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Everyday Mathematics Enrichment and Extension Ideas

Compiled by the GT/Everyday Mathematics Study Group

May, 2004

1

Table of Contents

A Letter to Math Teachers 2

Definitions for Differentiating Instruction 3

General Enrichment Ideas 5

Grade One 6

Grade Two 22

Grade Three 44

Grade Four 67

Grade Five 89

Grade Six 111

Exemplars 129

First Grade 131Second Grade 134Third Grade 137Fourth Grade 140Fifth Grade 145Sixth Grade 151

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A Letter to Math Teachers

Dear Colleagues,

The participants of the Gifted and Talented Everyday Mathematics Study Group have been thinking of you. “How can we share some of what we’ve learned about supporting students and teachers in our schools?” we have wondered. This book is one of our efforts.

Mathematically gifted students have needs that differ from those of other students. They require some differentiated instruction, defined by Tomlinson (1995) as “consistently using a variety of instructional approaches to modify content, process, and or products in response to learning readiness and interest of academically diverse students.” A student might be gifted in one math content strand-for example, geometry – and not in other areas of mathematics. Determining students understanding as each mathematical concept is introduced is important when deciding which students need enrichment opportunities. For most students, their enrichment needs can be met within the regular Everyday Mathematics classroom. This collection of enrichment ideas can be used to provide related, meaningful opportunities to deepen students’ mathematical understandings

In the following pages, we have compiled some resources for teachers, GT representatives, and math coaches to use with students who need enrichment to support and enhance their experiences with Everyday Mathematics. We have included information from the Everyday Mathematics Teacher’s Lesson Guides, from the supplemental University of Chicago School Mathematics Project Books, and from district and community resources such as Exemplars, PRISM Kits, Alma project materials, and Stock Market activities.

All activities are organized by grade level and unit, and we have also highlighted the secure goals and essential vocabulary for each unit. Our intent is that you can use this guide to support classroom instruction for those students who need something to extend their understanding of the mathematical concepts presented in Everyday Mathematics. Please use them in conjunction with the support offered to you by your colleagues and the math specialists.

Thank you for all your efforts with Denver Public Schools’ students. Your dedication is appreciated.

The G/T Everyday Mathematics Study Group

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Definitions for Differentiated Instruction

Adjusting Questions: In class discussions, tests, and homework, teachers adjust the level of questions posed to learners based on their readiness, interests, and learning profiles.

Compacting: A three-step process that (1) assesses what a student knows, (2) plans for what is not known and exempts the student from what is known, and (3) plans for math time to be spent in enriched or accelerated study.

Flexible Grouping: Students are part of many different groups, and also work independently, based on the match of the task to student readiness, interest, or learning profile. Teachers may create concept/skill-based or interest-based groups who are heterogeneous or homogeneous in readiness level. Sometimes students select work groups, and sometimes teachers select them. Sometimes student group assignments are purposeful and sometimes random.

Interest: Interest is the student’s curiosity and passion for a topic or subject. Students are more motivated to learn about topics they have an interest in, or a passion for what they are attempting to learn.

Learning Centers: Learning centers can be “stations” or collections of materials that learners use to explore topics or to practice skills. Teachers can adjust learning center tasks to readiness levels or learning profiles for different students. Everyday Mathematics games and activities from Part 3 are good for use in Learning Centers.

Learning Contracts: Learning contracts can take a number of forms that begin with an agreement between student and teacher. The teacher grants certain freedoms and choices about how a student will complete tasks, and the student agrees to use the freedom appropriately in designing and completing work according to specifications.

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Learning Profile: A student’s style of learning, including multiple intelligences, environmental factors, and cultural styles. Students learn in a wide variety of ways, influenced by how individual brains are wired, cultural and environmental factors.

Readiness: Readiness is a student’s skill level and understanding of a subject.

Research and IndependentStudy: Process through which student and teacher identify problems or topics of interest to the student. Both

student and teacher plan a method of investigating the problem or topic and identifying the type of product. The product should address the problem and demonstrate the student’s ability to apply skills and knowledge to the problem or topics.

Tiered Assignments: In a heterogeneous classroom, a teacher uses varied levels of activities to ensure that students explore ideas at a level that builds on their prior knowledge and prompts continued growth. Student groups use varied approaches to explore essential ideas. Part 3 of the lessons (grades 1-6) in Everyday Mathematics provides activities that can be used to tier assignments.

Adapted from Tomlinson, C.A. (1995). How to Differentiate Instruction in Mixed Ability Classrooms. Alexandria, VA: ASCD.

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General Enrichment Ideas(List created by Sonja Hassler, Facilitator

Everyday Mathematics and GT Study Group)

The following text provides some very specific enrichment ideas that are linked to units and lessons. This is a list of general enrichment options that can be modified for any unit and grade level.

Create a written response journal in which students can respond to specific exit slip questions (Are ½ and .50 equivalents? How do you know?), lessons, or questions that they have. Also, consider having a vocabulary section, in which students can list new vocabulary words and definitions.

Consider creating a “Query Corner” where students can post problems and/or questions that they have difficulty solving OR with which they want to challenge their fellow students. (If there are 5 students in a class and every student shakes every other student’s hand once, how many handshakes are there in all?) Students may post their answers next to the question for other students to read and respond.

Allow students to modify the games in the program to make them more challenging OR allow students to create their own games to demonstrate they have mastered the secure and/or developing/secure goals in the unit. This is a great way for students to analyze their own thinking, and writing directions can be much more complicated than they might think!

Incorporate some vocabulary games into your teaching—there are usually between 10-30 new vocabulary words in a unit, and students need to learn correct mathematical terminology in order to explain their thinking.

Literature extensions can link math and literacy, and activities can reinforce learning in both reading and math. Everyday Mathematics has an extensive literature link in the Home Connection Handbook. Use the lessons provided in the Teacher’s Lesson Guide and consider extending the use of the text into reading, writing, art…or ask students to create their own response activities that demonstrate their understanding of the mathematics—better yet, ask them to extend their understanding (Does this work with bigger numbers? Can you calculate this in a different way? How would you illustrate that?) and create a sequel to the book.

Projects (You know, the ones in the back of the Teacher’s Lesson Guide that you worry you’ll never get to!) can be helpful if you have kids that finish early. At the beginning of the unit, assign groups/partners to complete a project that correlates to what you are working on in class. Introduce the project to the whole class, outline expectations, and answer questions. Then, when students finish early (after they play the games), they may work on the long-term project. Set the due date for the day before or after the test, and have groups present their projects. (Suggestion: Consider grouping kids according to their speed at finishing their work.)

Math Stations can also be a “life-saver”! Put your favorite math activities in one area, including logic puzzles, extra pattern blocks, geoboards, Everyday Mathematics games, etc. You might also consider calling your PRISM representative and ordering the calculator kit for a few weeks. Kids can visit the math station when they have finished their daily assignments.

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First Grade

Unit Page

1 – Establishing Routines 7

2 – Everyday Uses of Numbers 8

3 – Visual Patterns, Number Patterns, and Counting 10

4 – Measurent and Basic Facts 12

5 – Place Value, Number Stories, and Basic Facts 14

6 – Developing Fact Power 16

7 – Geometry and Attributes 18

8 – Mental Arithmetic, Money, and Fractions 19

9 – Place Value and Fractions 20

10 – Year-End Review and Assessment 21

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1st Grade EMUnit Title Secure;

Developing/SecureGoals

Vocabulary Program Enrichment

Supplemental Enrichment

1Establishing Routines

Secure Goals1f: Count up and back by 1s, starting with any number up to and including 20

1g: Count 20 or more objects

Developing/Secure Goals1a: Count by 5s to 40

1b: Count by 2s to 40

1c: Write numbers from 1 – 20

1d: Compare pairs of numbers less than 16.

1.1 number linejob chart attendance1.2 absent1. 3 tool kitPattern-Block Template1.4 slate1.7 tally 1.9 calendardate1.11explorerExplorationpattern blocksbase-10 blocksgeoboard1.12thermometermercurydegreetemperatureFahrenheit1.13number story

Within the LessonAdjustment1.1, part 11.4, part11.5, part 21.6, part 21.7, part 21.11, part11.12, part 11.13, part 1Part III1.1 Drawing

Portraits1.3 MakingGeometric Designs1.7 A Listening Tally1.8 Scissors, Paper, Stone1.10 Pattern Block Designs1.11 Drawing Pattern-Block Designs1.12 Making a Weather Activity BookLiteracy ExtensionsLiterature

Exemplars1.8 Wrist Circumference100 Best Tasks1997

Math WebsitesKidsKonnect.com Math SitesMultiple math sitesJanBrett.com Home Page2,389 pages of free activities, coloring pages, and productsAAA MathLost of different math activitiesAunty MathA regular math challenge

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A Day with No Math

9


Developing/Secure Goals



2Everyday Uses of Numbers

Secure2g: Count by 2’s to 40, count by 5s to 50.

Developing/Secure2a: Calculate the value of combinations of pennies and nickels

2d: Count up and back by 1s on the number grid

2e: Tell time to the nearest hour

2f: Exchange pennies for nickels.

2.1 number grid2.2 area codeprefix2.3 Math boxes2.4unitunit box2.5analog clockhour handminute handestimate2.6 clockwisemidnightnoonA.M.P.M.2.7 ruler2.8 pennycent2.9 nickel2.11 addplusnumber model2.12 subtractminus

Within the LessonAdjustment2.2, part 12.4, part 12.5, part 12.6, part 12.9, part 12.10, part 12.11, part 1Part III2.1 Making a Number Line2.2 Classroom Telephone Book2.3 Playing Two-Fisted Penny Addition with Larger Numbers2.4 Combinationsof Two Numbers whose sum is 102.5 Illustrating Daily Activities2.6 Setting Clocks to Match the Times in a Song2.10 Playing Coin Top-It2.12 Shopping at Playing Who Am I

ExemplarsProject 3: Jack-O’Lanterns Fall 1999

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Thinking Of?2.13 Shopping at the Classroom StoreLiteracy ExtensionsLiterature2.2 Fish Eyes: A Book You Can Count On2.3 Two of Everything: A Chinese Folktale2.9 Twelve Ways to Get Eleven

Extensions ProjectsP1 -One: Apple Math P2 P2 -ProjectTwo: Autumn Leaves ProjectP3 -Three: Pumpkin Math ProjectGamesClock ConcentrationPrime Time

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3Visual Patterns, Number Patterns, and Counting

none 3.1 pattern3.2 even numberodd number3.3 columndiagonalrow3.5 number linehour handminute handestimatenegative number3.7 half-past3.8 Frames and Arrows diagramarrow ruleframe3.10 programdimedollars & cents notationdecimal point3.12 line plot

Within the LessonAdjustment3.2, parts 1, 23.4, part 13.6, part 13.7, part 1Individual3.1 Making Patterns with Colored Chalk3.3 Exploring the 4s Pattern3.6 Making Up andSolving Penny Stories3.7 Ordering Clock by Time Displayed3.11 Playing Coin Top-It3.12 Playing Dime-Nickel-Penny Grab3.14 Exploring Sums of Even and Odd NumbersLiteracy ExtensionsLiterature3.2 26 Letters and 99 Cents

ExtensionsProjects

Exemplars3.9 OctopusOctupus100 Best Tasks 1997

3.10 LegsWinter 2000

3.12 Nine CenterWinter 2000

Prism KitsFrog Math Observe, describe, and sort buttons, read Frog and Toad and play games

#32 Patterns and FractionsSix sets of pattern blocks to discover fractions, shapes, and symmetry

#20 Introduction to CalculatorsClassroom set of calculators with guide for teacher selection of problem solving activities, looking for patterns

UCSMP Math/Science

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P4 -Four: Geometric Gift Wrap and Greeting Cards Project

GamesMaking ChangeMoney Exchange GamePick a CoinSpinning for Money

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1st Grade EMUnit TitleSecure Goals

Secure;Developing/Secure Goals



4Measurement and Basic Facts

Developing/Secure4e: Order and compare numbers to 22

4f: Tell time to the nearest half hour

4.1 Math MessagemercurydegreethermometertemperatureFahrenheit4.2 unitmeasurelengthdigithandhand spanyardcubitarm span4.3 footstandard foot4.4 inchnearest inchin.4.5 estimate4.6 tape measure4.7 typicalbar graph4.8 half-pastquarter-afterquarter-pastquarter-beforequarter-to4.9 timeline4.10 scrolllong

Within the LessonAdjustment4.1, part 14.3, part 14.5, part 14.6, part 14.7, part 14.8, part 14.9, part 1Individual4.3 Naming Things That Are about 1 Foot Long4.4 Introducing the Yard4.5 Starting the Jack and the Bean stock Project4.6 Making a MeasurementBook4.7 Making an Inch Collection4.8 Making a Storybook Timeline4.12 Playing a Variation of Shaker Addition Top-It4.12 Playing High Roller to 20

Exemplars4.2 How Big is a Foot?100 Best Tasks 1997

4.6 Wrist Circumference100 Best Tasks 1997

Prism Kits#26 Measurement Toolsmaterials to measure a variety of liquid and linear objects

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cubebase-10 blocks4.11 addition factssumfact power

Literacy ExtensionsLiterature4.3 26 Letters and 99 Cents4.7 A Cloak for a Dreamer

ExtensionsProjectsP5 -Five: Calendar for the New Year Project P6 - Six: Celebrate the Hundredth DayIf I Walk in the Woods Will I Run Into A Bear?M1 – How Heavy is an Ounce?M2 – Be A Scale!M3 – Be a Scale!M4 – Be A Ruler!M5 – Animals and Their TalesM6 – How Long Are These Birds?M7 – What Does Big Mean?

