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Standards-based assessment and Instruction

Investigations

Dale Seymour Publications. Copyright 1998, 2004, 2006

To access alignments for Investigations in Numbers, Data and Space, please choose from the grade levels below:

Kindergarten

Investigations in Number, Data and Space
Kindergarten

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking in Kindergarten
  • Establishing 1:1 correspondence
  • Exploring attributes of concrete materials
  • Counting a set of objects
  • Creating a set of a given size
  • Recording numerical information
  • Developing a sense of time
  • Connecting number names, numerals, and quantities
  • Collecting and exploring data
CDI
Betty's Blocks, Field Trip, Marsupials, Paleontologist

CDII
New Necklace, Let's Play, Finicky Cat, Buttons for Snowmen, Riding at the Playground

CDIII
Boots and Hats, Apples and Bananas

Volume 9
Boots and Hats

Volume 10
Apples and Bananas, Baby Ducks

Pre K-K Math Series
All in a Row, Red and Blue Blocks, Beautiful Bows, Beads on a Stick, Coming to the Park, Playing on the Playground, Counting Cars, Counting Books, A Flower Pattern, A Crayon Pattern, Making Cards, Finding Friends
Pattern Trains and Hopscotch Paths
  • Recognizing, describing, representing a pattern
  • Creating, extending, recording patterns
  • Predicting what comes next
  • Comparing patterns
  • Determining a rule for how a patterns grows
CDI
Flags, Ten Feet Apartment Building

CDII
New Necklace, Farmer, Petal Power, Let's Play, Lynn's Ladder, Eating Jellybeans

CDIII
Eating Apples

Volume 9
Drawing Apples, Pennies in a Bag

Volume 10
Eating Apples, Hopping Henry, Birds in the Spring, Peg's Purple Pebbles

Pre K-K Math Series
All in a Row, Red and Blue Blocks, Beautiful Bows, Beads on a Stick, A Flower Pattern
Collecting, Counting, and Measuring
  • Recognizing number and numeral names
  • Connecting numerals to quantities
  • Creating & counting sets of objects
  • Representing quantities
  • Keeping track and recording quantities
  • Developing and using language to describe, compare, and order amounts
  • Measuring by direct comparison
  • Finding totals of two single-digit numbers
  • Solving a problem with many possible solutions
CDI
Bug Watching, Frog and Toad, Someone's Been Eating My Porridge, How Big is A Foot, Snail Trails

CDII
Calendar Problem 1, Lining Up, Wonderful Leaves, Eating Jellybeans, Flies and Frogs

CDIII
Socks for Everyone, Apples and Bananas, Dinosaur Models, How Many Apples

Volume 9
Socks for Everyone

Volume 10
Apples and Bananas, Dinosaur Models, Books, Books, Books, How Many Apples?

Pre K-K Math Series
Apples, Pennies in a Bowl, Balloons, Playing with Toy Cars, Coming to the Park, Playing on the Playground, Counting Cars, Counting Books, Finding White Rocks, Finding Pinecones, Making Cards, Finding Friends, Oranges in a Bowl, Carrot Sticks on a Plate, Pepperoni Pizza, Sticking Stars on a Car, Pumpkins on a Table, Cups on a Table, Turtledove Feet, Two Pigeons
Counting Ourselves and Others
  • Developing, using strategies for counting
  • Relating counting to the quantity of items
  • Using 1:1 correspondence
  • Exploring 2:1 correspondence
  • Representing data in a variety of ways
  • Sorting objects by attributes
  • Collecting, recording and representing data
  • Sorting and organizing data in more that one way
  • Discussing information in a data representation
  • Composing survey questions
  • Gathering and recording survey data
  • Making sense of data representation
  • Describing categories for a sort
  • Solving a problem based on the data
  • Building a model to explain a problem solving strategy
CDI
Worms, Typical Objects, Space Creatures, Valentine M&M® Problems,

CDII
Sharing Sleds, Betty's Blocks, Finicky Cat, Ice Cream

CDIII
Number Blocks

Volume 9
Pennies for Patty

Volume 10
Hopping Henry, Number Blocks, Baby Ducks

Pre K-K Math Series
Apples, Pennies in a Bowl, Balloons, Playing with Toy Cars, Coming to the Park, Playing on the Playground, Counting Cars, Counting Books, Finding White Rocks, Finding Pinecones, Making Cards, Finding Friends, Oranges in a Bowl, Carrot Sticks on a Plate, Pepperoni Pizza, Sticking Stars on a Car, Playing with Dinosaurs, Crackers on a Plate, Pumpkins on a Table, Cups on a Table, Rub-a-Dub-Dub, Jack and Jill, Snack Time, Mini Muffins for Snack, Sharing Apples, Sharing Red Paper, Turtledove Feet, Two Pigeons
Making Shapes and Building Blocks
  • Recognizing shapes in the environment
  • Observing and describing 2-D and 3-D figures
  • Developing vocabulary to describe 2-D and 3-D figures
  • Becoming familiar with names of 2-D and 3-D figures
  • Relating 2-D and 3-D figures to real world objects
  • Relating a d-D object to a 2-D shape
  • Visualizing how to move a shape so that it is oriented correctly to fit into a design
  • Finding combinations of shapes that fill an area
  • Building knowledge about the relationships among pattern block shapes
  • Looking at 3-D objects as whole and as having parts
CDI
Paleontologist, Sink or Float, Geometry, Pieces of Pizza, Bowls of Apples

