NCTM Standards and Expectations Grades...

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PROBLEM SOLVING EXPERIENCES ©2005

Correlated to

NCTM Standards and Expectations

Grades 3-5

Problem Solving Experiences ©2005 Authors Randall I. Charles Frank K. Lester

Diana V. Lambdin

PROBLEM SOLVING EXPERIENCES to the NCTM Standards and Expectations

Grades 3-5

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NUMBER AND OPERATIONS STANDARD Understand numbers, ways of representing numbers, relationships among numbers, and number systems understand the place-value structure of the base-ten number system and be able to represent and compare whole numbers and decimals; Grade 3: p. 12, problem 20, Mystery Number p. 18, problem 30, What’s My Number p. 24, problem 40, Making Numbers p. 36, problem 60, Making Trades p. 39, problem 65, High/Low p. 42, problem 70, What Could It Be? p. 48, problem 80, Order, Please! p. 51, problem 85, What Do You Know About That? p. 63, problem 104, Take A Hike p. 66, problem 110, Stuck in the Middle Grade 4: p. 15, problem 25, Devious Digits p. 21, problem35, Crazy 8s p. 38, problem 63, Score Card Grade 5: p. 6, problem 10, Spotting the Sixes p. 39, problem 65, What Decimal? recognize equivalent representations for the same number and generate them by decomposing and composing numbers; Grade 3: p. 12, problem 20, Mystery Number p. 24, problem 40, Making Numbers p. 36, problem 60, Making Trades p. 42, problem 70, What Could It Be? p. 48, problem 80, Order, Please! Grade 4: p. 12, problem 20, Make 100 Grade 5: p. 42, problem 70, Equivalents p. 57, problem 95, Five Ways develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; Grade 3: p. 60, problem 100, How Hungry? p. 63, problem 105, Party Treats p. 75, problem 125, Paving Job Grade 4: p. 24, problem 40, How Big Is One-Half? p. 27, problem 45, Shady Parts p. 39, problem 65, X Marks the Spot Grade 5: p. 24, problem 40, How Big Is 1/3? p. 27, problem 45, Shady Shapes p. 42, problem 70, Equivalents


Grades 3-5

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p. 51, problem 85, In-between Fractions p. 57, problem 95, Five Ways p. 87, problem 145, A New Area use models, benchmarks, and equivalent forms to judge the size of fractions; Grade 3: p. 60, problem 100, How Hungry? p. 63, problem 105, Party Treats p. 75, problem 125, Paving Job Grade 4: p. 24, problem 40, How Big Is One-Half? p. 27, problem 45, Shady Parts p. 39, problem 65, X Marks the Spot p. 51, problem 85, In-Between p. 78, problem 130, Place Your Order Grade 5: p. 42, problem 70, Equivalents p. 51, problem 85, In-between Fractions recognize and generate equivalent forms of commonly used fractions, decimals, and percents; Grade 3: p. 63, problem 105, Party Treats Grade 4: p. 84, problem 140, Gridlock Grade 5: p. 57, problem 95, Five Ways explore numbers less than 0 by extending the number line and through familiar applications; Can Be Developed From: p. 39, problem 65, X Marks The Spot Grade 5: Can Be Developed From: p. 72, problem 120, Line ‘Em Up describe classes of numbers according to characteristics such as the nature of their factors. Grade 4: p. 16, problem 26, Fair Ball p. 32, problem 53, Head Count p. 33, problem 55, Odd or Even? p. 72, problem 120, Arrays Grade 5: p. 84, problem 140, That’s a factor


Grades 3-5

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Understand meanings of operations and how they relate to one another understand various meanings of multiplication and division; Grade 3: Representative pages: p. 6, problem 10, Sticker Shock p. 9, problem 15, Making Lemonade p. 74, problem 123, Save It! p. 80, problem 133, We’re Full p. 87, problem 145, How Old Are They? Grade 4: Representative pages: p. 5, problem 7, Page Turner p. 26, problem 43, Carnival Fun p. 32, problem 53, Head Count p. 63, problem104, Berry Good Work p. 72, problem 120, Arrays Grade 5: Representative pages: p. 17, problem 28, Big Bucks p. 23, problem 37, Weight Gain p. 29, problem 48, Batter Up p. 62, problem 102, Ocean Front p. 78, problem 129, Teens and Twins understand the effects of multiplying and dividing whole numbers; Grade 3: p. 27. problem 45, Seashells by the Seashore p. 30, problem 50, Row After Row p. 52, problem 86, Hopping Up the Stairs p. 67, problem 111, Seashell Creatures p. 75, problem 124, Carpool to the Zoo Grade 4: Representative pages: p. 5, problem 7, Page Turner p. 11. problem 17, Muffins by the Dozen p. 14, problem 22, Climbing Chichén Itzá p. 32, problem 53, Head Count p. 72, problem 120, Arrays Grade 5: Representative pages: p. 3, problem 5, Pair Up p. 36, problem 60, Number Grinder p. 60, problem 99, Car Caravan p. 65, problem 108, Around the Park p. 71, problem 118, Green Thumbs identify and use relationships between operations, such as division as the inverse of multiplication, to solve problems; Grade 3: Can Be Developed From: p. 53, problem 88, Dandy Candy p. 59, problem98, Point Totals p. 71, problem 118, Write it Down p. 74, problem 123, Tickets Anyone?