Project

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5Place Value, Number Stories, and Basic Facts

None 5.1 longscubestens placeones place5.2 flat hundredshundreds placedigit5.3 is more thanis less than5.4 area5.7 difference5.9 multiple of 105.10 turn-around-factdoubles fact5.12 function machine5.13rule

Within the LessonAdjustmentAdustment5.1, part 15.3 part 15.5 part 15.6 part 15.8 part 1Part III5.5 Creating a Booklet or Bulletin-Board Display of Parallel Line Segments5.6 Exploring Tangrams5.8 Constructing a Decagon Out of Triangles5.9 Exploring Line Symmetry in Literature Literacy Extensions Literatur e5.3; 5.7 The Art of Shapes for Children and Adults5.9 Lao Lao of Dragon Mountain

Additional Exploration with Tangrams

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5.3; 5.7 Shapes, Shapes Shapes5.3 The Greedy Triangle

5.6 Grandfather Tang’s Story

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Developing/ Secure Goals



6 Developing Fact Power

Powr

None 6.1Addition/Subtraction Facts Table6.2 equivalent namesname collection box6.3 fact family6.4 Fact Triangle6.6 centimetermetric system6.10 digital clock6.11 second handsecond6.12 rangemiddle value

Within the LessonAdjustment6.1, part 16.3, part 36.4, part 36.7, part 16.8, part 16.9, parts 1, 36.10, part 1Part III6.3 Generating Fact Families6.6 Introducing6.11 Explore Ways to Count Seconds6.11 Writing a Timing Me Number StoryLiteracy ExtensionsLiterature6.8 Each Orange had Eight Slices: A Counting Book and Sea Squares6.9 One Hundred Hungry Ants6.11 A Remainder of One

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ExtensionsGamesDollar RummySpinning for MoneyBroken CalculatorMusical Name Collection BoxesName that NumberAddition Card DrawBasketball AdditionThree Addends

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Vocabulary Program Enrichment Supplementary Enrichment

7 Geometry and Attributes

None 7.1 trianglesquare rectangle hexagoncircleattribute7.3 trapezoidrhombussidecornersquare cornerpolygon7.5 spherecylinderrectangular prismsurfaceface7.6 pyramidcone cube7.7 symmetricalsymmetry

Within the LessonAdjustment7.2, part 17.3, part 17.4, parts 1, 27.5, part 27.6, part 1Part III7.3 Building and drawing a pattern block design7.5 Matching shape attributes7.6 Identifying shapes using touch7.7 Making symmetry cards

ExtensionsProjectsP7 – Amaryllis Plant GamesWhat’s my Attribute Rule?

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1st Grade EMUnit Title Secure/




8Mental Arithmetic, Money, and Fractions

Developing/Secure8e: Understand place value for 10’s and 1’s

8f: Know addition facts

8.2decimal point8.3hundredstensoneshundreds placetens placeones place8.5to make change8.6wholeequal partshalvesthirdsfourths8.7fractionfractional part8.9near double

Within the LessonAdjustment8.2, part 38.5, part 18.7, part 3Part III8.1 Solving coin riddles8.4 Opening a classroom store8.5 Paying with a dollar bill8.6 Reading about dividing shapes into equal parts8.7 Making a fraction book8.8 Making fraction creaturesLiteracy Extensions8.6 Gator Pie, Eating Fractions, and Ed Emery’s Picture: A Circle Drawing Book

WebsitesKidsBank.comA fun place to learn about money and banking

8 Mental Arithmetic, Money, and Fractions

8e Understand place value for 10’s and 1’s

8.2 decimal point8.3 hundredstens

Within the LessonAdjustment

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8f Know addition facts for +1, +0, doubles, and sums of 10

oneshundreds placetens placeones place8.5 to make change8.6 wholeequal parts halvesthirdsfourths8.7 fractionfractional part8.9 near double

8.2, part 38.5, part 18.7, part 3Individual8.1 Solving Coin Riddles8.4 Opening a Classroom Store8.5 Paying with a dollar bill8.6 Reading about Dividing Shapes into Equal Parts8.7 Making a Fraction Book8.8 Making Fraction CreaturesLiterature8.6 Gator Pie; Eating Fractions; and Ed Emberly’s Picture Pie: A Circle Drawing Book

Extra ChallengProjectsEight: A Flea Market ProjectGamesEquivalent Fractions GamesHit the TargetPick a Coin

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Supplementary Enrichment

9Place Value and Fractions

Developing/Secure9e: Identify and use patterns on the number grid.

9.3number grid puzzle9.7denominatornumerator

Within the LessonAdjustment9.1, part 19.5, part 19.6, part 19.7, part 19.8, part 1Part III9.2 Playing the NumberGrid Game (Advanced Version)9.3 Making a class Number-Grid Puzzle Book9.4 Making a class Number-Story Book9.6 Reading about FractionsLiteracy ExtensionsLiterature9.4 Three Billy Goats Gruff9.6 Fraction ActionExtensionsGamesDigit Discovery

Prism Kits#32 Patterns and FractionsSix sets of pattern blocks and activities to discover fractions, shapes, and symmetry

23

Unit Title Secure;Developing/Secure Goals


Supplementary Enrichment

10Year-End Review and Assessment

None None Within the LessonAdjustment10.4, part 110.5, part 210.7, part 3Part III10.4 Creating and solving number stories10.5 Discussing the five regular polyhedrons10.6Discussing the two-thermometer scales10.7Tallying vowels in reading materialsLiteracy Extensions10.5 Color Zoo10.6 Welcome to the Green House; Welcome to the Ice House; Cactus Desert; Arctic Tundra; and Tropical Rain Forests

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Second Grade

Unit Page

1 – Numbers and Routines23

2 – Addition and Subtraction Facts25

3 – Place Value, Money, and Time27

4 – Addition and Subtraction28

5 – 3-D and 2-D Shapes29

6 – Whole-Number Operations and Number Stories31

7 – Patterns and Rules33

8 – Fractions 35

9 – Measurement 37

10 – Decimals and Place Value39

11 – Whole-Number Operations Revisited41

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12 – Year End Reviews and Extensions43

2nd Grade EMUnit Title Secure;




1Numbers and Routines

Secure1g: Count by 2s; 5s; and 10s

1h: Make tallies and give a total

1.1math messagenumber line1.2tool kitlost and found boxpattern-block template1.3calendarordinal numbers1.5tally marks1.7digitmath boxes1.8number scrolleven numberodd number1.10equivalent names

Within the LessonAdjustment1.1, part 11.4, part11.5, part21.6, part 21.7, part 21.11, part 11.12, part 11.13,part 1Part III1.1 Counting aloud to estimate seconds1.2 Arranging children in order using their tool-kit numbers1.5 Using tally marks to record survey responses

Creative Game Making Provide students with the “raw materials” to develop a new game to teach/practice a given concept.

26

1.12is equal tois less thanis greater than1.13temperaturethermometerFahrenheitExplorationsbase-10 blockscubelongflat

1.8 Making individual number scrolls1.9 Making number-grid puzzles pieces1.10 Finding counting patterns in a number grid1.11 Playing “Pin the Number on the Number Grid”1.12 Playing “Digit Discovery”Literacy Extensions1.1 A Day with No Math

ExtensionsIf I Walk in the Woods Will I Run into A Bear?M8 – Think Like a ScientistM9 – Looks Can Be Deceiving

GamesNumber Top It

27





2Addition and Subtraction Facts

Secure2f: Know “easier” addition facts

2g: Construct fact families for addition and subtraction

2h: Complete simple Frames-and-Arrows diagrams

2i: Solve addition number stories

2j: Find equivalent names for numbers

Developing/Secure2b: Know “harder” addition facts

2c: Know “easier” subtraction facts

2d: Complete “What’s My Rule?” tables

2.1addition number storylabelunit boxnumber model2.2addition factfact power+0 facts+1 facts+0 shortcut2.3doubles factssumFacts TableRowColumnDiagonal2.4turn-around facts+9 facts+9 shortcut2.5doubles-plu-1 factsdoubles-plus-2 facts2.6subtraction number story-0 facts-1 facts

Within the LessonAdjustment2.2, part 12.4, part 12.5, part 12.9, part 12.10, part 12.11, part 1Part III2.1 Making up addition number stories2.4 Creating and solving riddles2.5 Looking for patterns2.10 Frames-and-Arrows problemsLiteracy ExtensionsLiterature2.2 Fish Eyes2.3 Two of Everything a Chinese Folktale2.9 Twelve Ways to Get Eleven

ExtensionsProjectsP1- Boxes, Boxes, Beautiful Boxes

Math Web SitesSeveral good math websites are listed on the DPS Math Curriculum homepage and provide topical problems of the week that can easily be differentiated for your advanced students

KidsKonnect.com Math SitesMultiple math sitesJanBrett.com Home Page2,389 pages of free activities, coloring pages, and productsAAA MathLots of different math activitiesAunty MathA regular math challenge

28

2e: Solve subtraction number stories

-0 shortcut-1 shortcut2.7ouncepoundpan balanceheavierlighter in balancespring scale2.8fact familyFact Triangle2.9name-collection box2.10Frames-and-Arrows diagramsframearrowarrow rule2.11“What’s My Rule?”function machine2.12difference2.13-9 facts-9 shortcut-8 facts-8 shortcut

P2 – Weather StationP3- Chinese CalendarIf I Walk in the Woods Will I Run into a Bear?M10 – What Am I?M 11a, b – How Long do Animals Live in the Wild?

GamesLess Than YouMemory Addition and SubtractionSubtraction Top-It

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Unit Title SecureGoals




3Place Value, Money, and Time

3e: Identify place value in 2 digit and 3 digit numbers3f: Show pennies, nickels, dimes and quarters for a given amount3g: Know all addition facts3h: Know easy subtraction facts

3d: Tell time to 5 minute intervals

3.1Base-10 blocksCubeLongFlatBase-10 system3.2NickelPennyDimeQuarter$1 bill3.3Minute handHour handClock faceAnalog clockDigital clock3.5PredictMiddle numberBar graph3.7Make change by counting up3.8Exact change light

Within the LessonAdjustment3.2, part 1, 23.4, part 13.6, part 13.7, part 1Individualizing3.1 Demonstrating 4-digit numbers with a thousands cube3.5 Comparing pockets data3.6 Making up and solving Frames-and-Arrows problems having two rules3.7 Solving a coin puzzleLiteracy3.2 26 Letters and 99 Cents

Extra ChallengeProjects P4 - Dates on PenniesFrom the Sea to the StarsP8 - So You Think You Can Tell Time!

Activities from the following books1. Murphy, Stuart J., The Penny Pot Play a Coin

Game

2. Murphy, Stuart J., Sluggers’ Car Wash Make a chart

showing the relative value of coins

3. Scieszka, Jon & Smith, Lane, Math Curse Money problem

adding Washington’s & Lincolns

Exemplars3.2, 3.7The Salad BarFall, 1999

3.3 Let’s Plan a Party

30

Winter 2000

31





3Place Value, Money, and Time

Place Value, Money, and Time

Secure3e: Identify place value in 2-digit and 3-digit numbers3f: Show money for a given amount3g: Know “easier” addition facts3h: Know “easier” subtraction facts

Developing/Secure 3d: Tell time to 5- minute intervals 3e: Identify place value in 2 digit and 3 digit numbers3f: Show pennies, nickels, dimes and quarters for a given amount3g: Know all addition facts3h: Know easy subtraction facts

3.3 5. .1trapezoidrhombuspolygonsidevertex (vertices)angletrianglequadranglepentagonhexagonheptagonoctagon3.5Base-10 blocksCubeLongFlatBase-10 system3.2NickelPennyDimeQuarter$1 bill3.3Minute handHour handClock faceAnalog clockDigital clock3..4

Within the LessonAdjustment5.1, part 15.3, part 15.5, part 153.2, part 1, 23.4, part 13..6, part 15.83.7, part 1Part III3.1 Demonstrating 4-digit numbers with a thousands cube3.5 Comparing pockets data3.6 Making up and solving frames-and-arrows problems having two rulessolving Frames-and-Arrows problems having two rules5.9 Exploring line symmetry in literacy3.7 Solving a coin puzzleLiteracy Extensions5.3, 5.7 The Art of Shapes for Children and Adults

Creative Game Making Provide students with the “raw materials” to develop a new game to teach/practice a given concept.