CDII
A Shower of Shapes

CDIII
Shapes on the Playground

Volume 9
Shapes on the Playground

Pre K-K Math Series
Justin's Placemat, Pattern-Block Shapes and a Paper, A New Shape, Helping Ken, Paper Snowman, A Paper Car
How Many in All?
  • Counting up to 20 objects
  • Representing quantities
  • Repeating a nonstandard measure to quantify length
  • Combinations of 5,6, and more
  • Developing Strategies
  • Recording Strategies
  • Comparing amounts
  • Finding totals of single-digit numbers
CDI
Octopus, Clay Pots, Marsupials, Pig Pens, Birthday Gift Shopping, Betty's Blocks, License Plates,

CDII
Farmer Brown, Riding at the Playground, Legs, Nine Cents

CDIII
Socks for Everyone, Crackers, Eathing Apples, Dinosaur Models, Car Wash, How Many Apples, Picking Up Shapes

Volume 9
Socks for Everyone

Volume 10
Crackers, Eating Apples, Dinosaur Models, Lots of Reading, Car Wash, The Ball cart, Books, Books, Books, How Many Apples?, Picking Up Shapes

Pre K-K Math Series
Apples, Pennies in a Bowl, Balloons, Playing with Toy Cars, Coming to the Park, Playing on the Playground, Counting Cars, Counting Books, Finding White Rocks, Finding Pinecones, Oranges in a Bowl, Carrot Sticks on a Plate, Pepperoni Pizza, Sticking Stars on a Car, Playing with Dinosaurs, Crackers on a Plate, Pumpkins on a Table, Cups on a Table, Rub-a-Dub-Dub, Jack and Jill, Sharing Apples, Sharing Red Paper, Snack Time, Mini Muffins for a Snack, Turtledove Feet, Two Pigeons

Grade One

Investigations in Number, Data and Space
First Grade

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking at Grade 1
  • Compare and find relationships among geometric shapes
  • Exploring concrete materials and tools
  • Developing strategies for comparing quantities
  • Finding combinations of numbers up to 10
  • Representing solutions to math problems with pictures, numbers, words
  • Describing, predicting and constructing patterns
  • Counting, recording, comparing sets of objects
  • Using counting, patterns, an other strategies to help solve problems
  • Making and explaining predictions
  • Inventing representations that show what a survey is about
  • Categorizing, representing, presenting data
  • Making sense of survey results
CDI
Muffins, Octopus, Hot Chocolate, Number Cube Game, In Line,

CDII
Lining Up, Legs, Nine Cents, Someone's Been Eating My Porridge, Holiday Fair Shopping

CDIII
Patty's Pennies, Boots and Hats, Socks for Everyone, Measuring a Tulip, Collecting Sea Shells

Volume 9
Pennies for Patty, Drawing Apples, Pennies in a Bag, Boots and Hats, Socks for Everyone, Measuring a Tulip, Collecting Shells

Volume 10
Apples and Bananas, Dinosaur Models, Crackers, Eating Apples, Hopping Henry, Number Blocks, Picking Up Shapes, Car Wash, Baby Ducks, Peg's Purple Pebbles, Picking Up Shapes, Stars
Building Number Sense
  • Counting quantities to 20, 40
  • Developing strategies for counting/comparing
  • Developing strategies for organizing collections
  • Using numerals to record how many
  • Finding combinations of numbers
  • Finding total of two quantities
  • Reading, writing, sequencing numbers to 100
  • Visualizing combining/separating problem situations
  • Developing and recording strategies for solving combining/separating problems
CDI
Frog and Toad, Bug Watching, Darts, Number Cube Game, Clay Pots, Marsupials, Witches Transportation

CDII
Petal Power, Betty's Blocks, Flies and Frog, Staying Warm, Ice Cream

CDIII
On Time, Pizza Time, New Stones for Jim, Dinosaur Models, Crackers, Eating Apples, Number Blocks, The School Store, Car Wash, How Many Apples