Grades 3-5

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Grade 4: p. 32, problem 53, Head Count p. 72, problem 120, Arrays Grade 5: p. 20, problem 33, Jewlery Makers understand and use properties of operations, such as the distributivity of multiplication over addition. Grade 3: Can Be Developed From: p. 9, problem 14, Paddle Power p. 72, problem 119, New Clothes p. 86, problem 142, Bicycle Fix-Up Grade 4: p. 12, problem 20, Make 100 Grade 5: p.2, problem 3, Captain Kidd p. 70, problem 116, Heavy Pumpkins Compute fluently and make reasonable estimates develop fluency with basic number combinations for multiplication and division and use these combinations to mentally compute related problems, such as 30 50; Grade 3: p. 4, problem 6, Baseball Cards p. 30, problem 50, Row After Row p. 52, problem 86, Hopping Up the Stairs p. 53, problem 88, Dandy Candy p. 56, problem 93, Cut Up p. 59, problem 98, Point Totals p. 65, problem 107, Sharing the Beans p. 67, problem 111, Seashell Creatures p. 71, problem 117, Lunch Bill p. 71, problem 118, Write It Down p. 75, problem 125, Paving Job p. 77, problem 128, Team Up! p. 86, problem 143, Easy Rider p. 89, problem, 148, Visiting Grandma Grade 4: Representative pages: p. 5, problem 7, Page Turner p. 11, problem 17, Muffins by the Dozen p. 14, problem 22, Climbing Chichén Itzá p. 47, problem 78, Shell Heap p. 62, problem 103, Team Totals Grade 5: Representative pages: p. 3, problem 5, Pair Up p. 11, problem 17, Yard Work p. 14, problem 23, Just Peachy p. 20, problem 33, Jewelry Makers p. 23, problem, 37, Weight Gain p. 35, problem 58, Rescue Me p. 41, problem 68, Aldo’s Art Supplies p. 53, problem 87, Cake Job p. 59, problem 98, Tickets, Anyone


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p. 62, problem 102, Ocean Front p. 62, problem 103, Home-Run Leaders p. 83, problem 137, Meals Aplenty develop fluency in adding, subtracting, multiplying, and dividing whole numbers; Grade 3: Representative pages: p. 5, problem 7, Selling Cookies p. 24, problem 39, Snow Bound p. 67, problem 111, Seashell Creatures p. 77, problem 127, Road Trip p. 86, problem 143, Easy Rider Grade 4: Representative pages: p. 8, problem 12, Tonya’s Travels p. 44, problem 73, Yankees vs. Oriels p. 53, problem 88, Patio Problems p. 68, problem 112, Ounces and Ounces of OJ p. 72, problem 120, Arrays Grade 5: Representative pages: p. 9 problem 14, A Three-Sided Matter p. 12, problem 19, Conservation Alert p. 29, problem 48, Batter Up p. 56, problem 93, Pickin’ Project p. 90, problem 149, Yards Around the Yard develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results; Grade 3: Representative pages: p. 2, problem 2, Collecting Bottles p 3, problem 5, A Family Of Facts p. 5, problem 8, Two Brothers p. 12, problem 20, Mystery Number p. 14, problem 22, Skiing the Slopes Grade 4: Representative pages: p. 2, problem 2, Dining Out p. 5, problem 7, Page Turner p. 8, problem 12, Tonya’s Travels p. 11, problem 17, Muffins by the Dozen p. 14, problem 22, Climbing Chichén Itzá Grade 5: Representative pages: p. 2. problem 2, Lemon Moose p. 8, problem 12, Fisherman’s Harvest p. 41, problem 67, Fresh Fish p. 77, problem 127, Travel Plans p. 80, problem 132, Buy New, Sell Use