Activities from the following books1. Murphy, Stuart J., The Penny Pot Play a Coin Game

2. Murphy, Stuart J., Sluggers’ Car Wash Make a chart showing the relative

value of coins

3. Scieszka, Jon & Smith, Lane, Math Curse Money problem adding Washingtons &

Lincolns Exemplars 3.2, 3.7The Salad BarFall, 1999

3.3 Let’s Plan a PartyWinter 2000

Activities from the Following Books

1. Murphy, Stuart J., The Penny Pot; Play a coin game

2. Murphy, Stuary J., Sluggers’ Car

32

pointstraightedgeline segmentendpoint5.5parallel5.6square cornersquarerhombusrectangletrapezoidparallelogramkite5PredictMiddle numberBar graph3.7cylinderconespherecurved surfacerectangular prismcube pyramidflat surfacefaceedge5Make change by counting up

baseapexsquare pyramidtriangular

Shapes Shapes Shapes5.9 Lao Lao of Dragon Mountain5.3 The Greedy Triangle5.6 Grandfather Tang’s Story3.2 26 Letters and 99 Cents

ExtensionsGamesPenny-Dime Exchange

Fastest Anima8. So You Think You Can Tell Time! Expands on concepts of estimating time, recording time, calculating percentGames

Wash; Make a chart showing the relative value of coins

3. Scieszka, Jon, & Smith, Lane, Math Curse; Money problem adding Washington’s and Lincoln’s

Math Web SitesSeveral good math websites are listed on the DPS Math Curriculum homepage and provide topical problems of the week that can easily be differentiated for your advanced students

33

pyramidrectangular pyramidpentagonal pyramidhexagonal pyramid5.9line symmetryline of symmetrysymmetri

34

Unit Title Secure; Developing/SecureGoals



4Addition and Subtraction

Secure4e: Add and subtract with multiples of 10

4.1change-to-more number storychange diagrammental arithmetic4.2part-and-total diagramparts-and-total numbers story4.3degrees Fahrenheitdegrees Celsiusthermometerdegree marks4.4thermometerdegree marks4.5estimate4.6inch (in)centimeter (cm)tilingattribute blocks4.8ballpark estimate4.9algorithm

Within the LessonAdjustment4.2, part 14.3, part 14.5, part 14.6, part 14.7, part 14.8, part 14.9, part 1Part III4.4 Identifying situations as change to more or change to less4.5 Using estimation to compare sums of weights4.9 Exploring pattern-block designsLiteracy Extensions4.3 26 Letters and 99 Cents4.7 A Cloak for a Dreamer

35

2nd Grade EM

36

3rd Grade EDMUnit Title Secure;







53-D and 2-D Shapes1Routines, Review and Assessment

Secure5f: Identify 2-dimensional shapes

Developing/Secure5e: Draw line segments1b: Count by 10s and 100s

1f: Find equivalent names for numbers

1g: Know addition facts

5.3trapezoidrhombuspolygonsidevertex (vertices)angletrianglequadranglepentagonhexagonheptagonoctagon5.4pointstraightedgeline segmentendpoint5.5parallel1.1 5 museum1.2 unit1.3 1.21.4 number grid1.5 number grid

puzzle1.6 odometer1.7 1.3table of

Within the LessonAdjustment5.1.6., part 15.3, part 15.5, part 15.6, part 15.8, part 1Part III5.5 Creating a booklet or bulletin-board display of parallel line segments5.6 Exploring tangrams5.8 Constructing a decagon out of triangles5.8 Making a connection between pyramids in math and social studies5.9 Exploring line symmetry in Literacy ExtensionsLiteracy Extensions


37

contents1.8 essay1.9 answer key1.10 glossary1.11 index1.12 data bank1.13 tool kit1.14 tally chart1.15 bar graph1.16 range1.17 mode

maximum1.18 minimum1.19 1.6square cornersquarerhombusrectangletrapezoidparallelogramkite5name-collection box1.7cylinderconespherecurved surfacerectangular prismcube pyramidflat surfacefaceedge5.8base

5.3, 5.7 The Art of Shapes for Children and AdultsShapes Shapes Shapes5.9 Lao Lao of Dragon Mountain5.3 The Greedy Triangle5.6 Grandfather Tang’s Story1.8, Part 11.11, Part 11.12, part 1Individualization1.1: Comparing common uses of numbers1.2: making number grid puzzles1.5: Finding which name has the greater total number of letters1.6: making name-collecting boxes1.7: Counting back past zero1.11: Coloring a designLiterature1.6 Twelve Ways to Get to Eleven1.9 26 Letters and

38

apexsquare pyramidtriangular pyramidrectangular pyramidpentagonal pyramidhexagonal pyramid5difference1.9line symmetryline of symmetrysymmetrical1a: Identify and use number patterns to solve problems

1c: Apply place value concepts in 4-digit numbers

1d: Tell and show times to the nearest minute

1e: Calculate the values of bills and coins and write the total using dollars and cents notation.

99 Cents

ExtensionsIf I Walk in the Woods Will I Run into a Bear?M12 a, b – The Mysterious HummingbirdM13 a, b - Who is the Fastest Animal in the Word?

GeometryAngle RaceRobotdecimaldecimal pointmake change1.10sale priceregular priceestimateestimationcalculate1.11 Frames-and-Arrows diagramframearrow rule1.12elapsed time

39





6Whole-Number Operations and Number Stories2Adding and Subtracting Whole Numbers

Secure6i: Add three 1-digit numbers mentally

Developing/Secure6h2b: Use basic facts to solve fact extensions

2c Complete “What’s My Rule?” tables

2f: Solve addition and subtraction multi-digit number stories2d: Know addition and subtraction facts

2e:Complete fact and number families

6.2.1unit boxlabelmeasurement unitfact familyturn-around rulenumber family2.2higher-decade factscomplement2.3function machineinputoutputrule“What’s My Rule?”2.4parts-and-total number storyparts-and-total diagramnumber model2.5trade-first algorithm2.6comparison number storydifferencecomparison

Within the LessonAdjustment6.1, part 16.3, part 36.4, part 36.7, part 16.8, part 12.2, Part 22.3, Part 12.6, Part 1Part 162.9, parts 1, 3Part16.10, part 1Part III6.1 Three Addends – Individual 2.2: Playing name that number using multiples of 106.3 Categorizing foods6.3 Favorite food data6.4 Number2.4: solving missing-addend number stories6.6 Making up 2.5: Writing and solving

WebsitesMathStories.com Math problem solving and critical thinking

41

diagram6.3basic food groupsFood Guide PyramidData tableBar graph6.5tradevariable6.62.7ballpark estimatepartial-sums method2.8trade-first (subtraction)method6.8equal groupsmultiplicationtimesmultiplied by62.9multiplication diagramx-by-y arrayaddend

subtractionchange number stories6.8 Equal groups in Literacy Extensions6.9 Describing arrays found in Literacy Extensions6.10 Extending Array Bingo6.11 Describing division situations found in Literacy ExtensionsLiteracy Extensions6.8 Each Orange Had Eight Slice: A Counting BookSea Squares6.9 One Hundred Hungry Ants6.11 A Remainder of One2.6: Comparing data2.7:Making up addition problems based on a mileage map

ExtensionsProjectsP5 – SnowflakesIf I Walk in the Woods Will I Run into a Bear?M14 a, b, c – Big

42

Hearted and Hungry Birds

GamesMissing Terms

43





7Patterns and Rules3Linear Measures and Area

Secure7f: Know complements of 107g: Count by 2s, 5s, and 10s and describe the patterns7h: Find missing addends for the next multiple of 107i: Solve number-grid puzzles7j: Plot data on a bar graph

Developing/Secure

7d3c: Measure line segments to the nearest ¼ inch7e: Measure to the nearest centimeter3d: Measure line segments to the nearest centimeter

73.1standard unitlength3.2number-grid puzzlearrow patharrow-path puzzle7.5halfdouble7.7arm span7.8sort (the data)medianmiddle value7.9inch, in.line plotsegmentcentimeter, cmmillimeter, mm3.3U.S. customary systemmetric systemfoot yardpersonal referencesmillicentimeterdecimeter

Within the LessonAdjustment7.1, part 17.2, part 173.2, Part 13.5, Part 13.6, part17.7, part 1Part III7.1 Making patterns by coloring grids7.2 Making up arrow-path puzzles7.2 Playing the Attribute Train Game7.3 Playing Hit the Target7.5 Doubling and halving situations found in Literacy Extensions7.7 Making up and solving number stories3.7, Part 1Individualization3.1 Comparing Random Samplings

Prism Kits#20 Introduction to CalculatorsClassroom set of calculators with guide for teacher selection of problem activities, looking for patterns

44

3.4trianglesquarerhombusrectangleparallelogramtrapezoidperimeterpolygongirth3.5tilingarea

3.6areasquare footsquare yard3.8circumferencediametercenter“about 3 times”circle rule

3.2 Nonzero mark on a ruler3.3 Estimation scavenger hunt3.4 Shipping requirements for packages3.8 Circumferences in literature and historyLiteracy Extensions7.5 Melisande; 3.1 Counting on Frank3.1 How Big is a Foot?A Cloak for the DreamerThe King’s Chessboard; One Grain of Rice; A Mathematical Folktale; The Token Gift; Two of Everything : A Chinese Folktale; Anno’s Magic Seeds Libraria 7.6 A Cloak for a DreamerWho Measured the Earth

45

ExtensionsProjectsP1 – Boxes, Boxes, Beautiful BoxesP2- Chinese CalendarP6 – Time CapsuleP7 – CollectionsFrom the Sea to the StarsP5 – How Big Are your Feet?

46

2nd Grade EMUnit Title Secure ;




8Fractions

Secure8g: Shade a specified fractional part of a region

8h: Give the fraction name for the shaded part of a region

8.1ONE (the whole)fractiondenominatornumerator8.2cubic centimetervolume8.4equivalentequivalent fractions

Within the LessonAdjustment8.2, part 18.3, part 1Part III8.1 Naming equal parts of situations found in Literacy Extensions8.5 Playing an advanced version of the Equivalent Fractions Game8.6 Playing the advanced version of Fraction Top-itLiteracy Extensions8.1 Gator Pie; Eating Fractions; Ed Ember ley’s Picture Pie; A Circle Drawing Book8.3 A Circle Drawing Book

ExtensionsProjectsP2 – Weather StationP5 – Snowflakes


47

If I Walk in the Woods Will I Run into a Bear?15a, b – If I Walk in the Woods Will I Run into a Bear?

48





9Measurement

Secure9h: Use a ruler, tape measure, and meter/yardstick correctly

Developing/Secure9g: Identify equivalencies for inches, feet, and yards

9.1standard unityardmeter9.2inchcentimeterfootdecimeter9.3millimeter9.4perimeter9.5milekilometer9.6linear measuremeasure of weightmeasures of volume and capacityunits of measure9.7areasquare centimetersquare inch9.8surfaceareasquare unit

Within the LessonAdjustment9.1, part 19.2, part 19.4, part 19.8, part 29.9, part 1Part III9.1 Measurement in Literacy Extensions9.2 Exploring equivalent U.S. customary linear measures in Literacy Extensions9.3 Comparing Unit of metric linear measure9.4 Measuring perimeter in paces9.5 Researching a pretend trip9.8 Finding the areas of grid-paper drawings9.9 Measuring the capacity of irregular containersLiteracy Extensions

#26 Measurement ToolsMaterials to measure a variety of liquid and linear objects

49

9.9capacitycuppintquartgallonliter9.10weighscaleweightouncepoundgramkilogram

9.1 How Big is a Foot?; Counting on Frank9.2 Twelve Snails to One Lizard: A Tale of Mischief and Measurement 9.9 Pigs in the Pantry: Fun with Math and Cooking

ExtensionsFrom the Sea to the StarsP6 – Body TemperatureIf I Walk in the Woods Will I Run Into A Bear?M1 – How Heavy is an Ounce?M2 – Be A Scale!M3 – Be a Scale!M4 – Be A Ruler!M5 – Animals and Their TalesM6 – How Long Are These Birds?M7 – What Does Big Mean?

GamesRobot

50





10Decimals and Place Value

Secure10e: Read and write money amounts in decimal notation

10f: Use equivalent coins to show money amounts in decimal notation

10g: Use a calculator to compute money amounts

10h: Exchange pennies, nickels, dimes, and quarters

10i: Know and express automatically the values of digits in 2-, 3-, and 4-digit numbers

10.2decimal point10.6counting up to make change10.11parentheses

Within the LessonAdjustment10.1, part 110.3, part 110.5, part 110.7, part 110.8, part 1Part III10.1 Investigating money from other countries10.3 Using mental arithmetic and a calculator to find Pick-a-Coin totals10.6 Using money in Literacy Extensions10.10 Ordering 5-digit numbers10.11 Making up and solving parentheses puzzlesLiteracy Extensions10.1 26 Letters and 99 Cents10.6 Pigs Will Be Pigs; Alexander Who Used to Be

WebsitesKidsBank.comA fun place to learn about money and banking

51

Rich Last Sunday

ExtensionsProjectsP8 – How Far Can I Run in 10 seconds?

52

2nd Grade EMUnit Title Secure




11Whole-Number Operations Revisited

Secure11g: Multiply numbers with 0 or 1 as a factor

11.3multiplication diagramfactorproductperin eachfor each11.4multiplication/division diagramdivisionquotientremainderdivided by11.5multiplication factfact power11.6factorproductsquare (of a number)turn-around rule for multiplication11.7multiplication/division diagramfact family11.9precipitation

Within the LessonAdjustment11.1, part 111.3, part 111.4, part 111.6, part 1Part III11.1 Making up and solving number stories about purchases11.2 Making up and solving number stories11.3 Connecting equal groups to literacy extensions11.4 Connecting division with remainders to Literacy Extensions11.6 Investigating square numbers11.7 Making up and solving multiplication and division number storiesLiteracy Extensions11.3 Each Orange

53

middle valuerange

Had Eight Slices: A Counting Book; Sea Squares; One Hundred Hungry Ants11.4 A Remainder of One11.6 Sea Squares

ExtensionsProjectsP7 – CollectionsP8 – How Far Can I Run in 10 Seconds?

54





12Year End Review and Assessment

Secure12g: Tell time to 5-minute intervals

12h: Demonstrate calendar concepts and skills

12i: Compare quantities on a bar graph

Developing/Secure12e: Construct multiplication/ division fact families

12f: Multiply numbers with 2, 5, and 10 as a factor

12.3communicatetimelinedecadecentury12.4factorproductturn-around rule12.6medianrange12.7mode

Within the LessonAdjustment12.1, part 112.2, part 1Part III12.3 Creating a timeline of a person’s life12.4 Introducing the “9s facts on fingers” shortcut12.6 Connecting comparisons of animal speeds to Literacy ExtensionsLiteracy Extensions12.6 The Tortoise and the Hair

ExtensionsProjectsP8 – How Far Can I Run in 10 Seconds?From the Sea to the StarsP11 – S-s-s-s sizzle!P12 – Brrrr!