Volume 9
Michael's Minutes, On Time, Pizza Time, New Stones for Jim

Volume 10
Dinosaur Models, Crackers, Eating Apples, Hopping Henry, Lots of Reading, Number Blocks, The School Store, Car Wash, Birds in the Spring, Books, Books, Books, How Many Apples?
Survey Questions and Secret Rules
  • Identifying/describing attributes
  • Using an attribute for sorting/categorizing
  • Developing strategies to guess a rule
  • Creating representations of sorted objects
  • Making a plan for gathering and recording data
  • Inventing and constructing data representations
  • Explaining and interpreting results of surveys
  • Presenting data to others clearly
  • Developing familiarity with calendars
  • Describing data quantitatively and qualitatively
  • Comparing two data sets
CDI
Typical Objects, Worms, Chip Chance, Fishing, Hats and Scarves, Valentine M&M® Problem, Number Cube Game,

CDII
Finicky Cat, Perplexing Palindromes, Share and Share Alike, Calendar Problem

CDIII
Fudge, Feeding Fred, How Many Apples

Volume 9
Fudge, Feeding Fred

Volume 10
How Many Apples, The Ball Cart
Quilt Squares and Block Towns
  • Observing, describing, comparing 2-D/3-D shapes
  • Developing geometric vocabulary/names/terms
  • Sorting shapes
  • Composing/decomposing shapes
  • Observing relationships among shapes
  • Using rotations/reflections
  • Filling a region
  • Visualizing/representing 2-D shapes, rectangular prisms
  • Building a pattern with shapes
  • Constructing 3-D shapes using 2-D representations
CDI
Paleontologist, Pentomino Problem, Seats and Tables, Geometry, Making a Necklace

CDII
Shower of Shapes, Happy Birthday Abby

CDIII
Fudge, Shapes on a Playground, Number Blocks

Volume 9
Prisms, Fudge, Pretty Shapes, Shapes on the Playground

Volume 10
Number Blocks
Number Games and Story Problems
  • Finding combinations of numbers
  • Finding total of 2 or more numbers
  • Exploring relationships among different combinations of a numbers
  • Developing strategies for organizing sets of objects
  • Finding total of 2's, 4's, 5's, or 10's
  • Recording strategies for counting and combining
  • Reading, writing, and sequencing numbers to 100
  • Becoming familiar with coins and equivalencies
CDI
Birthday Gift Shopping, Muffins, Whoo is Hunting? Stacking Caps, License Plates, Six-Pack of Soda, Snow Play, Field Trip, Average Number of Letters, Pig Pens

CDII
Mary Quite Contrary, Flies and Frogs, Lining Up, Sweet Sale, Legs

CDIII
Collecting Seashells, Patty's Pennies, Pizza Time, Dinosaur Models, Crackers, Eating Apples, Number Blocks, The School Store, Car Wash, How Many Apples

Volume 9
Collecting Shells, Pennies for Patty, Pizza Time

Volume 10
Dinosaur Models, Crackers, Eating Apples, Hopping Henry, Lots of Reading, Number Blocks, The School Store, Car Wash, Birds in the Spring, Books, Books, Books, How Many Apples?
Bigger, Taller, Heavier, Smaller
  • Developing sense of heavier and lighter
  • Developing language to describe and compare weight, capacity, lengths
  • Learning to use a balance; order lengths
  • Comparing weights, capacities, lengths of objects
  • Measuring and comparing capacity, lengths, using nonstandard units
  • Collecting and keeping track of data
  • Representing measurements with numbers, concrete materials, and pictures
CDI
Coin Combinations, How Big is a Foot? Marshmallow Peeps all in a Row, Sink or Float, Snail Trails, Wonderful Leaves

CDII
Dandelion Dilemma!

CDIII
On Time, Measuring A Tulip

Volume 9
On Time, Measuring a Tulip

Grade Two

Investigations in Number, Data and Space
Second Grade

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking at Grade 2
  • Explore materials; describe, sort based on attributes; count sets of objects, write number expressions
  • Keep track of school days, write equations; make combinations of 10; identify uses of numbers
  • Explore, describe 2-D geometric shapes; explore, sort, and describe 3-D shapes; find different shapes for area; find and record several solutions to a problem
  • Count objects; count by 2's, 5's, 10's; compare sets; add two digit numbers; identify coins and values; combine coins to make 25 and 50
  • Sort and classify information, collect, record, and represent data; count and compare amounts; count groups of objects in more than one way; talk and write about problem-solving strategies
CDI
Muffins, Piggy Bank, Paleontologist, Ten Feet Apartment, Frog and Toad, Canoe Trip, Darts, Six-Pack of Soda

CDII
Chaperones, Dandelion Dilemma, Flies and Frogs, Let's Play, Someone's Been Eating My Porridge!

