner

Formulate and answer

questions on mean,

median, mode and range

of gathered data with a

partner

Compare and contrast

the mean, median,

mode and range of

gathered data with

those of another

partnership

(e.g., “I got _____.

What did you get?”

RE

AD

ING

Identify mean, median,

mode and range of


table and illustrated text

with a partner

Distinguish between

mean, median, mode

and range of gathered

data from online videos


Brainpop)

Compare mean, median,

mode and range of

gathered data with a

partner

Analyze for accuracy the

completed mean, median,

mode and range of

gathered data with a

partner

Evaluate another

partnership’s mean,

median, mode and

range of gathered data

with a partner

Lev

el 6-

Rea

chin

g

WR

ITIN

G

Record mean, median,

mode and range of


written model and a

graphic organizer

(e.g., foldable) with a

partner

Record mean, median,

mode and range of


written model and a

graphic organizer

(e.g., foldable)

Solve mean, median,

mode and range of


graphic organize

Explain mean, median,

mode and range of


template or graphic

organizer

Summarize findings

from mean, median,

mode and range of

gathered data in a math

journal


such as: mean, median, mode, measures of center, range, measure of variation, data, set, fair share, identify, distinguish, apply, compare and

contrast, describe, justify, formulate, identify, analyze, evaluate, record, solve, explain, summarize

Documents

GRADE 5 MATHEMATICS CURRICULUM GUIDE · GRADE 5 MATHEMATICS CURRICULUM GUIDE Loudoun County Public Schools 2016-2017 ... consensus of Loudoun’s teachers concerning the implementation