55

Third Grade

Unit Page

1 – Routines, Review, and Assessment 45

2 – Adding and Subtracting Whole Numbers 46

3 – Linear Measures and Area 48

4 – Multiplication and Division 50

5 – Place Value in Whole Numbers and Decimals 52

6 – Geometry 54


8 – Fractions 58


10 – Measurement and Data 62

11 – Probability (End-of-Year Review) 64

56

3rd Grade EMUnit Title Secure ;




1Routines, Review and Assessment

Secure1g: Know basic addition facts

Developing/Secure1b: Count by 10s and 100s

1c: Apply place-value concepts in 4-digit numbers

1d: Tell and show times to the nearest minute

1e: Count combinations of bills and coins and write the total in dollars and cents notation

1f: Find equivalent names for numbers

1.2number gridnumber grid puzzleodometer1.3data bank1.4 tool kit1.5bar graphrangemode maximumminimum1.6name-collection box1.7difference1.9decimaldecimal pointmake change1.10sale priceregular priceestimateestimationcalculate1.12elapsed time

Within the LessonAdjustment1.6., part 11.8, Part 11.11, Part 11.12, part 1Part III1.1: Comparing common uses of numbers1.2: making number grid puzzles1.5: Finding which name has the greater total number of letters1.6: making name-collecting boxes1.7: Counting back past zero1.11: Coloring a designLiteracy Extensions1.7 Twelve Ways to Get to Eleven1.9 26 Letters and


57

99 Cents

58





2Adding and Subtracting Whole Numbers

Secure2d: Know basic addition and subtraction facts

2e:Complete fact and number families

2f: Solve addition and subtraction multi digit number stories

2g: Add multi digit numbers

2h: Subtract multi digit numbers

Developing/Secure2b: Use basic facts to solve fact extensions

2c Complete “What’s My Rule?” tables

2.1measurement unitfact familyturn-around rulenumber family2.2complement2.3function machineinputoutput2.4parts-and-total number storyparts-and-total diagramnumber modelballpark estimatepartial-sums method2.8trade-first method2.9addend

Adjustment2.2, Part 22.3, Part 12.6, Part 12.8, Part 12.9, Part1Part III2.2: Playing name that number using multiples of 102.4: solving missing-addend number stories2.5: Writing and solving change number stories2.6: Comparing data2.7:Making up addition problems based on a mileage map

ExtensionsFrom the Sea to the Stars P1 - Our Presidents P7 - Hawaiian Volcanoes

59

GamesSubtraction Target PracticeHigh Number TossBuzz Games

60





3Linear Measures and Area

Secure3c: Measure line segments to the nearest ¼ inch

3d: Measure line segments to the nearest centimeter

3.1standard unitlength3.2inch, in.line segmentcentimeter, cmmillimeter, mm3.3U.S. customary systemmetric systemfoot yardpersonal referencesmillicentimeterdecimeter3.4trianglesquarerhombusrectangleparallelogramtrapezoidperimeterpolygongirth3.5tilingarea

Within the LessonAdjustment3.2, Part 13.5, Part 13.6, Part 13.7, Part 1Part III3.1 Comparing Random Samplings3.2 Nonzero mark on a ruler3.3 Estimation scavenger hunt3.4 Shipping requirements for packages3.8 Circumferences in Literacy Extensions and historyLiteracy Extensions3.1 Counting on Frank3.1 How Big is a Foot?3.5 A Cloak for the Dreamer3.8 The Librarian Who Measured the

Exemplars3.4 Valentine PartySet UpMarch, 19973.5 Patty’s PartySpring Math, 19993.5 Garden FencesSpring Math, 20003.6 Grandfather TangMarch 19973.6 Jazzing Up YourBedroomWinter Math, 1998

Prism Kits#26 Measurement ToolsMaterials to measure a variety of liquid and linear objects

61

3.6areasquare footsquare yard3.8circumferencediametercentercircle rule

EarthExtensionsGamesGrid SearchProjectsP1 – Solid WasteP2 – Watermelon Feast & Seed Spitting ContestP3 - Illusions

62

3rd Grade EMUnit Title Secure;




4Multiplication and Division

Secure4f: Know multiplication facts having 0 or 1 as a factor

Developing/Secure4d: Know multiplication facts having 2, 5, or 10 as a factor

4e: Complete multiplication/division fact families

4.1multiplication/division diagrammultiplicationmultiples of equal groups4.2arrayfactorproduct4.4quotientdividenddivisorremainder4.5factorproductfact powerturn-around shortcutsquare numbers4.9map scalescale factor

Within the LessonAdjustment4.1, Part 14.6, Part 14.8, Parts 1,24.9, Part 1Part III4.1 Multiplication and Literacy Extensionsliterature4.2 Solving multiplication number stories with “thinking extensions”4.2 Arrays in Literacy Extensionsliterature4.5 square facts and Literacy Extensionsliterature4.7 Playing baseball multiplication4.9 Estimating distances4.9 Researching a

Exemplars4.3 Shovel, Shovel, Shovel100 Best Tasks of 1997

63

“Pretend Trip”Literacy Extensions4.1 Each Orange Had Eight Slices: A Counting Book4.1 Sea Squares 4.2 One Hundred Hungry Ants4.8 A Remainder

ofOne

ExtensionsGamesDivision DashMultiplication WrestlingCalculator 10,000ProjectsP2 – Watermelon Feast and Seed Spitting ContestFrom the Sea to the StarsP14 - Leap Year

64

3rd Grade EMUnit Title Secure;




5Place Value in Whole Numbers and Decimals

Secure5g. Read, write, and compare whole numbers up to 5 digits

5h. Identify place value in whole numbers up to 5 digits

Developing/Secure5f. Know multiplication facts from the first set of Fact Triangles

5.1onestenshundredsthousandsten-thousands5.2maximummedian< (is greater than)> (is less than)5.3hundred-thousandmillion5.4populationcensus5.5pie graph5.6cube longflatbig cube5.7tenthshundreds5.9decimeter5.10thousandths

Within the LessonAdjustment5.2, p 15.3, p 15.4, p 15.7, p 15.8, p 15.9, P 15.10, p 1Part III5.1 Working with patterns on a 100- number grid5.3 Collecting very large numbers5.4 Examining world population growth data5.5 Reading about very large numbers5.5 Calculating the age of presidents5.7 Collecting very small numbers5.9 Writing about tenths and hundredths5.10 Exploring place value beyond thousandths

65

precipitationmillimeter5.12line graph

5.12 Examining head-size dataLiteracy Extensions5.3 A Million Fish…More or Less How Much is a Million? If You Made a Million

ExtensionsGamesFraction/Percent ConcentrationGetting to OneProjectsP5 – Dodecahedron CalendarFrom the Sea to the StarsP2 - Big Hunk of British P3 - The Magnitude of Stars

66

3rd Grade EMUnit Title Secure




6Geometry

Secure6d. Know multiplication facts from the first set up Fact Triangles

6e. Identify right angles

6f. Identify and name 2-D and 3-D shapes

6g. Identify symmetric figures and draw lines of symmetry

6.1line segmentsgmentendpointrayline6.2parallelintersectangle6.3clockwiseanglevertexside (of an angle)clockwise (right turn)counterclockwise (left turn)right angle6.4triangleside (of a triangle)vertex (of a triangle)angle (of a triangle)equilateral triangleright triangle6.5quadrangle

Within the LessonAdjustment6.1, p 1,26.5, p 16.8, p 16.9, p 16.10, p 16.12, p 1Part III6.1 Creating “Curved” patterns6.3 Playing the Robot Game6.5 Adding to the Polygon Museum6.6 Solving a polygon cut-up problem6.8 Solving degree problems using a clock6.9 Line symmetry in Literacy Extensionsliterature6.11 Constructing a cube6.12 Modeling a slanted cylinder6.12 Examining a

Prism Kits#32 Six sets of pattern blocks and activities to discover fractions, shapes, and symmetry

67

squarerhombusparallelogramrectangletrapezoidadjacent sideskite6.6polygonregular polygon6.7rotationvertical6.8degree6.9symmetryline of symmetry6.10congruent3-dimenstional2-dimensionalconecylinderspherepyramidprismpolyhedronfaceedge vertexbase of a pyramidparallelbases of a prismrectangular prismtriangular prism

slanted prism

Literacy Extensions6.1 Opt: An Illusionary Tale6.5; 6.11 Shapes, Shapes, Shapes6.5, 6.11 The Art of Shapes for Children and Adults6.6 The Greedy Triangle6.9 Lao Lao of Dragon Mountain

ExtensionsGamesDart GameGeometry 5 QuestionsName That PolygonPocket Billiards GameProjectsP4 - Constellations

68

hexagonal prism






None 7.1square productsquare number factorproduct7.4parentheses7.6extended fact7.7estimate7.8range7.9similar figures

Within the LessonAdjustment7.0, p. 1Part III7.1 exploring a pattern in a sequence of products7.1 Reading a story about square numbers7.3 Playing the advanced version of multiplication bingo7.5 Examining basketball scores7.7 Calculating paper consumptionLiteracy Extensions7.1 Sea Squares 7.2 Cupid and PsychePegasusPersephone and the Pomegranate: A Myth from Greece

69

ExtensionsGamesPick Extensions games from Unit 3, 4, 5, 6 based on students needsProjectsP2 – Watermelon Feast & Seed Spitting Contest

70





8Fractions

None 8.1whole (the ONE)denominatornumerator8.4equivalent fractions8.6mixed number

Within the LessonAdjustment8.4, P 18.5, P 1,28.6, P 18.7, P 1Individual8.1 Fractions in Literacy Extensionsliterature8.2 making fraction name-collection boxes8.4 Playing the advanced version of the Equivalent Fractions Game8.5 Ordering sport balls by diameter8.7 Connecting to Literacy Extensions8.1 Ed Ember ley’s Picture Pie: A Book of Circle ArtGator PieEating Fractions8.7 Math Curse

Extensions

Exemplars8.1 Renting Craft SpaceFall Math, 1999

71

GamesFraction % Concentration

ProjectsP5 – AttributesFrom the Sea to the StarsP2- Big Hunk of British P3 - Our Presidents

72






None 9.4algorithmpartial-products algorithm9.6factor9.9lattice multiplication9.10equilateral triangle9.13Fahrenheit scaleDegrees FahrenheitCelsius scaleDegrees Celsius

Within the LessonAdjustment9.5, P 19.6, P 19.7, P 19.8, P 19.13, P 1Part III9.1 Finding out more about animals9.2 Solving an allowance problem9.4 Using count by patterns9.8 Solving division number stories9.9 Multiplying and dividing multiples of 10 in the context of time9.12 Using the Lattice method to multiply 2-digit numbers by 2 - digit numbers9.13 Using data expressed with positive and negative numbers

ExemplarsRenting Craft SpaceFall Math, 1999

73

from a tableLiteracy Extensions9.1 Anno’s Magic SeedsDK Nature EncyclopediaThe Simon & Schuster Encyclopedia of Animals: A Visual Who’s Who of the World’s CreaturesEyewitness Natural World

ExtensionsGamesPick from multiplication and fraction Extensions games from earlier units based on student needsProjectsP2 – Watermelon Feast & Seed Spitting Contest

74





10Measurement and Data

Developing/Secure10h. Make a bar graph

10.2height of a prismvolumecubic centimetersquare centimetersquare inchesweightcapacity of a scaleprecisioncapacity (of a container)mean averagemedianfrequency tablemodecoordinate gridcoordinateordered pair

Within the Lesson10.3, P 110.4, P 110.10, P 1Part III10.1 Finding a hidden treasure10.2 Exploring the volume and weight of popcorn10.4 Connecting math to Literacy Extensionsliterature10.5 Finding the volume and weight of popcorn10.6 A volume experiment10.7 Finding a median time for holding one’s breath10.8 Comparing height

ExtensionsGame s Grid SearchProjects

Prism Kits#26 Measurement ToolsMaterials to measure a variety of liquid and linear objects

#25 Measurement 1 and 2Discover area, mass, volume, and density

#17 Height-O-MeterGEMS measure heights of tall things

75

P6 – How far can you go in a million steps?

From the Sea to the StarsP6 - Body Temperature P5 - How Big are Your Feet?P7 -Hawaiian Volcanoes P9 - Hot & Cold P10 -All Over the World P11 - S-s-s-sizzle!P12 – Brrr!P13 - Predicting the Weather

76





11ProbabilityEnd-of-Year Review

None 11.1event11.2headtailsfairequally likely11.6random draw11.8winter solsticesummer solsticeautumnal equinoxvernal equinox

Within the LessonAdjustment11.2, P 311.5, P 111.6, P 111.7, P 111.9, P 1Part III11.1 Doing probability activities from The I Hate Mathematics! book11.2 Predicating the results of rolling 2 dice11.3 Sorting a large set of coins by heads or tails 11.4 Designing and testing spinners whose outcomes are not equally likely11.5 Designing, describing, and testing spinners11.5 Playing Spinning to Win11.6 Playing The

Prism Kits#19 In All ProbabilityGEMS penny flip, spinner, dice, and game sticks

77

Block-Drawing Game11.9 Finding the highest and lowest temperatures on earthLiteracy Extensions11.111.1 The I

Hate Mathematics! Book

ExtensionsGamesGreedyFrac-tac-toeFraction ActionFraction Fiction

78

Fourth Grade

Unit Page

1 – Naming and Constructing Geometric Figures 67

2 – Using Numbers and Organizing Data 69

3 – Multiplication and Division; Number Sentences and Algebra 71

4 – Decimals and Their Uses 73

5 – Big Numbers, Estimation, and Computation 75

6 – Division; Map Reference Frames; Measures of Angles 77

7 – Fractions and Their Uses; Chance and Probability 79

8 – Perimeter and Area 81

9 – Percents 82

10 – Reflections and Symmetry 84

11 – 3-D Shapes, Weight, Volume and Capacity 85

12 – Rates 87

79

5th5th5th5th5th5th5th4th Grade EMUnit Title Secure;




1Naming and Constructing Geometric Figures

Number Theory

Secure1d: Name, draw, and label line segments, lines, and rays 1e: Name, draw, and label angles, triangles, and quadrangles 1f: Identify and describe right angles, parallel lines, and line segments 1g: Know addition and subtraction facts1f: Draw arrays to model multiplication1g: Know basic multiplication facts1h: Identify even and odd numbers1i: List the factors of a number