CDIII
Patty's Pennies, Baking Brownies, Number Blocks, Oranges for Snacks, Picking Up Shapes

Volume 9
Pennies for Patty (introductory), Baking Brownies, Drawing Apples

Volume 10
Number Blocks, The Ball Cart, Oranges for Snacks, Peg's Purple Pebbles, Picking Up Shapes, Stars
Coins, Coupons and Combinations
  • Develop familiarity with 10, work with combinations of 10 and doubles; develop strategies for adding two or more numbers
  • Explore patterns, develop fluency in skip counting 2s, 5s, 10s; explore recording large groups; become familiar with coin equivalencies; use money as model for 5s and 10s
  • Develop models of add/sub situations; solve problems using add/sub notation
  • Become familiar with structure of 100; use 100 chart; use familiar add combinations to find totals; develop add/sub strategies
CDI
Birthday Gift Shopping, Coin Combinations, Coins, Stacking Caps, Another Domino Dilemma, Ten Feet Apartment, Bug Watching

CDII
Seedlings to Timber, Mary Quite Contrary, How Does Your Garden Grow? Sweet Sale

CDIII
The School Store, Car Wash, Oranges for Snacks

Volume 9
Piggy Bank

Volume 10
Feeding the Goats, Hopping Henry, Sally's Marble Collection, The School Store, The Ball Cart, Birds in the Spring, Books, Books, Books, Car Wash, Oranges for Snacks, Stars
Does It Walk, Crawl, or Swim?
  • Examine similarities, differences in data; clarify categories; sort, classify information; collect, record, represent data; use Venn diagrams
  • Use characteristics of data, articulate logic, construct categories for data; invent representation of data; use more than one representation to view data
  • Work on constructing categories to describe data; organize categorical data
  • Collect, record survey data; compare data sets; make presentation graphs; report on data analysis
CDI
Chip Chance, Field Trip, Sink or Float, Space Creatures

CDII
Finicky Cat, Ice Cream
Shapes, Halves, and Symmetry
  • Sort, describe, identify shapes by attributes; compose/decompose 2/3 D shapes; describe spatial relationships
  • Identify triangles/rectangles based on number of sides/corners; visualize, construct, draw arrays; use numbers to compare arrays
  • Work with arrays and geometric solids to investigate fractional parts; design, construct rectangular regions that are divided into halves, thirds, or fourths
CDI
Bowls of Apples, Geometry, Paleontologist, Pentomino Problem, Seats and Tables,

CDII
Happy Birthday, Abby, Hatching Chicks, Renting Craft Space, A Shower of Shapes, Pizza Party

CDIII
Baking Brownies, Fudge, Pizza Time, How Many Apples

Volume 9
Baking Brownies, Fudge, Prisms, Pretty Shapes, Pizza Time

Volume 10
How Many Apples?
Putting Together and Taking Apart
  • Develop models of add/sub; solve problems using numerical reasoning; record strategies; use horizontal and vertical notation for add/subtraction
  • Become familiar with structure and patterns of numbers from 1-100; use coins as model for add/sub multiples of 5, 10; use 100 chart; compare numbers to 100
  • Develop ways to approach different add/sub problems; recognize, solve variety problem structures; compare solution strategies; create situations for equations
  • Work with 100, combinations up to 100; add string of numbers; write story for addition equation
  • Develop strategies for comparing; calculate distance between two numbers using 100 chart; develop ways to approach, recognize, solve variety of problem structures
CDI
Average Number of Letters, 100th Birthday Celebration, Valentine's Day Party Plan, Witches Transportation

CDII
Holiday Fair Shopping Spree

CDIII
Socks for Everyone, Collecting Seashells, Dinosaur Models, Number Blocks, The School Store, Car Wash

Volume 9
Socks for Everyone, Collecting Shells

Volume 10
Dinosaur Models, Feeding the Goats, Number Blocks, The School Store, The Ball Cart, Books, Books, Books, Car Wash
How Long? How Far?
  • Use direct, indirect comparison to compare lengths; construct a nonstandard unit to measure length; compare effects of measurement using different size units; communicate need for using standard units
  • Focus on moving on a path; visualize, represent path; determine path length by iterating; compare lengths of path
CDI
Fencing, Hard Workers, How Big is a Foot? Marshmallow Peeps® all in a Row, Snail Trails, Wrist Circumference

CDII
Wonderful Leaves

CDIII
Measuring a Tulip

Volume 9
Measuring a Tulip
How Many Pockets? How Many Teeth?
  • Collect, keep track of, organize numerical data; create representations of data; describe, interpret representations
  • Focus on features of data; compare, interpret, hypothesize about data sets
  • Plan a data-analysis project
CDI
Easter Baskets, Number Cube Game, Stacking Caps, Typical Objects, Valentine M&M® Problem

CDII
Finicky Cat, Ice Cream, Perplexing Palindrome Problem

CDIII
Feeding Fred

Volume 9
Feeding Fred
Timelines and Rhythm Patterns
  • Sequence events; represent events in time; compare durations of time of a day; learn time notation
  • Invent rhythm patterns; communicate with and interpret written symbols and codes
CDI
Eggsactly, Piano Schedule