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develop and use strategies to estimate computations involving fractions and decimals in situations relevant to students' experience; Grade 3: p. 50, problem 82, Birthday Party p. 68, problem 112, Friendly Gifts Grade 4: p. 17 problem 27, Jackie’s Jacket p. 26, problem 42, Hotel Fare p. 41, problem 67, Paper Routes p. 47. problem 77, Marble Mania p. 68, problem 112, Ounces and Ounces of OJ p. 74, problem 122, Well Supplied p. 77, problem 127, Every Bit Counts p. 80, problem 132, Thirsty Business Grade 5: p. 20, problem 32, Bake Sale Expenses p. 35, problem 57, Shopping Spree p. 47, problem 77, Chatty Chen use visual models, benchmarks, and equivalent forms to add and subtract commonly used fractions and decimals; Grade 3: p. 33, problem 54, Getting in Shape p. 36, problem 59, Overseas Burgers p. 39, problem 64, Side Long p. 68, problem 113, School Supplies Grade 4: Representative pages: p. 9, problem 14, My Change, Please p. 17 problem 27, Jackie’s Jacket p. 78, problem 130, Place Your Order p. 80, problem 133, Batter Up p. 86, problem 143, Daily Jogger Grade 5: Representative pages: p. 21, problem 34, A Group Gift p. 69 problem 114, Sundays Off p. 75, problem 125, A Square Deal p. 86, problem 143, Fruit Punch p. 89, problem 148, Library Leta select appropriate methods and tools for computing with whole numbers from among mental computation, estimation, calculators, and paper and pencil according to the context and nature of the computation and use the selected method or tools. Grade 3-5: p. xvi, “Using Mathematical Tools” and “Plan and Solve” paragraphs help student choose method for computing.


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ALGEBRA STANDARD Understand patterns, relations, and functions describe, extend, and make generalizations about geometric and numeric patterns; Grade 3: p. 19, problem 31, Find the Missing Numbers p. 40, problem 66, Squares and More Squares p. 61, problem 101, Steps to a Pattern p. 82, problem 136, Pretty Patterns Grade 4: p. 3, problem 5, Agreeable Sums p. 7, problem 11, Weight Watching p. 49, problem 81, What Comes Next? p. 52, problem 86, Apple Picking p. 85, problem 141, What a Square! p. 88, problem 146, Bikes and Trikes Grade 5: p. 3, problem 5, Pair Up p. 7, problem 11, Shell Triangles p. 18, problem 30, That’s Odd p. 46, problem 76, Hidden Squares represent and analyze patterns and functions, using words, tables, and graphs. Grade 3: p. 19, problem 31, Find the Missing Numbers p. 40, problem 66, Squares and More Squares p. 61, problem 101, Steps to a Pattern p. 82, problem 136, Pretty Patterns Grade 4: p. 3, problem 5, Agreeable Sums p. 7, problem 11, Weight Watching p. 49, problem 81, What Comes Next? p. 52, problem 86, Apple Picking p. 85, problem 141, What a Square! p. 88, problem 146, Bikes and Trikes Grade 5: p. 3, problem 5, Pair Up p. 7, problem 11, Shell Triangles p. 18, problem 30, That’s Odd p. 46, problem 76, Hidden Squares Represent and analyze mathematical situations and structures using algebraic symbols identify such properties as commutativity, associativity, and distributivity and use them to compute with whole numbers; Grade 3: Can Be Developed From: p. 3, problem 5, A Family of Facts p. 69, problem 114, Nuts to You p. 72, problem 119, New Clothes p. 86, problem 142, Bicycle Fix-Up