1.2line segmentendpoint ray1.3 anglevertexquadrangle quadrilateral, rhombus parallelogram trapezoid1.4parallel linesintersect1.5 polygon convexconvex polygon

nonconvex or concave polygon1.2 rectangular arraynumber modelturn-around ruleperpetual calendar1.3 factorproductfactor pair1.5

Within the LessonAdjustment1.4, part 11.6, part 11.7, part 1Part III1.1 Reading a math story1.5 Connecting Polygons to literature1.6 Creating circle designs1.7 Drawing Tangent Circles1.8 Creating 6-point DesignsLiteracy Extensions1.1 Math Curse1.3 The Art of Shapes for Children and Adults; Shapes, Shapes, Shapes1.5 The Greedy Triangle 1.6 Ed Ember ley’s Picture Pie: A Circle Drawing


Writing ProjectNimble with Numbers

80

factor rainbowdivisiblequotientdivisibility test1.7square arraysquare numberexponential notationexponent kyexponent1.8“unsquaring” a numbersquare rootsquare-root key1.9name collection boxfactor stringlength of factor stringprime factorization

Book

ExtensionsGamesAngle TanglePolygon Capture3-D Shape Sort

Within the LessonAdjustment1.2, part 11.4, part 11.6, part 11.9, part 1Individual1.1 Appreciatingarithmetic in poetry1.2 Findingrectangular arrays in a perpetual calendar1.4 Playingthe advanced version of Factor Captor1.5 Exploring a divisibility test by 41.6 Investigating Goldbach’s conjecture1.7 Completing patternsLiteracy1.1 “Arithmetic”

81

by Carl SandburgGamesBaseball MultiplicationBeat the CalculatorFactor BingoFactor CaptorFactor Top-ItMultiplication Top-ItName That NumberProjectsOne: The Sieve of EratosthenesTwo: Deficient, Abundant, and Perfect Numbers

82

4th Grade EMUnit Title Secure




2Using Numbers and Organizing Data

Secure2c. Use the statistical landmarks maximum and minimum 2d. Subtract multi digit numbers2e. Add multi digit numbers2g. Find equivalent names for numbers

Developing/Secure2a. Display data with a line plot, bar graph, or tally chart

2f. Read and write numerals to hundred-millions; give the value of the digits in numerals to hundred-millions

2.3digitplace2.5guessestimatetally marklandmarkmaximumminimumrangemode2.6line-plotmedian2.7partial-sums methodcolumn edition method2.8bar graph2.9trade-first methodpartial-differences method

Within the LessonAdjustment2.3, part 12.4, part 12.5, part 22.6, part 22.7, part 12.9, part 1Part III2.1 Using a Map Scale to Find Distance2.2 Playing Name that Number with multiples of 102.3 Reading about large numbers2.5 Making a prediction based on a sample2.6 Comparing family size data2.8 Determining the validity of the “one size fits all” claimLiteracy Extensions2.2 Twelve Ways To Get Eleven2.3 If You Made A

2.6 A Fair Snack?Fall, Math 1999

83

Million; How Much Is A Million

ExtensionsFrom the Backyard to the Great WallP12 – Investigating Your Own Garbage

84

Unit Title SecureDeveloping/SecureGoals



3Multiplication and Division; Number Sentences and Algebra

Secure3h: Understand the relationship between multiplication and division

Developing/Secure3d: Solve addition and subtraction number stories

3g: Know basic multiplication facts

3.1multiplication factsfactorproductsquare numbersturn-around facts3.2percent3.4dividenddivisorquotientremainderfact family3.8number sentencetrue number sentencefalse number sentence3.9parentheses3.10variableopen sentencesolvesolution3.11logic gridlogic

Within the LessonAdjustment3.3, part 13.3, part 23.9, part 1Part III3.5 Using the internet to find country facts3.7 Solving and writing number stories3.10 Writing open sentences3.11 Creating logic puzzles3.11 Solving mathematical puzzlesLiteracy Extensions3.1 Sea Squares ;

Each Orange Had Eight Slices: A Counting Book3.11 Anno’s Hat Tricks; National Geographic Atlas for Young Explorers

Exemplars3.11 Another Domino Dilemma100 Best Tasks,1997

WebsitesMathStories.comMath problem-solving and critical thinking

Southwest Missouri State University’s Links to Other Puzzles and Problem Web PagesLinks to math puzzles and pages

85

ExtensionsGamesMultiplication BullsyeFactor CaptorFactor Top-ItAlgebra ElectionFirst to 100500Top It Games with Positive and Negative NumbersFrom Your Backyard to the Great WallP19 – Dinosaur Weights

86





4Decimals and Their Uses

Secure4h: Draw and measure line segments to the nearest centimeter 4i: Use dollars-and-cents notation

4.1ONE whole unittenthhundredth4.3odometertrip meterspeedometer4.5depositwithdrawalbalanceinterest4.6thousandths4.7centimeter (cm)millimeter (mm)meter (m)decimeter (dm),4.8personal measurement reference

Within the LessonAdjustment4.5, part 24.8, part 14.9, part 14.10, part 1Part III4.2 Writing Decimal Riddles4.3 Finding a Car’s Gasoline Mileage4.5 Solving Hiking Trail Problems4.7 Searching For Superlatives for Metric Units of Length4.8 Designing a Measurement Scavenger Hunt; Writing4.10 Solving Place-Value Puzzles

Exemplars4.4 Zeno the Xylophone Maker100 Best Tasks, 1997

LiteratureTop Ten of Everything 2000; Scholastic Kids Almanac for the 21 st Century

87

Literacy Extensions4.2 Kids Are Puny: Jokes Sent By Kids to the Rosie O’Donnell Show; Kids Are Puny 2: More Jokes Sent By Kids to the Rosie O’Donnell Show

ExtensionsGamesHigh Number Toss Decimal Version

From Your Backyard to the Great WallP5 – Maple SyrupP6 – Figuring the FigureP10 – How Much Does Your Garbage Weigh?P17 – Drawing Dinosaurs to Scale

88





5Big Numbers, Estimation, and Computation

Secure5g: Compare large numbers

5h: Estimate sums

5.1extended multiplication facts5.3estimation5.4rough estimate5.5partial-products methodpartial product5.7lattice methodlattice5.8millionbillion5.9trillionquadrillionquintillionsextillionpowers of 10exponent5.10rounding

Within the LessonAdjustment5.6, part 15.9, part 15.10, part 1Part III5.1 Solving multiplication/division puzzles; writing and solving multiplication number stories with multiples of 105.3 Solving number puzzles; solving a traveling salesperson problem5.4 Making prediction from data5.7 Comparing calculation speeds for the partial-products and lattice methods5.8 Exploring big numbers in literature; estimating the number of dots and the weight of paper needed to fill the

89

classroom5.9 Beginning a big numbers list5.10 Comparing marathon data; representing population counts with dot paper5.11 Understanding geographical measurementsLiteracy Extensions5.4 In the Next

Three Seconds 5.8 How Much is a Million?; If You Made a Million

ExtensionsFrom the Sea to the StarsP3 – The Magnitude of the StarsP4 – The ConstellationsP5 – A Day and a Year in SpaceGamesEstimation SqueezeAlgebra ElectionTop It Game with Positive and Negative NumbersExponent BallScientific Notation

90

Toss

91

4th Grade EMUnit Title Secure;




6Division; Map Reference Frames; Measures of Angles

None Adjustment6.4, part 26.6, part 16.8, part 1Part III6.2 Taking the calculator challenge6.4 Exploring remainders in literature6.5 Playing Grid Search6.6 Solving

elapsed-time problems6.9 Making a model of a world globeLiteracy Extensions6.4 A Remainder of One

ExtensionsProjectsP1 – Making a Cutaway GlobeP2 – Using a Magnetic CompassFrom Your Backyard to the Great Wall

Digging a tunnel

Looking up latitudes and longitudes on the Internet

Finding out about compasses and orienteering

92

P9 – Not In My Backyard!P4 – The Great Wall of ChinaP15 – Did Dinosaurs Really Live in the United States?GamesAngle TangleHidden Treasure

93

4th Grade EMUnit Secure;




7Fractions and Their Uses; Chance and Probability

Secure7f: Identify the whole for fractions

7g: Identify fractional parts of a collection of objects

7h: Identify fractional parts of regions

7.1whole (or ONE or unit)denominatornumerator“whole” boxmixed number7..7equivalent fractionsEquivalent Fractions Rule7.11fair (die or spinner)equal chanceexpectequally (more, less) likely

Within the LessonAdjustment7.6, part 17.7, part 1Part III7.1 Constructing an equilateral triangle7.1 Creating fraction art7.2 Writing and solving “fraction-of” number stories7.3 Exploring tangrams7.5 Modeling fractions with other denominators on a clock face7.9 Using digits to create fractions7.10 Naming fractional parts of a region7.11 Reading about chance events7.12 Comparing actual and expected results of 1,000 cube drops

Exemplars7.3 Tan gram MoneyOctober, 1993Stained Glass Surprise100 Best Tasks 1997

7.7 Great Pizza DilemmaMarch, 1994

Prism Kits#19 In All ProbabilityGEMS penny flip, spinners, dice, and game sticks

Have students create their own games

94

Literacy Extensions7.1 Gator Pie; Eating Fractions7.3 Grandfather Tang’s Story7.11 Do You Wanna Bet? Your Chance to Find Out about Probability

ExtensionsProjectsP7 – A Carnival GameFrom Your Backyard to the Great WallP6 – Figuring the FigureGamesFrac-Tac-ToesFraction Action, Fraction FrictionFraction Multiplication Top-ItFraction SpinMixed Number Spin

95

4th Grade EMUnit Secure;




8Perimeter and Area

Developing/Secure8d: Find the area of a figure by counting unit squares and fractions of unit squares inside the figure

8.1time-and-motion studywork triangleperimeter8.2rough floor planscale drawingscale8.3areasquare units8.5basewidthlengthheightareaformulavariable8.6baseheightperpendicular8.7equilateral triangleisosceles trianglebase height

Within the LessonAdjustment8.3, part 18.4, part 28.6, part 28.7, part 18.8, part 1Individualizing8.2 Making a scale drawing of your bedroom8.6 Constructing figures with a compass and straightedge8.7 Comparing areas8.8 Using division to compare numbers of mammal species

ExtensionsGamesFrom Your Backyard to the Great WallP11 – Can You Make Less Garbage?

Prism Kits#25 Measurement 1 and 2Discover area, mass, volume, and density

96

P16 – Dinosaurs – The long and short P17 – Drawing Dinosaurs to Scale

97





9Percents

Secure9e: Convert between “easy” fractions (fourths, fifths, and tenths), decimals, and percents9f: Use a calculator to rename any fraction as a decimal or percent.

9.1percent100% box9.3terminating decimalrepeating decimal9.4regular price or list pricediscountpercent or fraction of discountsale price9.7urbanrurallife expectancyliterate and illiteratepercent of

9.1 Making a Percent Booklet or Poster9.4 Solving Challenging Discount Number Stories9.4 Estimating What Percent of a Circle Graph is Shaded9.6 Graphing Survey Results9.6 Reading about comparisons9.7 Ranking Countries and Coloring a Map to Show Literacy Extensions Data9.9 Writing and Solving Division Number Stories with DecimalsLiteracy Extensions9.3 Gator Pie; Eating Fractions9.6Incredible

Literature ExtensionsInside the Amazon by Lessen, Don and Michael Rothman

The Brazilian Rain Forest, by Siy, Alexandra

Rain Forest, by Taylor, Barbara

Math WebsitesMighty M& M MathPercentages with M & M’s

98

Comparisons

ExtensionsFrom Your Backyard to the Great WallP7 – PenniesP9 – Not in My Backyard

99





10Reflections and Symmetry

Secure10d: Use a transparent mirror to draw the reflection of a figure

10e: Identify lines of symmetry, lines of reflection, reflected figures, and figures with line symmetry

10.1transparent mirrorrecessedimagepreimage10.2reflectionline of reflection10.4line of symmetrysymmetricturn symmetry10.5frieze patternreflection (flip)translation (slide)rotation (turn)10.6opposite (of a number)creditdebit

10.1 Exploring Reflected Images and Symmetry in Literature10.3 Researching the Reflecting Pool in Washington, D.C.10.4 Exploring Turn Symmetry10.5 Creating Frieze Patterns10.6 Solving a Temperature Number StoryProjectsP4 – Making a QuiltP7 – Numbers, Maya StyleExtensionsGamesCredits/Debits Game

Literature ConnectionsShadows and Reflections, by Hoban, Tana

Reflections, by Jonas, Ann

Round Trip, by Jonas, Ann

The Mirror Puzzle Book, by Walter, Marion

The Monster Money, by Leedy, Loreen

How the Second Grade Got $8205.50 to Visit the Statue of Liberty, by Zimelman, Nathan

Prism Kits#28 MIRA MathDiscover symmetry by using reflections

100


GoalsDeveloping/ Secure Goals



113-D Shapes, Weight, Volume, and Capacity

None 11.1gram11.2rectangular prismtriangular prismsquare pyramidcylinderconespheregeometric solidcurved surfacecubeedge faceflat surface11.3polyhedrontriangular pyramiddodecahedron11.4cubic unitsvolumedimensions11.7capacity

Within the LessonAdjustment11.2, part 111.3, part 1, 311.4, part 1, 211.7, part 1Part III11.1 Comparing Mammals’ Weights11.3 Writing and Solving “What Am I?” Riddles11.3 Drawing a Cube11.3 Making a Model of a Tetrahedron11.5 Estimating the Volume of a Sheet of Paper11.7 Modeling the Capacity of Annual Rice Consumption11.7 Doubling Grains of RiceLiteracy Extensions 11.3 Ed Emberley’s Big Green (Orange, Purple, and Red Drawing Book

Prism Kits#25 Measurement 1 and 2Discover areas, mass, volume, and density

101

11.1 Is a Blue Whale the Biggest Thing There is?What’s Smaller Than a Pygmy Shrew?11.7The King’s Chessboard

ExtensionsGamesAngle TanglePolygon Capture3D Shape SortProjectsP6 – Building and Viewing StructureFrom Your Backyard to the Great WallP11 – Can You Make Less Garbage?