CDII
Let's Plan a Party, Calendar Problem, Eating Jellybeans

CDIII
On Time

Volume 9
On Time, Michael's Minutes

Volume 10
Lots of Reading, Birds in the Spring

Grade Three

Investigations in Number, Data and Space
Third Grade

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking at Grade 3
  • Count, group quantities to 100; become familiar with patterns on 100 chart; explore materials; communicate math thinking through written and spoken language
  • Construct symmetrical patterns for addition combinations; develop add strategies; explore numbers divided into halves
  • Sort, classify information; collect, record, and represent data; describe data in tallies or graphs; use groupings; use strategies for combining and comparing quantities
  • Explore characteristics of odd, even numbers; examine their combinations; become familiar with calculators
CDI
Presents, Ant in the Well, Chocolate Chip Cookie Rubric

CDII
Chick-a-dee-dee, Good-bye Party Fun, Lost Count

CDIII
A Challenge?, Letter Patterns, Playing Checkers, Pattern Block Walls, Calling All Students, Picture Frames, Improving His Aim, Pumpkin Character Challenge, Bobsled Blunders, Jeff's Marbles, Barney's Bakeries, Lunch at the Hot Dog Hut, Saving Money

Volume 9
Pattern Block Walls, Calling All Students, Picture Frames, Improving His Aim, Pumpkin Character Challenge

Volume 10
Bird Watching, Bobsled Blunders, Jeff's Marbles, Olympic Medal Count, Barney's Bakeries, Barnum's Animal Cracker Circus, Building with Blocks, Collections, Fishing Worms, Kate's Flower Garden, Lunch at the Hot Dog Hut, Over in the Meadow, Saving Money
Things That Come in Groups
  • Find things that come in groups; use multiplication notation; use multiplication to mean groups of groups; write and illustrate multiplication sentences
  • Recognize the relationship of skip counting, area, and arrays to multiplication; look for patterns in multiples
  • Find factor pairs; make connections between number and arrays
  • Understand the relationship between mult and division and use notation for number sentences
  • Multiply and divide in real-life situations; use patterns to solve problems; organize, present data in tables and line plots; use tables and line plots
CDI
Camping, Checkerboard Investigation, Great Pizza Dilemma

CDII
Meddling with the Medals, A Very Fishy Story

CDIII
Picture Frames, Jeff's marbles, Raising Chicks, Barney's Bakeries, Lunch at the Hot Dog Hut, Saving Money

Volume 9
Fruit Punch, Picture Frames

Volume 10
Jeff's Marbles, Raising Chicks, Snack Shopping, Barney's Bakeries, Barnum's Animal Cracker Circus , Building with Blocks , Hiking , Kate's Flower Garden t, Lunch at the Hot Dog Hut, Over in the Meadow, Saving Money
Flips, Turns, and Area
  • Measure area; find patterns for area; compare areas; describe flips, slides, and turns; compare shapes for congruency
  • Measure areas; explore relationships among and within shapes; find areas of complex shapes by cutting apart
CDI
Checkerboard Investigation, Two-Inch Square, Mrs. Hasson's Decorating Dilemma, Tangram Areas - Grandfather Tang's Story

CDII
Cookie Cutters, Right-Equilateral Triangle?

CDIII
Pattern Block Walls

Volume 9
Pattern Block Walls
From Paces to Feet
  • Use nonstandard units to measure distance; experience iteration; estimate length; compare using different-sized unit; analyze data; write and follow directions for distance
  • Understand reason for standard measures; become familiar with inches, ft, yd, cm, m; represent data on a line plot
  • Use standard measures for complex problems to gather, analyze data; collect, organize, represent, analyze data
  • Develop awareness of cm during a project
CDI
Miss Guy's Puppy Problem, Playground Committee, Post Office Display, Sandbox for Geoffrey, Zeno the Xylophone Maker

CDII
Valentine's Day Cards

CDIII
Barney's Bakeries

Volume 9
Getting Ready

Volume 10
Making Candles, Barney's Bakeries
Landmarks in the Hundreds
  • Understand relationship between skip counting and grouping; understand relationship between factors and multiples; become familiar with factors of 100 and use as a landmark;
  • Develop strategies to solve mult and div problems; estimate quantities close to 200, 300, 400, up to 1000, using landmark numbers; use standard multiplication/division notation for problems
  • Work with factors of 100 to build understanding of 1000; estimate quantities to 1000; use landmarks
CDI
Missing Key Dilemma, I-Did-A-Read, Necco® Mania

CDII
Chick-a-dee-dee, Good-bye Party Fun

CDIII
Improving His Aim

Volume 9
Improving His Aim

Volume 10
Bird Watching, Over in the Meadow
Up and Down the Number Line
  • Develop concept of net change and strategies for computing; construct knowledge of positive and negative numbers
  • Represent numbers graphically; interpret change on a number line, graph; compare overall shapes of graphs
  • Relate direction to positive, negative numbers
CDI
Ant in the Well, Filling the Pool, Miss Guy's Puppy Problem, Pedal Power, Penny a Day, Winning Ticket