Grades 3-5

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Grade 4: Can Be Developed From: p. 12, problem 20, Make 100 Grade 5: Can Be Developed From: p. 2. problem 3, Captain Kidd p. 70, problem 116, Heavy Pumpkins represent the idea of a variable as an unknown quantity using a letter or a symbol; Grade 3: p. 28, problem 46, Cheer Them On! p. 67, problem 111, Seashell Creatures Grade 4: p. 25, problem 41, Picnic Lunch p. 67, problem 111, Dog Dollars Grade 5: p. 10, problem 16, Buried Treasure p. 25, problem 41, Summer Savings p. 52, problem 86, Prize Packages p. 70, problem 116, Heavy Pumpkins p. 85, problem 141, Marmots express mathematical relationships using equations. Grade 3: p. 28, problem 46, Cheer Them On! p. 67, problem 111, Seashell Creatures Grade 4: p. 25, problem 41, Picnic Lunch p. 67, problem 111, Dog Dollars Grade 5: p. 10, problem 16, Buried Treasure p. 25, problem 41, Summer Savings p. 52, problem 86, Prize Packages p. 70, problem 116, Heavy Pumpkins p. 85, problem 141, Marmots Use mathematical models to represent and understand quantitative relationships model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions. Grade 3: p. 1, problem 1, Square Dancing p. 4, problem 6, Baseball Cards p. 16, problem 26, Growing Pains p. 22, problem 36, A Puppy’s Pen p. 28, problem 46, Cheer Them On! p. 43, problem 71, Triangle Art p. 46, problem 76, Circus Elephants p. 58, problem 96, No More Room! p. 67, problem 111, Seashell Creatures p. 70, problem 116, Locker Pals p. 88, problem 146, Save! Save! Save!


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Grade 4: p. 1, problem 1, How Many Outfits? p. 10, problem 16, Running for Dollars p. 19, problem 31, Car Wash p. 25, problem 41, Picnic Lunch p. 28, problem 46, Page by Page p. 43, problem 71, Trio of Stamps p. 52, problem 86, Apple Picking p. 61, problem 101, Books Galore p. 67, problem 111, Dog Dollars p. 70, problem 116, Apples and Bananas p. 85, problem 141, What a Square p. 88, problem 146, Bikes and Trikes Grade 5: p. 19, problem 31, Book Building p. 37, problem 61, Traveling Bluebirds p. 49, problem 81, Shoe Story p. 58, problem 96, Meeting of the Elves p. 67, problem 111, Packing Boxes p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business p. 88, problem 146, Hot Dogs and Hamburgers Analyze change in various contexts investigate how a change in one variable relates to a change in a second variable; Grade 3: Can Be Developed From: p. 28, problem 46, Cheer Them On! p. 67, problem 111, Seashell Creatures Grade 4: Can Be Developed From: p. 25, problem 41, Picnic Lunch p. 67, problem 111, Dog Dollars Grade 5: Can Be Developed From: p. 10 problem 16, Buried Treasure p. 25, problem 41, Summer Savings p. 52, problem 86, Prize Packages p. 70, problem 116, Heavy Pumpkins p. 85, problem 141, Marmots identify and describe situations with constant or varying rates of change and compare them. Grade 3: p. 16, problem 26, Growing Pains p. 58, problem 96, No More Room! Grade 4: p. 14, problem 23, Oh, Deer! p. 42, problem 69, Rising Prices p. 45, problem 74, Winter Fun p. 45, problem 75, Miguel’s Bike Race


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Grade 5: p. 19, problem 31, Book Building p. 24, problem 39, Scope it Out p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business GEOMETRY STANDARD Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships identify, compare, and analyze attributes of two- and three-dimensional shapes and develop vocabulary to describe the attributes; Grade 3: p. 15, problem 25, A Polygon Problem p. 22, problem36, A Puppy’s Pen p. 30, problem 49, Playing Around p. 39, problem 64, Side Long Grade 4: p. 4, problem 6, Wrap It Up! p. 27, problem 45, Shady Parts p. 46, problem 76, The Pyramids p. 66, problem 110, Who Is Right? p. 81, problem 135, What’s Your Angle? p. 84, problem 139, All Boxed In p. 87, problem 145, Name That Figure! Grade 5: p. 27, problem 45, Shady Shapes p. 30, problem 50, Who is Right? p. 63, problem 105, Toothpick, Triangles p. 81, problem 135, A Matter of Degrees classify two- and three-dimensional shapes according to their properties and develop definitions of classes of shapes such as triangles and pyramids; Grade 3: p. 15, problem 25, A Polygon Problem p. 22, problem36, A Puppy’s Pen p. 30, problem 49, Playing Around p. 39, problem 64, Side Long Grade 4: p. 4, problem 6, Wrap It Up! p. 27, problem 45, Shady Parts p. 46, problem 76, The Pyramids p. 66, problem 110, Who Is Right? p. 81, problem 135, What’s Your Angle? p. 84, problem 139, All Boxed In p. 87, problem 145, Name That Figure! Grade 5: p. 30, problem 50, Who is Right? p. 63, problem 105, Toothpick, Triangles p. 81, problem 135, A Matter of Degrees