102

Grade 4 EMUnit Title Secure;




12Rates

Secure 12e: Use rate tables, if necessary, to solve rate problems

12.1rate per12.2 rate table unit rate12.3unit-price label12.4 consumerproducts servicescomparison shopping unit price

12.1 Collecting Follow-Up Data on Eye-Blinking Rates12.2 Solving Mammal Speeds Problems12.3 Solving Mammal Heart Rates Problems12.3 Analyzing Data12.4 Testing Products with Zillions Magazine12.5 Comparing Prices12.6 Exploring the Culture, Geography, and History of Countries through NumbersProjectsP5 – Which Soft Drink is the Best to Buy?GamesSpoon ScrambleExponent Ball

Count Your Way Through…(Series), by Haskins, Jim and Kathleen Benson

Alma UnitsMayan Mathematics and Architecture

103

Fifth Grade

Unit Page

1 – Number Theory 89

2 – Estimation and Computation 91

3 – Geometry Explorations and the American Tour 93

4 – Division 95

5 – Fractions, Decimals, and Percents 96

6 – Using Data: Addition and Subtraction of Fractions 98

7 – Exponents and Negative Numbers 100

8 – Fractions and Ratios 102

9 – Coordinates, Area, Volume, and Capacity 104

10 – Algebra Concepts and Skills 106

11 – Volume 108

12 – Probability, Ratios, and Rates 109

104

5th Grade EM

105

5th Grade EDMUnit Title Secure;




2Estimation and Computation1Number Theory

Secure1f: Draw arrays to model multiplication and decimals2g: Identify the maximum, minimum, median, mode, and mean for a data set1g: Know basic multiplication facts1h: Identify even and odd numbers1i: List the factors of a number

Developing/Secure1c: Use a divisibility test to determine if a number is divisible by another number1d: Identify prime and composite numbers1e: Understand how square numbers and their

1.1.2.2 valuedigitplaceplace valuealgorithmpartial-sums methodcolumn-addition method2 rectangular arraynumber modelturn-around ruleperpetual calendar1.3 trade-first methodpartial-differences method2.4number sentencesrelations symboloperations symbolvariableopen sentencesolutioncomparison story2factorproductfactor pair1.5mean

Within the LessonAdjustment1.1.2.1, part 11.4 part 11.6, part 11.9, part 1Part III1.1 2.1 Reading a book about estimation2.2 Solving place-value puzzles2.4 Solving challenging number stories2.5 Making predictions based on outcomes of a probability experiment2.9 Exploring an ancient multiplication method2.10 Solving a large number problem2.10 Reading about large numbers

Exemplars2.6 The Valentine Candy Challenge100 Best Tricks of 19972.8 Job Hunting100 Best Tasks of 1997Writing ProjectNimble with Numbers

Dale Seymour Calendar

Math WebsitesKidsKonnect.com Math SitesMultiple math sitesJanBrett.com Home Page2,389 pages of free activities, coloring pages, and productsAAA MathLots of different math activitiesAunty MathA regular math challenge

106

square roots are related

stimulusreaction timeminimummaximumrangemode median

2.6impossiblecertainProbability Meter Posterlikelyunlikely50-50 chance2factor rainbowdivisiblequotientdivisibility test1.7square arraysquare numberexponential notationexponent1.square arraysquare numberexponential notationexponent kyexponent18“unsquaring” a numbersquare root1.9factor string

Appreciatingarithmetic in poetry1.2 Findingrectangular arrays in a perpetual calendar1.5 Playingthe advanced version of Factor Captor1.5 Exploring a divisibility test by 41.6 Investigating Goldbach’s conjecture1.7 Completing patternsLiteracy Extensions2.1 Counting on Frank2.10 How Much is a Million?

Extra Challenge1.2 “Arithmetic” by Carl SandburgProjectsP3 - An Ancient Multiplication AlgorithmP4 - Magic Computation TricksFrom the Sea to the Stars

107

length of a factor string

prime factorizationname collection boxfactor stringlength of factor stringprime factorization

P2 – Big Hunk of BritishP1 - The SieveSeive of Eratosthenes

P2 - Deficient, Abundant, and Perfect Numbers

108





2Estimation and Computation

Secure2f: Find the sum and difference of multi digit whole numbers and decimals

2g: Identify the maximum, minimum, median, mode, and mean for a data set

Developing/Secure2c: Make magnitude estimates

2d: Find the product of multidigit whole numbers and decimals

2e: Know place value to billions

2.2valuedigitplaceplace valuealgorithmpartial-sums methodcolumn-addition method2.3trade-first methodpartial-differences method2.4number sentencesrelations symbolvariableopen sentencesolution2.5meanminimummaximumrangemode median

Within the LessonAdjustment2.1, part 12.6, part 1Part III2.1 Reading a book about estimation2.2 Solving place-value puzzles2.4 Solving challenging number stories2.5 Displaying reaction time in line plots2.6 Making predications based on outcomes of a probability experiment2.9 Exploring ancient multiplication methods2.10 Solving a large number problem2.10 Reading about large numbersLiteracy Extensions

Exemplars2.6 The Valentine Candy Challenge100 Best Tasks of 19972.8 Job Hunting100 Best Tasks of 1997


109

2.1 Counting on Frank2.10 How Much is a Million?

ExtensionsProjectsP3 – An Ancient Multiplication AlgorithmP3 – Magic Computation Tricks

110

5th Grade EM

111




3Geometry Explorations and the American Tour3Geometry Explorations and the American Tour

Secure3f: Identify place value in numbers to billions3g: Know properties of polygons3h: Define and createtessellations

Developing/Secure 3b: Estimate the measure of an angle3e: Identify types of triangles3c: Measure an angle within 2 degrees3d: Identify types of angles3e: Identify types of triangles2f: Find the sum and difference of multidigit whole numbers and decimals2g: Identify the maximum,

2.2valuedigitplaceplace valuealgorithmpartial-sums methodcolumn-addition method2.3.1 census3trade-first methodpartial-differences method2.4 acute angleobtuse angleright anglestraight anglereflex anglegeometry template3number sentencesrelations symboloperations symbolvariableopen sentencesolutioncomparison story2.5 radiuscenter

Within the LessonAdjustment3.3,3.3, part 13.4, part 133.4, part 13.6, part 1Individual izing 3.1 Reporting on census information3.2 Ranking states by their Native-American populations3.4 Exploring the geometry template3.5 Solving a baseball challenge3.5 Inscribing a regular hexagon in a circle3.7 Reading about polygons3.82.1 Reading a book about estimation2.2 Solving place-value puzzles2.4 Solving challenging number stories

Fractiles – 72525 Arapahoe Ave.Suite E4-110Boulder, CO 80302

Math WebsitesGeometry from the Land of the IncasAn eclectic mix of sounds, science, and Incan history intended to interest students in Euclidean geometryExemplars2.6 The Valentine Candy Challenge100 Best Tricks of 19972.8 Job Hunting100 Best Tasks of 1997

112

minimum, median, mode, and mean for a data set

diametervertical anglesadjacent angles3meanstimulusreaction timeminimummaximumrangemode median

2.6equilateral triangleisosceles trianglescalene triangle 3impossiblecertainProbability Meter Posterlikelyunlikely50-50 chance2.7magnitude estimate2.8congruentregular polygontessellate3partial-products method2.9lattice methodlattice2.10radius

2.5 Making predictions based on outcomes of a probability experiment2.9 Exploring an ancient multiplication method2.10 Solving a large number problem2.10 Reading about polygons that tessellatelarge numbers3.9 Tessellating quadrangles3.10 Solving geometry template challengesLiteracy Extensions3.7 The Greedy Triangle3.8 A Cloak for a Dreamer3.10 Grandfather Tang’s Story3.7 The Greedy Triangle3.8 A Cloak for a Dreamer3.10 Grandfather Tang’s StoryExtensionsFour: Magic

113

diameterparallelunitperimeterparallelogrampentagonsample

Computation TricksFrom the Sea to the StarsP4 – The Constellations

P2 – Big Hunk of British

114





3Geometry Explorations and the American Tour

3f: Identify place value in numbers to billions3g: Know properties of polygons3h: Define and create

3b: Estimate the measure of an angle3c: Measure an angle to within 2 degrees3d: Identify types an angles3e: Identify types of triangles

3.1 census3.4 acute angleobtuse angleright anglestraight anglereflex anglegeometry template3.5 radiuscenterdiametervertical anglesadjacent angles3.6equilateralequlaterial triangleisosceles trianglescalene triangle 3.8congruentregular polygontessellate3.10radiusdiameterparallelunitperimeterparallelogrampentagon

Within the LessonAdjustment3.3, part 13.4, part 13.6, part 1Individualizing3.1 Reporting on census information3.2 Ranking states by their Native-American populations3.4 Exploring the geometry template3.5 solving a baseball challenge3.5 Inscribing a regular hexagon in a circle3.7 Reading about polygons3.8 Reading about polygons that tessellate3.9 Tessellating quadrangles3.10 Solving geometry template challengesLiteracy3.7 The Greedy

Fractiles – 72525 Arapahoe Ave.Suite E4-110Boulder, CO 80302

115

Triangle3.8 A Cloak for a Dreamer3.10 Grandfather Tang’s Story

Extra ChallengeGamesAngle TanglePolygon CaptureRobotFrom the Sea to the StarsP4 – The Constellations

116

5th Grade EM

117




4Division

Secure4h: Know place value to hundredths

4.1divisordividendquotientremainder4.2dividenddivisorpartial quotientremainder4.3map legend or keydirection symbolmap scale4.4magnitude estimate4.6variableopen number sentence

Within the LessonAdjustment4.1, part 14.2, part 14.5, part 14.6, part 1Part III4.4 Exploring an alternative division algorithm4.5 Writingdivision number stories4.6 Playing Algebra Election

ExtensionsFrom the Sea to the StarsP14 – Leap YearFrom Your Backyard to the Great WallP3 – Banjo, A Sailing StoryP4 – The Great Wall of China

WebsitesMathStories.comMath problem-solving and critical thinking

118

5th Grade EM

119

Unit Title Secure;Developing/SecureGoals



5Fractions, Decimals, and Percents

Developing/Secure5f: Convert between fractions and mixed numbers

5g: Find equivalent fractions

5.1 wholedenominatornumeratorunit fractions5.2improper fractionmixed number5.3equivalent fractionsfraction stick5.5round downround upround to the nearest…5.7repeating decimal5.8percent5.9bar graphcircle (or pie) graphpercent circle

Within the LessonAdjustment5.2, part 15.4, part 15.5, part 15.6, part 15.7, part 15.8, part 15.11, part 25.12, part 15.13, part 1Part III5.4 Introducing “fraction-of” problems with fraction sticks5.7 Extending the partial-quotients division algorithms to decimals5.9 Acting out the construction of a circle graph5.10 Conducting an eye test5.11 Making a graph museum5.12 Finding out about American historyHistory

Exemplars5.3 Candy PartyVolume 7Spring, 2000

Play the Stock Market Game with the Denver Post. Interpreting graphs and data, making decisions based on financial information, graphing stocks, and team work are skills included.

120

ExtensionsGamesDoggone DecimalProjectsP5 -Five: How Would You Spend $1,000,000?From the Sea to the StarsP2 – Big Hunk of the BritishP12 – Brrr!From the Backyard to the Great WallP10 – How much does your garbage weigh?

121

5th Grade EM

122




6Using Data; Addition and Subtraction of Fractions

Secure6h: Find and use data landmarks

Developing/Secure6g: Convert among fractions, decimals, and percents

6.1organizing datalandmarkminimummaximumrangemodemedianmean (average)line plot6.2span cubitfathomfair game6.3spannormal spangreat spanstemleafstem and leaf plotangle of separation6.5sample6.6surveydecennialpopulationsamplefrequency table

Within the LessonAdjustment6.1, part 16.2, part 16.5, part 16.7, part 16.9, part 1Individualizing6.1 Identifying states visited by most students6.2 Learning about nonstandard units of measure6.3 Making a stem-and-leaf plot6.5 Investigating how sample size effects the results of chance events6.6 Interpreting data in the news6.7 Finding contour maps6.9 Writing elapsed time number storiesExtensionsFrom the Sea to the Stars

123

6.7contour mapclimateprecipitationcontour line6.8slide rulesliderholder6.9common denominatorunlike denominators6.10quick common denominatorsimplest form

P5 – How Big Are Your Feet?From the Backyard to the Great WallP13 – How Many Trees Does Your Class Use?GamesGreedyLandmark Shark

124

5th Grade EM

125




7Exponents and Negative Numbers

Developing/Secure7e: Understand and apply exponential notation

7f: Identify number sentences: tell whether a number sentence is true or false

7g: Understand and apply the use of parentheses in number sentences

7h: Order and compare positive and negative numbers

.