CDII
Fair's Fair?, Good-bye Party Fun

CDIII
Batting Practice

Volume 10
Batting Practice, Bird Watching, Kate's Flower Garden
Combining and Comparing
  • Compare numbers and develop strategies to determine differences; develop ways to get to 100 by combining numbers; use landmark numbers to compare quantities
  • Develop understanding "change" in weight, time, distance; find how far a number is from next multiple of 10, 100
  • Solve addition problems with multiple addends; develop addition strategies; use standard addition & subtraction notation; use equivalencies in time, money, linear measures
  • Collecting, recording, graphing data and making predictions about data
  • Exploring math characteristics of calendar
CDI
Another Domino Dilemma, Busy Day, Raccoons, Kwanza Celebration, Necco® Mania

CDII
"Planely" a Problem, Getting Ready

CDIII
Celebrating My Birthday, Bobsled Blunder, Saving Money

Volume 9
Fruit Punch, Spilled Milk, Getting Ready, Celebrating My Birthday, Breakfast with Grandmother

Volume 10
Bird Watching, Bobsled Blunders, Snack Shopping, Fishing Worms, Hiking, Kate's Flower Garden, Over in the Meadow, Saving Money
Turtle Paths
  • Understand paths and movement representations; apply math processes such as add, sub, estimation
  • Describe attributes of triangles, including degrees of rotation; apply addition, subtraction, estimation, logic skills for missing measures of figures
  • Construct geometric figures; understand shapes' movements; estimate and measuring perimeters; pose and solve original geometric problems
CDI
Bulletin Board Border, Tangram Areas - Grandfather Tang's Story, Carpet Caper

CDII
Valentine's Day Cards

CDIII
Pattern Block Walls, Picture Frames

Volume 9
Pattern Block Walls, Right-Equilateral Triangle? Picture Frames,
Fair Shares
  • Realize fractional parts must be equal; understand conventional fraction words and notation
  • Become familiar with unit fractions, equivalent fractions
  • Understand relationships between fractions and division; relate notation for division and fractions on the calculator
CDI
Deluxe Birthday Cake, Equal Snacks, Great Pizza Dilemma, Is Dan Losing His Marbles?, Making a Fair Decision

CDII
A Lucky Draw, Fair's Fair?, Pattern Block Thinking, "M&M" Cookie Combos

CDIII
Lugging Water, Lost Spinner

Volume 9
Spilled Milk

Volume 10
Lugging Water, Fishing Worms
Exploring Solids and Boxes
  • Explore, sort, and describe geometric solids; analyze similarities and differences among solids
  • Recognize attributes of polygons, polyhedra
  • Explore 2-D geometric patterns & relationship to 3-D shapes; improve spatial visualization
  • Predict volume; understand structure of rectangular prism arrays of cubes
  • Problem-solving involves planning, trial and error, analysis, and visualization, as well as appropriate computation techniques
CDI
Party Seating, Playground Fun, Tangram Areas - Grandfather Tang's Story

CDII
Valentine's Day Cards

CDIII
Pattern Block Walls, Calling All Students, Picture Frames

Volume 9
Pattern Block Walls, Right-Equilateral Triangle? Calling All Students, Picture Frames

Volume 10
Follow My Lead

Grade Four

Investigations in Number, Data and Space
Fourth Grade

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking at Grade 4
  • Learn to group items for more efficient counting; reorder number for efficient mental math; explore materials; estimates hundreds in 3 digit numbers; communicate math thinking through spoken and written language
  • Group coins for efficient counting; recognize values of coins; recognize use of decimal point on the calculator (with money)
  • Focus on known answer to find unknown ones; subtract on a 300 chart; add, subtract multiples of ten
  • Distinguish between geometric patterns and random designs; between mirror and rotational symmetry; write about designs
CDI
Raccoons, Portfolio Pizza Party, Another Domino Dilemma, Dominoes, Fish Dilemma, Missing Key Dilemma

CDII
Dependable Parent Volunteers, M&M® Cookie Combos

CDIII
A Challenge?, Letter Patterns, Playing Checkers, Pattern Block Fish, Calling All Students, A Pyramid of Crunchkins, Batting Practice, Bobsled Blunder, Saving Money