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investigate, describe, and reason about the results of subdividing, combining, and transforming shapes; Grade 3: p. 22, problem36, A Puppy’s Pen Grade 4: p. 27, problem 45, Shady Parts Grade 5: p. 27, problem 45, Shady Shapes p. 63, problem 105, Toothpick, Triangles explore congruence and similarity; Grade 4: p. 66, problem 110, Who Is Right? p. 69, problem 115, Symmetric Letters p. 90, problem 150, Same Shape and Size Grade 5: p. 30, problem 50, Who is Right? make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions. Grade 3: p. 15, problem 25, A Polygon Problem p. 22, problem36, A Puppy’s Pen p. 30, problem 49, Playing Around p. 39, problem 64, Side Long Grade 4: p. 66, problem 110, Who Is Right? p. 69, problem 115, Symmetric Letters p. 81, problem 135, What’s Your Angle? p. 90, problem 150, Same Shape and Size Grade 5: p. 27, problem 45, Shady Shapes p. 63, problem 105, Toothpick, Triangles p. 81, problem 135, A Matter of Degrees Specify locations and describe spatial relationships using coordinate geometry and other representational systems describe location and movement using common language and geometric vocabulary; Grade 4: p. 66, problem 110, Who Is Right? p. 90, problem 150, Same Shape and Size Grade 5: p. 30, problem 50, Who is Right? make and use coordinate systems to specify locations and to describe paths; Grade 3: Can Be Developed From: p. 16, problem 26, Growing Pains p. 27 problem 44, Shark Alert! p. 29, problem 47, Oh, Baby! p. 58, problem 96, No More Room!


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Grade 4: Can Be Developed From: p. 14, problem 23, Oh, Deer! p. 42, problem 69, Rising Prices p. 45, problem 75, Miguel’s Bike Race Grade 5: Can Be Developed From: p. 19, problem 31, Book Building p. 24, problem 39, Scope it Out p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business find the distance between points along horizontal and vertical lines of a coordinate system. Grade 3: Can Be Developed From: p. 16, problem 26, Growing Pains p. 27 problem 44, Shark Alert! p. 29, problem 47, Oh, Baby! p. 58, problem 96, No More Room! Grade 4: Can Be Developed From: p. 14, problem 23, Oh, Deer! p. 42, problem 69, Rising Prices p. 45, problem 75, Miguel’s Bike Race Grade 5: p. 19, problem 31, Book Building p. 24, problem 39, Scope it Out p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business Apply transformations and use symmetry to analyze mathematical situations predict and describe the results of sliding, flipping, and turning two-dimensional shapes; Grade 3: Can Be Developed From: p. 15, problem 25, A Polygon Problem Grade 4: Can Be Developed From: p. 66, problem 110, Who Is Right? p. 90, problem 150, Same Shape and Size Grade 5: p. 30, problem 50, Who is Right? describe a motion or a series of motions that will show that two shapes are congruent; Grade 3: Can Be Developed From: p. 15, problem 25, A Polygon Problem


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Grade 4: Can Be Developed From: p. 66, problem 110, Who Is Right? p. 90, problem 150, Same Shape and Size Grade 5: Can Be Developed From: p. 30, problem 50, Who is Right? identify and describe line and rotational symmetry in two- and three-dimensional shapes and designs. Grade 4: p. 69, problem 115, Symmetric Letters Grade 5: p. 30, problem 50, Who is Right? p. 54, problem 90, Symmetry Use visualization, spatial reasoning, and geometric modeling to solve problems build and draw geometric objects; Grade 3: p. 15, problem 25, A Polygon Problem Grade 4: p. 46, problem 76, The Pyramids Grade 5: p. 15, problem 25, All Lined Up p. 21, problem 35, Square Up p. 23, problem 38, All Over the Map p. 30, problem 50, Who is Right? p. 46, problem 76, Hidden Squares p. 30, problem 50, Who is Right? p. 46, problem 76, Hidden Squares create and describe mental images of objects, patterns, and paths; Grade 3: p. 15, problem 25, A Polygon Problem Grade 4: p. 1, problem 1, How Many Outfits? p. 15, problem 24, Short Cut p. 27, problem 45, Shady Parts p. 72, problem 120, Arrays p. 89, problem 148, Between Friends Grade 5: p. 7, problem 11, Shell Triangles p. 15, problem 25, All Lined Up p. 21, problem 35, Square Up p. 30, problem 50, Who is Right? p. 46, problem 76, Hidden Squares p. 30, problem 50, Who is Right? p. 46, problem 76, Hidden Squares p. 81, problem 135, A Matter of Degrees