7.1exponential notationexponentbasefactorstandard notationpower7.3scientific notation7.4nested parentheses7.5order of operations7.6negative number7.7account balancein the blackdebt in the red7.8change diagram

Within the LessonAdjustment7.1, parts 1, 37.2, part 17.3, part 17.5, part 17.6, parts 1, 37.7, part 17.8, part 17.9, part 1Part III7.1 Exploring exponent patterns in Fibonacci numbers7.2 Introducing negative exponents and powers of 0.17.3 Students are introduced to negative powers of 107.5 Making up memories7.9 Solving missing addend, minuend, and subtrahend problems7.9 Comparing

Websiteswww.mcs.surrey.ac.uk/Personal/R.knott/Fiboanacci/fib.htmlFibonacci Numbers and the Golden Section

126

http://www.mcs.surrey.ac.uk/Personal/R.knott/

http://www.mcs.surrey.ac.uk/Personal/R.knott/

elevations7.10 Playing Broken Calculator to practice operations with positive and negative numbersLiteracy Extensions7.3 The Kings Chessboard by David Birch

ExtensionsFrom the Sea to the StarsP3 – The Magnitude of the Stars

127

5th Grade EM

128




8Fractions and Ratios

Secure8g: Convert among fractions, decimals, and percents

8h: Convert between fractions and mixed or whole numbers

8i: Find common denominators

Developing/Secure 8e: Use an algorithm to add mixed numbers

8f: Order and compare fractions

8.1quick common denominator8.4unit fraction8.5horizontalvertical8.6area model8.9discount8.10unit fractionunit percent8.11majority

Within the LessonAdjustment8.3, part 28.5, parts 1, 28.7, part 18.8, part 1Part III8.3 Playing Mixed Number Spin8.4 Playing the advanced version of Fraction Action, Fraction Friction8.6 Playing Fraction Multiplication Top-It8.7 Playing

Fraction/ Whole-Number Multiplication Top-It8.11 Students

write about population trends8.12 Solving division problems with fraction or mixed-number

129

answers

ExtensionsFrom the Sea to the StarsP16 – Knives and ForksP17 – Arleta and AngelaF18 – Selene Sits in a ShoeFrom the Backyard to the Great WallP6 – Figuring the Figure

130

5th Grade EM

131




9Coordinates, Area, Volume, and Capacity

Secure9g: Understand the concept of area of a figure9h: Use a formula to find the area of rectanglesDeveloping/Secure9d: Plot ordered pairs on a one-quadrant coordinate grid9e: Identify the base and height of triangles and parallelograms9f: Use a formula to find the area of triangles and parallelograms

9.1coordinate gridordered number paircoordinateaxis9.2transformation9.4baseheightformulavariablesquare unitsarea9.6perpendicular9.7latitudelongitude9.8volumecubic unitfacebase (of a rectangular prism)9.9prism9.10capacityliter

Within the LessonAdjustment9.1, part 29.3, part 19.6, part 19.7, part 29.10, part 1Part III9.1 Reading a story about coordinate grids9.3 Making reflected pictures9.5 Reading Spaghetti and Meatballs for All9.6 Calculating Area9.7 Solving area problems9.9 Finding the volume of one stick-on-note9.10 Reading a story about volumeStudents consider situations in which coordinate grids are used to represent

132

quartcupmillilitercubic centimeter

informationLiteracy Extensions9.1 The Fly on the Ceiling9.5 Spaghetti and Meatballs for All9.10 Mr. Archimedes’ Bath

ExtensionsProjectsP6 -Six: Sports ArenasP7 - Seven: Polygon Areas and Pick’s FormulaGamesHidden Treasure (Advanced)From the Backyard to the Great WallP15 – Did Dinosaurs Really Live in the United States?

133

5th Grade EM

134




10Algebra Concepts and Skills

Developing/Secure

10f: Solve one-step pan-balance problems

10g: Interpret mystery line plots and graphs

10.3algebraic expression10.4 raterate of speedformulavariableline graph10.5geyserpredict10.6ordered number pairscoordinates10.7mystery graph

Within the LessonAdjustment10.1, part 110.2, part 110.4, part 110.6, part 110.7, part 1Part III10.1 Solving a penny riddle10.2 Writing equations10.5 Graphing values from a table10.6 Graphing race results10.7 Collecting data for mystery graphs10.8 Passing your body through an index card10.8 Reading The Librarian Who Measured the Earth 10.8 Exploring internet resourcesLiteracy Extensions10.8 The Librarian Who Measured the

Exemplars10.4Winning Ticket100 Best Tasks of 199710.5 The Tower Problem100 Best Tasks of 1997

WebsitesSouthwest Missouri State University’s Links to Other Puzzles and Problems Web PagesLinks to math problem solving and puzzles

135

EarthExtensionsProjectsP8 - Eight: PendulumsGamesSolution SearchSpreadsheet Scramble

136

5th Grade EM

137




11Volume

Secure11f: Use formulas to find the area of polygons and circles

11g: Know the properties of geometric solids

Developing/Secure11e: Use formulas to find the volume of prisms and cylinders

11.1geometric solidprismpyramidcylinderconesphereedgevertexflat surfacecurved surfacefacepolyhedroncube11.2baseapex11.5displacementcalibrate11.7surface area

Within the LessonAdjustment11.2, part 111.5, part 111.7, part 1Part III11.1 Investigatingpolyhedral dice 11.2Writing stories about a 2-dimensional world11.5Reading about displacement11.6Researching about rice11.7Finding the smallest surface area for any given volumeLiteracy Extensions11.2 Flatland ;

TheBoy Who Reversed Himself11.5 Who Sank the Boat?

ExtensionsFrom the Backyard to the Great Wall

138

P5 – Maple Syrup

5th Grade EM

139




12Probability, Ratios, and Rates

Secure12g: Find and identify factors of numbers

12h: Find the prime factorizations of numbersDeveloping/Secure12f: Solve ratio and rate number stories

12.1 Factor treePrime factorizationCommon factorGreatest common factorLeast common multiple12.2 ProbabilityMultiplication Counting PrincipleTree diagramEqually likely12.3 RatioRatio comparisonMagnitude12.6 Heart ratePulsePulse rate12.7 RateProfileTarget heart rate12.8 OxygenNutrientsCarbon dioxideCardiac output

Within the LessonAdjustment12.1, part 112.2, part 112.3, part 112.4, part 212.6, part 212.7, part 112.8, part 1Part III12.2 Reading about probability12.3 Imagining 10 times more or 10 times less12.5 Introducing cross multiplication for solving ratio problems12.7 Collecting exercise data12.8 Searching the internetLiteracy Extensions12.2 Jumanji

ExtensionsFrom the Backyard to the Great WallP1 – Rattlesnake

Prism Kits#19 In All ProbabilityGEMS penny flip, spinners, dice, and games sticks

140

P2 – It’s All Relative

141

Sixth GradeUnit Page

1 – Collection, Display, and Interpretation of Data 112

2 – Operations with Whole Numbers and Decimals 114

3 – Variables, Formulas, and Graphs 115

4 – Rational Number Use and Operation 117

5 – Geometry, Congruence, Constructions, and Parallel Lines118

6 – Number Systems and Algebraic Concepts 120

7 – Probability and Discrete Mathematics 122

8 – Rates and Ratios 124

9 – More about Variables, Formulas, and Graphs 126

10 – Geometry Topics 128

142

6th Grade EMUnit Title Secure ;




1Collection, Display, and Interpretation of Data

Secure1d: Find equivalent names for numbers

1e: Identify landmarks of data sets

1f:Compute and understand the mean

1g: Interpret and understand broken line graphs

1h: Interpret and construct bar graphs

Developing/Secure1c: Use a % circle to interpret circle graphs

1.2line plotlandmarkminimummaximummedianmode range1.3name-collection boxoutliers1.5line graphbroken line graphprecipitation1.6bar graphside-by-side bar graphgraph keystacked bar graph1.7step graph1.8 % circlearcsectorradiuscircle graph

Within the LessonAdjustmentPart III1.3 Mystery plots1.4 Compare mean and median with a spreadsheet program on the computer1.5 Modify Game: Landmark Shark1.6 Using almanacs and other reference books, students draw bar graphs1.9 Solving

perimeter and area problems1.10 Create a persuasive paragraph1.11 Collect and analyze data

ExtensionsFrom the Sea to the StarsP2 – Big Hunk of

Play the Stock Market Game with the Denver Post. Interpreting graphs and data, making decisions based on financial information, graphing stocks, and team work are skills included.

Math WebsitesKidsKonnect.com Math SitesMultiple math sitesJanBrett.com Home Page2,389 pages of free activities, coloring pages, and productsAAA MathLost of different math activitiesAunty MathA regular math challengeSouthwest Missouri State University’s Links to Other Puzzles and Problems Web PagesLinks to math puzzles and problemsMathStories.comMath problem solving and critical thinking

ExemplarsQuest Team- NovemberWhat Does Mother Nature Have Planned for my Birthday? – JanuaryTwelve Days of Math Class – JanuaryValentine Candy Challenge - February

143

1.9areaperimeter1.11gallonquartpintcup fluid ouncerecall survey

the BritishP6 – Body TemperatureP7 – Hawaiin VolcanoesP8 – So You Think You Can Tell Time?From the Backyard to the Great WallP7 – PenniesP12 – Investigating Your Own Garbage

Books

Color It on the Hundred Chart – Marcy Cook

144





2Operations with whole numbers and decimals

Secure Goals2h: Use exponential notation for large numbers

2j: Add and subtract decimals

2k: Estimate quotients and divide whole numbers

Developing/Secure2i: Read, write and compare numbers from thousandths to trillions

2.1precision2.6magnitudepowerexponentbaseexponential notation2.7powers keyfactor2.8magnitude benchmarkspositive power of 10negative power of 10scientific notation2.10partial quotientsdivision algorithmdivisorquotientremainder2.11dividend

Within the LessonAdjustmentPart III2.5 Research the term googol and read poem of the same name from Math Talk: Mathematical Ideas in Poems for Two Voices2.7 Explore use of prefixes to express large and small numbers

ExtensionsProjevtsP2 – Modeling the Solar SystemP3 – Distances in the Solar SystemFrom the Sea to the StarsP15 – A Day and a Year in SpaceFrom the Backyard to the Great WallP1 – RattlesnakesP5 – Maple Syrup

ExemplarsLake Erie – OctoberWindow Design – JanuaryMolly Mathematicians – FebruaryPizza Hut Promotions – May

BooksFind the Numbers and Words by Marcy Cook

AimsSquare 2 Rules - December

145





3Variables, Formulas, and Graphs

Secure3f: Mentally add 1 digit integers

3g: Represent rates with formulas, tables, and graphs

3h: Convert between fractions and mixed numbers

3i: Find the least common multiple of two numbers

3j: Find the greatest common factor of two numbers

Developing/Secure3c: Interpret mystery graphs

3.1general patternvariablespecial case3.2commutative property3.3 algebraic expressionevaluate an expression3.4formulasubstitute3.5multipleleast common multipleratespeedline graph3.7factorgreatest common factorspreadsheetupdate or revise a spreadsheetcellcolumnrow

Within the LessonAdjustmentPart III3.2 True and not true special cases3.3 Geometric patterns and algebraic expressions3.4 Deriving a brick wall formula3.6 Conducting a ball throwing experiment3.7 Spreadsheet Scramble3.9 Constructing mystery graphs

ExtensionsProjectsP4 – Movements of the PlanetsP5 – Will It Be Possible to Travel to Other Planets in Student’s Lifetime?From the Sea to the StarsP3 – The Magnitude

ExemplarsTale of the Scale – SeptemberBlinking Lights – MarchMolly Mathematician - February

Math Starters and Stumpers by Marcy Cook

147

3.8horizonsquare root3.9life expectancytime graph

of the StarsP4 – The ConstellationsP15 – A Day and a Year in Space From the Backyard to the Great WallP8 – What Happens to your Garbage?P10 – How Much Does Your Garbage Weigh?P14 – The Dinosaur Time Line

148





4Rational Number Use and Operation

Secure4f: Use an algorithm to add mixed numbers and fractions with like denominators

4g: Use an algorithm to add and subtract fractions with like and unlike denominators

4h: Compare and order fractions

4i: Convert between fractions, decimals, mixed numbers, and percents

4j: Write fractions and mixed numbers in simpliest form

4.1equivalent fractionssimplest formgreatest common factorcommon factor4.2quick common denominatorleast common denominator4.4mixed number proper fraction improper fraction simplest form of a mixed number4.8percent4.11regular pricediscountsale priceinterest

Within the LessonAdjustmentPart III4.3 Exploring the Egyptian method of writing fractions; Exploring Zeno’s paradox4.10 StudentsConduct a Survey4.12 Play Spoon Scramble

ExtensionsProjectsP6 – Formulas for Height and Neck CircumferenceFrom the Sea to the StarsP8 – So You Think You Can Tell Time?P5 – How Big Are Your Feet?From the Backyard to the Great WallP4 – The Great Wall of ChinaP6 – Figuring the

Jim and the Beanstock Marilyn Burns


ExemplarsSink or Swim – SeptemberQuilting Quandry – OctoberLet It Snow! – DecemberWho Wins the Dough – MarchWinning Back the Dough – AprilPacking Predicament - May

149

Figure

150





5Geometry, Congruence, Constructions, and Parallel Lines

Secure5g: Translate figures on a coordinate grid

5h: Plot ordered numbers in four quadrants; use ordered number pairs to name points in four quadrants

5i: Draw or form a figure congruent to any given figure

5j: Classify angles

5k: Measure and draw angles using a protractor

Developing/Secure5f: Apply properties of sums of angle measure of triangles and quadrangles

5.1right, straight, reflect, acute, obtuse angles5.2supplementary, vertical, adjacent angles5.3sector5.4coordinatecoordinate gridmidpointaxisoriginordered number pair5.5transformationreflection or fliptranslation or sliderotation or turnimagepreimageisometery 5.6congruentcorresponding sides and anglesrough sketch

Within the LessonAdjustmentPart III5.5 Unit on Tessellations5.7 PentominoesLiteracy Extensions5.6 Math Talk: Mathematical Ideas in Poems for Two Voices, (triangles)5.9 Polygon Capture

ExtensionsGamesAngle TangleHidden TreasuresPolygon CaptureProjectsP7- Paper throwing experimentsFrom the Sea to the StarsP4 – The ConstellationsFrom the Backyard to the Great WallP11- Can You Make Less Garbage?