Volume 9
Pattern Block Fish, Calling All Students, A Pyramid of Crunchkins

Volume 10
Batting Practice, Bird Watching, Bobsled Blunders, Olympic Medal Count, Barnum's Animal Cracker Circus, Collections, Hiking, Kate's Flower Garden, Over in the Meadow, Saving Money
Arrays and Shares
  • Use skip counting; look for multiplication patterns; interpret standard mult/div notation; use known multiplication relationships to solve more complicated ones
  • Use an array as model for multiplication; recognize prime numbers; use variety of notations for multiplication and division; understand how division notation represents sharing and partitioning; determine what to do with "leftovers" in division
  • Partition numbers to multiply more easily; represent mult/div situations using math sentences; use patterns for multiplication by 10
CDI
Carpet Caper, Miss Guy's Puppy Problem, Missing Key Dilemma, More for the Money

CDII
Chick-a-Dee Dee

CDIII
Batting Practice, Raising Chicks, Lunch at the Hot Dog Cart, Saving Money

Volume 10
Batting Practice, Bird Watching, Raising Chicks, Snack Shopping, Lunch at the Hot Dog Hut, Over in the Meadow, Saving Money
Seeing Solids and Silhouettes Students
  • Develop concept and language for3-D spatial relationships; explore these among components of 3-D figures; develop visualization skills; think about volume
  • See how 3-D solids project 2-D shadows; learn about perspective; learn to visualize objects;
  • Interpret instructions; integrate information gathered from views or discussion
  • Work in centers creating toys, writing instructions; focus on effective communication skills
CDI
Checkerboard Investigation, Two-Inch Square, Carpet Caper, Miss Guy's Puppy Problem

CDII
Cookie Cutters

Volume 10
Follow My Lead
Landmarks in the Thousands Students
  • Find and count by factors of 100; use landmarks to find differences between numbers under 100
  • Use knowledge of factors of 100 to explore multiples of 100; relate knowledge of factors to division situations; add multiples of 10 to and subtract from numbers in the hundreds; communicate strategies
  • Read and write numbers to 1000; gain sense of magnitude up to 1000; use landmarks to 1000; develop strategies for add/sub numbers in the hundreds; estimate to 1000
  • Read, write, and sequence numbers in the 1000's
CDI
New Year's Party, Necco(r) Mania, I-Did-A-Read, M&M® Mini-Bus Challenge, Missing Key Dilemma, More for the Money

CDII
Starring the Washington Monument!

CDIII
Jeff's Marbles, Lugging Water

Volume 10
Jeff's Marbles, Lugging Water
Different Shapes, Equal Pieces
  • Understand that equal fractions of a whole have same area; equal shapes are not necessarily congruent
  • Become familiar with relationships among thirds, sixths, and twelfths; use different combinations to make a whole; compare fractions; work with numerators greater than 1
  • Compare fractions to landmarks; order fractions; identify equivalent fractions
CDI
Deluxe Birthday Cake, Disappearing Cookies, Great Pizza Dilemma, Is Dan Losing His Marbles? Party Seating, Sandbox for Geoffrey, Should We Burst Their Bubble?

CDII
Dependable Parent Volunteers, Feverish Freddy, Fun Night, Ollie Owl's Food Court, Who Owns the Most Land?

CDIII
Lost Spinner, Pumpkin Character Challenge, A Pyramid of Crunchkins

Volume 9
Right-Equilateral Triangle? Pumpkin Character Challenge, A Pyramid of Crunchkins

Volume 10
Fishing Worms
The Shape of the Data
  • Make sketches of data; describe shape of data distribution; define ways data will be collected; summarize typical aspects of data
  • Invent ways to compare two sets of data; use linear measurement; visualize and estimate lengths and heights; use median to describe data; find the median
  • Organize a complete data-analysis project (from question to display)
CDI
Theodore Bear, Necco® Mania, Bulletin Board Border, Camping, The Early Bird Catches the Worm, Job Hunting, M&M® Mini-Bus Challenge, Making a Fair Decision, Miss Amico's Birthday Bash, Spring Seeds, Theodore Teddy Bear

CDII
Bridge Building on Lake Champlain

CDIII
Pattern Block Fish, Batting Practice, Bobsled Blunders, Barney's Bakeries

Volume 9
Pattern Block Fish, New Equipment, Pavich Organic Snack Raisins

Volume 10
Batting Practice, Bird Watching, Bobsled Blunders, Making Candles, Barney's Bakeries
Money, Miles and Large Numbers
  • Estimate sums of money; explore relationships with money; develop strategies for combining; use tens as landmarks for money; use standard add/sub notation; interpret decimals
  • Estimate distances; compare, combine, find differences for decimal numbers;
  • Measure distances on maps using a scale; become familiar with common decimal and fraction equivalents
CDI
Portfolio Pizza Party, Zeno the Xylophone Maker, Blue Print, Job Hunting, Necco® Mania, Penny a Day

CDII
Bridge Building on Lake Champlain, "Planely" a Problem, Who Owns the Most Land?