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identify and build a three-dimensional object from two-dimensional representations of that object; Grade 4: p. 46, problem 76, The Pyramids Grade 5: p. 90, problem 150, Get the Net identify and draw a two-dimensional representation of a three-dimensional object; Grade 4: p. 46, problem 76, The Pyramids Grade 5 p. 90, problem 150, Get the Net use geometric models to solve problems in other areas of mathematics, such as number and measurement; Grade 3: p. 38, problem 63, Hit the Road p. 39, problem 64, Side Long p. 47, problem77, A Roomy Problem p. 53, problem 87, Back and Forth p. 90, problem 149, Perimeter Problems Grade 4: p. 15, problem 24, Short Cut p. 27, problem 44, Park Side p. 35, problem 57, Deer Proof p. 43, problem 71, A Trio of Stamps p. 46, problem 76, The Pyramids p. 74, problem 123, Door Jam p. 86, problem 143, Dialy Jogger Grade 5: p. 9. problem 14, A Three-Sided Matter p. 11, problem 17, Yard Work p. 27, problem 45, Shady Shapes p. 65, problem 108, Around the Park p. 67, problem 111, Packing Boxes p. 90, problem 149, Yards Around the Yard recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life. Grade 3: p. 38, problem 63, Hit the Road p. 44, problem 72, Around the Pool p. 53, problem 87, Back and Forth p. 60, problem 100, How Hungry? p. 79, problem 131, Mending Fences p. 81, problem 135, I Want the Big Slice! p. 85, problem 141, From Town to Town p. 89, problem 147, Around and Around and Around Grade 4: p. 15, problem 24, Short Cut p. 27, problem 44, Park Side p. 35, problem 57, Deer Proof p. 43, problem 71, A Trio of Stamps p. 46, problem 76, The Pyramids p. 74, problem 123, Door Jam p. 86, problem 143, Dialy Jogger


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Grade 5: p. 7, problem 11, Shell Triangles p. 11, problem 17, Yard Work p. 36, problem 59, Fenced In p. 40, problem 66, Table Talk p. 65, problem 108, Around the Park p. 71, problem 118, Green Thumbs p. 90, problem 149, Yards Around the Yard MEASUREMENT STANDARD Understand measurable attributes of objects and the units, systems, and processes of measurement understand such attributes as length, area, weight, volume, and size of angle and select the appropriate type of unit for measuring each attribute; Grade 3: p. 30, problem 49, Playing Around p. 39, problem 64, Side Long p. 89, problem 147, Around and Around and Around Grade 4: p. 27, problem 44, Park Side Grade 5: p. 66, problem 110, Pint-Size p. 71, problem 118, Green Thumbs understand the need for measuring with standard units and become familiar with standard units in the customary and metric systems; Grade 3: p. 9, problem 15, Making Lemonade p. 30, problem 49, Playing Around p. 39, problem 64, Side Long Grade 4: p. 27, problem 44, Park Side p. 74, problem 123, Door Jam Grade 5: p. 66, problem 110, Pint-Size p. 90, problem 149, Yards Around the Yard carry out simple unit conversions, such as from centimeters to meters, within a system of measurement; Grade 3: p. 9, problem 15, Making Lemonade Grade 4: p. 48, problem 80, Tight Space p. 51, problem 84, A Busy Time p. 74, problem 123, Door Jam Grade 5: p. 65, problem 107, The Local Pool p. 66, problem 110, Pint-Size


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understand that measurements are approximations and how differences in units affect precision; Grade 3: Can Be Developed From: p. 9, problem 15, Making Lemonade Grade 4: Can Be Developed From: p. 27, problem 44, Park Side p. 35, problem 57, Deer Proof p. 48, problem 80, Tight Space Grade 5: Can Be Developed From: p. 9, problem 14, A Three-Sided Matter p. 36, problem 59, Fenced In p. 66, problem 110, Pint-Size p. 71, problem 118, Green Thumbs explore what happens to measurements of a two-dimensional shape such as its perimeter and area when the shape is changed in some way. Grade 5: p. 75, problem 125, A Square Deal Apply appropriate techniques, tools, and formulas to determine measurements develop strategies for estimating the perimeters, areas, and volumes of irregular shapes; Grade 3: p. 57, problem 95, Let’s Talk Perimeter p. 90, problem 149, Perimeter Problems Grade 4: p. 27, problem 44, Park Side Grade 5: p. 11, problem 17, Yard Work p. 62, problem 102, Ocean Front p. 65, problem 107, The Local Pool select and apply appropriate standard units and tools to measure length, area, volume, weight, time, temperature, and the size of angles; Grade 3: p. 9, problem 15, Making Lemonade p. 23, problem 38, On Time for School p. 30, problem 49, Playing Around p. 45, problem 75, A Thanksgiving Birthday p. 54, problem 90, School Days, School Days p. 72, problem 120, Doctor’s Orders Grade 4: p. 51, problem 84, A Busy Time p. 81, problem134, Goose Bumps p. 81, problem 135, What’s Your Angle? Grade 5: p. 39, problem 64 San Francisco Bound p. 81, problem 134, A Cut Above