Anno’s Hat TricksBinary logic is introduced

Talk It Over by Marcy Cook

Math WebsitesGeometry from the Land of the IncasAn eclectic mix of sound, science, and Incan history intended to interest students in Euclidean Geometry

www.abc.lv/thinkquest/tqentries/16661/index2.htmlA website about tessellations

151

http://www.abc.lv/thinkquest/tgentries/16661/


accurate drawing5.7compass and straightedge constructionanchor of a compassconcentric circles5.8perpendicularbisectperpendicularinscribe5.9parallel linessegmentsskew linestransversaladjacent anglessupplementary anglesvertical angles5.10consecutive angles

152





6Number Systems and Algebraic Concepts

Secure6h: Compare and order integers

6i: Understand and apply the identify property of multiplication

6j: Understand and apply the commutative property for addition and multiplication

6k: Understand and apply the associative property for addition and multiplication

Developing/Secure6d: Find opposites and reciprocals of numbers

6e: Add, subtract,

6.1reciprocal6.2Division of Fractions property6.3opposite of a number6.4multiplication property of -16.5constant termcoefficientvariable termterms of an equationproperty of -1counting numberswhole numbersintegersrational numbersterminating decimalsrepeating decimalsirrational numbersreal numbers6.6order of operations6.7relational symbol

Within the LessonAdjustment6.1, part 16.7, part 16.8, part 16.9, part 16.10, part 1Part III6.2: Studying a proof6.3: Adding and subtracting positive and negative numbers using absolute value6.4 Reading about division by zero6.5 Investigating properties of rational numbers; solving puzzles6.6 Exploring scientific calculators6.8 Solving challenging equations6.9 Solving more challenging pan-

Hands-On-Equations

ExemplarsWindow Design – JanuaryCloak for the Dreamer – JuneCandy Bar Madness – April

Domino Algebra by Marcy CookMental Math with Tiles by Marcy CookThe Hundred Chart by Marcy Cook

153

multiply, and divide integers

6f: Understand and apply order of operations to evaluate expressions and solve number sentences

6g: Determine whether number sentences are true or false

equationinequalityoperation symbolfalse number sentencetrue number sentence6.8variableopen sentencesolutionconsecutivecover-up methodtrial-and-error method6.9pan balance6.10equivalent fractions6.11terms of an equationvariable termconstant termcoefficient6.12inequalitysolution set

balance problems6.12 Graphing inequalities; playing Search Solution with Student-Created CardsGamesCredit/Debits GameTop-It Games with Positive and Negative NumbersAlgebra ElectionBroken CalculatorName that NumberSolution Search (with solution created cards) From the Sea to the StarsP3 – The Magnitude of the Stars

154





7Probability and Discrete Mathematics

Secure7f: Solve “fraction-of-a-fraction” problems

7g: Understand how sample size affects results

Developing/Secure7c: Calculate probability in simple solutions

7d: Understand what constitutes a fair game

7e: Understand and apply the concept of rational numbers to probability situations

7.1outcomeequally likelyprobability7.2 outcomegenerate random numbersrandom number7.3simulationsimulate7.4tree diagramexpected outcomesactual results7.5probability tree diagram7.6Venn diagram7.7fair gameunfair game

Within the LessonAdjustment7.1, part 37.5, part 37.7, part 1; 37.8 part 1Part III7.1 Playing carnival games; reading a book about probability7.2 Examining a table of random digits7.4 Running an amazing contest7.6 Relating tables and Venn diagram;Making Venn diagrams from internet searches7.7 Investigating a coin flipping problemLiteracy Extensions7.1 Do you Want to Bet?

ExtensionsGames

Have student create their own games using the concepts they use in this unit.

The Sneaky Square and 113 Other Math Activities for Kids

155

Fraction Action, Fraction FictionFract-Tac-ToeAngle TangleName that Number

156





8Rates and Ratios

Secure8i: Use rate tables to solve problems

Developing/Secure8d: Use cross-multiplication to solve open proportions

8e: Solve rate number stories

8f: Solve ratio number stories

8g: Estimate equivalent percents for fractions

8h: Solve division problems involving decimals

8.1rateper-unit rateequivalent raterate tableproportion8.2open proportionsolution of a proportion8.3cross productscross multiplication8.4calorie8.5balanced dietfat carbohydrateprotein8.6ratioequivalent ratiospart-to-whole ratiopart-to-part ratio8.9size-changefactorGolden Ration-to-1 ratioenlargementreduction

Within the LessonAdjustment8.2, parts 1; 38.3, part 18.4, part 18.5, part 1; 38.9, part 18.10, part 18.11, part 1Part III8.3 Finding rates in the story Math Curse8.5 Making a circle graph to represent a meal8.6 Solving challenging ratio problems8.9 Investigating map scales8.10 Using a grid to draw an enlargement of a picture; Enlarging a triangle with rubber bands;Reducing designs8.12 Exploring the relationship

ExemplarsHeight Dilemma – November

Calculator Companions by Learning Resources

157

scale model8.10similar figurescongruent figuressimilar polygonscorresponding sidescorresponding angles8.11Golden Rectangle8.12Golden Ratio

between Fibonacci sequence and the Golden RatioLiteracy Extensions8.3 Math Curse8.12 Mathematical Ideas in Poems for Two Voices (The Golden Mean)

ExtensionsGamesSpoon Scramble

From the Sea to the StarsP16 – Knives and ForksP18 – Selene Sits in a ShoeFrom the Backyard to the Great WallP6 – Figuring the FigureP10 – How Much Does Your Garbage Weigh?P11 – Can You Make Less Garbage?P19 – Dinosaur Weights

158





9More About Variables, Formulas, and Graphs

Secure9h: Evaluate expressions and formulas

Developing/Secure9b: Apply the distributive property

9c: Combine like terms to simplify expressions and equations

9d: Solve equations

9e: Write and identify equivalent expressions and equivalent equations

9f: Write and solve equations that represent problem situations

9g: Use formulas to

9.2distributive property9.3like termscombine like terms9.4simplify an expression9.5simplify an equationequivalent equations9.6mobilefulcrum9.7spreadsheet programcelladdress of a celladdress boxdisplay barlabelsnumberformulas9.10trial-and-error methodtest number

Within the LessonAdjustment9.2, part 19.3, part 19.4, part 19.7, part 19.10, part 19.11, part 1Part III9.2 Writing number stories9.3 Interpreting an Algebra Cartoon9.4 Reading a math dictionary 9.6 Researching mobiles; Balancing a complicated mobile9.7 Using formulas to complete a spreadsheet9.9 Comparing capacities9.10 Maximizing the volume of a rectangular prismInvestigating9.11 Solving perimeter

Table and Graph Skills Weekly Reader Skills Book

Math Word Power 2000

159

solve problems

Developing/SecureSimplify expressions and equations with parentheses

9.12square of a numbersquare root of a numberlegs of a right trianglehypotenusePythagorean Theoremright angletheorem9.13indirect measurement

problems 9.12 Pythagorean Theorem and math

Literacy Extensions9.4 G is for Google9.11 Sir Conference and the First Round Table

ExtensionsGamesName that NumberPolygon Capture3-D shape sortFrom the Sea to the StarsP5 – How Big Are Your Feet?P6 – Body TemperatureP7 – Hawaiian VolcanoesP10 – All Over the WorldFrom the Backyard to the Great WallP10 – How Much Does Your Garbage Weigh?

160





10Geometry Topics

None regular polygontessellationvertex pointregular tessellationsemi regular tessellationtranslation tessellationrotation symmetryorder of rotation symmetrypoint symmetrycross sectiontopologytopologically equivalenttopological transformationgenusrobber sheet geometrytopological propertytransference of curvesMobius Strip

Within the LessonAdjustment10.1, parts 1; 210.2, parts 1; 2; 310.4, part 1Part III10.1 Using a calculator to explore tessellations10.2 Reading a poem about tessellations10.3 Performing a point-symmetry magic trick10.4 Solving cross-section problems10.6 Reading an essay about Mobius; Reading a mathematical poemLiteracy Extensions10.2 Math Talk: Mathematical Ideas in Poem s for Two Voices (Tessellations)10.6 Math Talk:

Investigate the work of M.C. Escher and create similar art projects

Math WebsitesGeometry from the Land of the IncasAn eclectic mix of sound, science, and Incan history intended to interest students in Euclidean Geometry

www.abc.lv/thinkquest/tqentries/16661/index2.htmlA website about tessellations

ExemplarsTiling Tribulation – June

A Geometry Lesson – Pantomimes (Chapter 12) A Collection of Math Lessons From Grades 3 Through 6 by Marilyn Burns

161



Mathematical Ideas in Poems for Two Voices (Mobius Strip)ExtensionsGamesSolution Search

162

Exemplars Correlated to EM LessonsFirst Grade

Strand or Skill/Concept

1st Grade Goal Lessons Exemplars Task

Numeration/Operations/Measurement

Beginning Project 3: Pumpkin Math

Jack-O-Lanterns, Fall, 1999

Measurement Beginning 4.2 Nonstandard Linear Measure

How Big is a Foot?

100 Best Tasks1997

MeasurementData & Chance

Developing 4.6 Measuring with a Tape

Measure

Wrist Circumference100 Best Tasks

1997

Patterns, Functions & Developing 3.9 More Octopus

163

Algebra Frames-and Arrows Problems

3.10 Counting with a Calculator

100 Best Tasks 1997

LegsWinter 2000

Number and Operation Skills & Concepts/

Measurement

Developing 3.12 Counting Dimes, Nickels

& Pennies

Nine CentsWinter 2000

164

Exemplars Correlated to EM LessonsSecond Grade


2nd Grade Goal Lessons Exemplars Task

Addition/Money/Number and

Operations Skills & Concepts

Beginning 3.2 Using Coins to Buy Things3.7 Making Change by

Counting Up

The Salad BarFall, 1999

Geometry/Measurement/Number and

OperationSkills and Concepts

Beginning 3.3 Telling Time Let’s Plan a Party

Winter, 2000

Problem Solving/ Reasoning/

Communication/Money

Developing 4.3 Exploration B:Making Coin

Stamp Booklets

Piggy Bank100 Best

Tasks of 1997

Problem Solving/ Reasoning/

Communication/Money

Developing 4.9 The Partial Sums Addition

Algorithm: “Ongoing

Eggsactly100 Best

Tasks 1997

165

Learning and Practice”

Review Telling Time

Number and Operations Skills

and Concepts

Secure 4.6 A Shopping Activity

Holiday Fair Shopping

SpreeFall, 1999

166

Exemplars Correlated to EM LessonsThird Grade


3rd Grade Goal

Lessons ExemplarsTask

Operations Developing 4.3 Equal Shares & Equal Groups

Shovel, Shovel, Shovel

100 Best Tasks of 1997

Geometry/Measurement

Developing 3.4 Perimeter

3.5 Exploring Perimeter

Valentine PartySet-up/March,

1997

Patty’s PartySpring Math,

1999Geometry/

MeasurementDeveloping 3.5 Exploring

Perimeter & AreaGarden FencesSpring, Math

2000Operations & Computation/Numeration

Developing 8.1 Naming Parts with Fractions

9.7 Sharing

Rents Craft Space

Fall Math,1999

167

MoneyGeometry/

MeasurementDeveloping 3.6 Area

3.7 Number Models for Area

Grand Father Tang

March, 1997

Jazzing Up Your Bedroom

Winter Math,1998

168

Exemplars Correlated to EM LessonsFourth Grade


4th Grade Goal Lessons Exemplars Task

Probability & Statistics

Developing 2.6 The Median A Fair Snack?Fall, Math

1999Patterns,

Functions & Algebra

Beginning 3.11 Logic Problems

Another Domino Dilemma

100 Best Tasks1997

Numeration Secure 7.7 Equivalent Fractions

Great Pizza Dilemma

March, 1994Numeration &

OperationDeveloping 4.1 Decimal

Addition and Subtraction

Zeno the Xylophone

Maker100 Best Tasks,

1997Geometry/Numeration

Secure 7.3 Pattern-BlockFractions

Tangram MoneyOctober, 1993

169

Stained Glass Surprise

100 Best Tasks, 1997

170

Exemplars Correlated to EM LessonsFifth Grade



Probability & Statistics

Beginning 2.6 Chance Events

The Valentine Candy Challenge100 Best Tasks

of 1997Patterns,

Functions & Algebra

Beginning 10.4 Rules, Tables, and

Graphs

Winning Ticket100 Best Tasks

of 1997Number and

Operation Skills & Concepts

Developing 2.8 Multiplication of Whole Numbers

and Decimals

Job Hunting100 Best Tasks

of 1997

Numeration Developing 5.3 Ordering Fractions

Candy PartyVolume 7

Spring, 2000Patterns,

Functions & Algebra

Developing 10.4 Rules, Tables & Graphs:

Part 1: Study Links

The Tower Problem


171

10.5 American Tour: Old

Faithful’s Next Eruption

172

Exemplars Correlated to EM LessonsSixth Grade



Data & Chance Beginning 4.10 Graphing Garbage

The Environmental

Friendly ShopperVol. 7

Spring, 2000Patterns,

Functions & Algebra

Beginning/Developing

3.3 AlgebraicExpressions

MarshmallowPeepsVol. &

Spring, 2000Numeration Developing 4.1 Equivalent

Fractions (Part 3: Reteaching)

Tangram Fractions


Measurement &Reference

Frames

Developing/Secure

9.8 Area Formulas

w/Applications

Gum-dilly-icisous

Volume 7Spring, 2000

173

9.9 Volume Formulas w/ Applications

Developing Geometry/Measurement

5.9 Parallel Lines and Angle

Relationships

5.10 Parallelograms

Tan PatternsBlock Angles

100 Best Tasks1997

174

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