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select and use benchmarks to estimate measurements; Grade 3: p. 44, problem 72, Around the Pool p. 47, problem77, A Roomy Problem Grade 4: p. 35, problem 57, Deer Proof p. 65, problem 107, Ready to Go? Grade 5: p. 11, problem 17, Yard Work p. 62, problem 102, Ocean Front p. 65, problem 107, The Local Pool develop, understand, and use formulas to find the area of rectangles and related triangles and parallelograms; Grade 5: p. 75, problem 125, A Square Deal develop strategies to determine the surface areas and volumes of rectangular solids. Grade 4: p. 84, problem 139, All Boxed In Grade 5: p. 67, problem 111, Packing Boxes p. 90, problem 150, Get the Net DATA ANALYSIS AND PROBABILITY STANDARD Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them design investigations to address a question and consider how data-collection methods affect the nature of the data set; Grade 3: Can Be Developed From: p. 11, problem 17, Inching Up p. 20, problem 32, Tallying Traffic p. 23, problem37, Can Do p. 24, problem 39, Snow Bound p. 32, problem 53, Red Hot p. 78, problem 130, Reach for the Sky! Grade 4: Can Be Developed From: p. 2, problem 3, That’s Life p. 14, problem 23, Oh, Deer! p. 20, problem 34, Bowled Over p. 21, problem 33, Paper Drive p. 38, problem 63, Score Card Grade 5: Can Be Developed From: p. 12, problem 19, Conservation Alert p. 29, problem 47, Yes, We Can p. 30, problem 49, Weekly Renter


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collect data using observations, surveys, and experiments; Grade 3: Can Be Developed From: p. 11, problem 17, Inching Up p. 20, problem 32, Tallying Traffic p. 23, problem37, Can Do p. 24, problem 39, Snow Bound p. 32, problem 53, Red Hot p. 78, problem 130, Reach for the Sky! Grade 4: Can Be Developed From: p. 2, problem 3, That’s Life p. 14, problem 23, Oh, Deer! p. 20, problem 34, Bowled Over p. 21, problem 33, Paper Drive p. 38, problem 63, Score Card Grade 5: Can Be Developed From: p. 12, problem 19, Conservation Alert p. 29, problem 47, Yes, We Can p. 30, problem 49, Weekly Renter represent data using tables and graphs such as line plots, bar graphs, and line graphs; Grade 3: p. 12, problem 19, Winter Favorites p. 21, problem 34, Pizza Pizza p. 27, problem 44, Shark Alert! p. 29, problem 47, Oh, Baby! p. 56, problem 92, Trip by Car, Train, or Plane? Grade 4: p. 2, problem 3, That’s Life p. 14, problem 23, Oh, Deer! p. 19, problem 31, Car Wash p. 24, problem 39, Deep Snow p. 36, problem 60, Rain, Rain, Go Away p. 42, problem 69, Rising Prices Grade 5: p. 19, problem 31, Book Binding p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business recognize the differences in representing categorical and numerical data. Grade 3: Can Be Developed From: p. 12, problem 19, Winter Favorites p. 29, problem 47, Oh, Baby! p. 56, problem 92, Trip by Car, Train, or Plane? Grade 4: Can Be Developed From: p. 19, problem 31, Car Wash p. 20, problem 34, Bowled Over p. 45, problem 74, Winter Fun


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Grade 5: Can Be Developed From: p. 19, problem 31, Book Binding p. 73, problem 121, Inch by Inch Select and use appropriate statistical methods to analyze data describe the shape and important features of a set of data and compare related data sets, with an emphasis on how the data are distributed; Grade 3: p. 12, problem 19, Winter Favorites Grade 4: p. 14, problem 23, Oh, Deer! p. 20, problem 34, Bowled Over p. 45, problem 74, Winter Fun Grade 5: p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business use measures of center, focusing on the median, and understand what each does and does not indicate about the data set; Grade 4: p. 62, problem 103, Team Totals compare different representations of the same data and evaluate how well each representation shows important aspects of the data. Grade 3: p. 27, problem 44, Shark Alert! Grade 4: p. 36, problem 60, Rain, Rain, Go Away Grade 5: p. 19, problem 31, Book Binding p. 49, problem 81, Shoe Story p. 73, problem 121, Inch by Inch p. 79, problem 131, Toy Business Develop and evaluate inferences and predictions that are based on data propose and justify conclusions and predictions that are based on data and design studies to further investigate the conclusions or predictions. Grade 3: p. 12, problem 19, Winter Favorites p. 20, problem 32, Tallying Traffic p. 23, problem37, Can Do p. 24, problem 39, Snow Bound p. 35, problem 57, Adding Ants Grade 4: p. 2, problem 3, That’s Life p. 19, problem 31, Car Wash p. 20, problem 32, Summer Camp p. 36, problem 60, Rain, Rain, Go Away p. 57, problem 94, Animal Lovers p. 61, problem 101, Books Galore


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Grade 5: p. 19, problem 31, Book Binding p. 24, problem 39, Scope It Out p. 29, problem 47, Yes, We Can! p. 35, problem 57, Shopping Spree p. 77, problem 127, Travel Plans Understand and apply basic concepts of probability describe events as likely or unlikely and discuss the degree of likelihood using such words as certain, equally likely, and impossible; Grade 3: p. 84, problem 140, A Horse Race Game Grade 4: p. 60, problem 100, What’s More Likely? p. 75, problem 125, Is It Fair? Grade 5: p. 33, problem 55, Spinners predict the probability of outcomes of simple experiments and test the predictions; Grade 3: p. 84, problem 140, A Horse Race Game Grade 4: p. 60, problem 100, What’s More Likely? Grade 5: p. 33, problem 55, Spinners p. 45, problem 75, More Spinners p. 60 problem 100, Rolling Numbers understand that the measure of the likelihood of an event can be represented by a number from 0 to 1. Grade 3: Can Be Developed From: p. 84, problem 140, A Horse Race Game Grade 4: Can Be Developed From: p. 75, problem 125, Is It Fair? Grade 5: Can Be Developed From: p. 33, problem 55, Spinners p. 45, problem 75, More Spinners p. 60 problem 100, Rolling Numbers PROBLEM SOLVING STANDARD solve problems that arise in mathematics and in other contexts; apply and adapt a variety of appropriate strategies to solve problems; monitor and reflect on the process of mathematical problem solving. In Problem Solving Experiences Grades 3-6, three strategies are emphasized at each grade level. In Grade 5 and 6, a strategy is used to develop algebra readiness. Chart on p. x shows problems related to each strategy. Problems are selected and sequenced to develop knowledge and study skills.


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REASONING AND PROOF STANDARD recognize reasoning and proof as fundamental aspects of mathematics; make and investigate mathematical conjectures; develop and evaluate mathematical arguments and proofs; select and use various types of reasoning and methods of proof. Grades 3-5: “Think Boxes” are included within each type of problem to help student understand and solve the problem. COMMUNICATION STANDARD organize and consolidate their mathematical thinking through communication; communicate their mathematical thinking coherently and clearly to peers, teachers, and others; analyze and evaluate the mathematical thinking and strategies of others; use the language of mathematics to express mathematical ideas precisely. Grades 3-5: All problems, other than estimation problems, should be completed in a small group setting to develop communication of mathematical thinking to others using the language of Mathematics. p. xv CONNECTIONS STANDARD recognize and use connections among mathematical ideas; understand how mathematical ideas interconnect and build on one another to produce a coherent whole; recognize and apply mathematics in contexts outside of mathematics. Grades 3-5: Problems are designed to connect mathematical ideas and recognize and apply mathematics in contexts outside of mathematics REPRESENTATION STANDARD create and use representations to organize, record, and communicate mathematical ideas; select, apply, and translate among mathematical representations to solve problems; use representations to model and interpret physical, social, and mathematical phenomena. Grades 3-5: Strategy problems at each grade level are designed to use representations to model and interpret physical, social, and mathematical phenomena and to organize, record, and communicate mathematical ideas.

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