CDIII
Lunch at the Hot Dog Cart, Saving Money

Volume 10
Bird Watching, Snack Shopping, Fishing Worms, Lunch at the Hot Dog Hut, Saving Money
Changes Over Time
  • Plant beans and follow growth of plants
  • Make graphs to show change over time; invent representations of data; interpret graphs; develop a scale
  • Examine real situations, events that show change; interpret representation that show change
  • Use curves to communicate information; compare slow and fast growth; integrate quantitative, qualitative, and graphical descriptions of same data
CDI
Spring Seeds, Busy Day, Fillilng the Pool, I-Did-A-Read, Spring Seeds

CDII
Don't Let the Bedbugs Bite! To the Detail

CDIII
Batting Practice

Volume 9
Pavich Organic Snack Raisins

Volume 10
Batting Practice, Bird Watching, Barney's Bakeries, Barnum's Animal Cracker Circus, Building with Blocks, Collections, Hiking, Kate's Flower Garden
Packages and Groups
  • Look for and use multiplication patterns of numbers; become familiar with multiples of large numbers and identify their factors
  • Use familiar landmarks to solve problems; partition large numbers to multiply them easily; solve double-digit multiplication problems
  • Understand division notation; create context representative of a division equation; use landmarks to solve problems; use mult/division relationships to solve problems
CDI
Dominoes, More for the Money, Mrs. Hasson's Decorating Dilemma, Playground Committee

CDII
Chick-a-dee-dee

CDIII
Picture Frames, Ls for Linda, Jeff's Marbles, Lugging Water, Saving Money

Volume 9
Picture Frames, L's For Linda, Pavich Organic Snack Raisins

Volume 10
Jeff's Marbles, Lugging Water, Snack Shopping, Saving Money
Sunken Ships and Grid Patterns
  • Use positive/negative coordinates to name and locate points; calculate distances on a grid; explore numerical patterns; connect visual and numerical descriptions
  • Apply knowledge of coordinates to locate points; describe geometric figures in different ways; create and apply patterns and mental math to solve problems; use mirror and rotational symmetry to place rectangles on a grid
CDI
Ant in the Well, Tangram Areas, Tangram Money, Terrific Tiles

CDII
Chick-a-Dee Dee

CDIII
Picture Frames, Ls for Linda

Volume 9
Picture Frames, L's For Linda
Three out of Four Like Spaghetti
  • Learn to partition a group according to a rule; find familiar fractions; estimate fractions; collect and analyze categorical data; describe data in terms of fractions; use fractions to compare data
  • Use fractions to describe/compare data; try different ways to classify data; classify, display, describe, interpret data collected
CDI
Theodore Bear, Spring Seeds, Portfolio Pizza Party, New Year's Party, Necco® Mania, Equal Snacks, Disappearing Cookies, New Year's Party, s, Spring Seeds

CDII
A Fair Snack? Galaxy Arca Pavich Organic Snack Raisins

Grade Five

Investigations in Number, Data and Space
Fifth Grade

Dale Seymour Publications. Copyright 1998, 2004, 2006
Investigations Unit Math Concepts Exemplars Tasks/Location
Mathematical Thinking at Grade 5
  • Describe numbers, relationships using terminology; develop, discuss, compare strategies for solving problems; learn that problems have more than one solution; communicate thinking
  • Use knowledge of landmark numbers; develop strategies for explore number compositions; read, write, order numbers to 1000; become familiar with factors of 1000, 10,000; skip counting patterns that lead to 1000, 10,000
  • Develop mult/division strategies that rely on landmarks up to 10,000
  • Develop mental, written strategies for finding sums/differences of 3 and 4-digit numbers; read, write, order numbers to 10,000
CDI
Raccoons, Portfolio Pizza Party, Ant in the Well, Carpet Caper, Is Dan Losing His Marbles? Missing Key Dilemma, Playground Fun, Portfolio Pizza Party, Should We Burst Their Bubble? Sleigh Rides, Stacks of Coins, What is Fair?

CDII
Chick-a-dee-dee, Skating Party, Starring the Washington Monument

CDIII
Letter Patterns, Batting Practice, Bobsled Blunders

Volume 9
New Equipment

Volume 10
Batting Practice, Bird Watching, Bobsled Blunders, Olympic Medal Count, Barnum's Animal Cracker Circus, Collections, Hiking, Kate's Flower Garden
Picturing Polygons
  • Distinguish between polygons, nonpolygons; draw them; locate points on coordinate grid; recognize, name polygons by number of sides
  • Reason, communicate about properties of shapes; sort, classify, develop terminology triangles, quadrilaterals; estimate, measure sizes of angles
  • Explore relationship between number of sides on polygon, sums of its turns and angles; explore relationships among angles, line lengths, and areas of similar polygons; compare areas of shapes
CDI
Carpet Caper, Checkerboard Investigation, Deluxe Birthday Cake, Stained Glass Surprise

CDII
Cookie Cutters, Feverish Freddy, Fun Night, Ollie Owl's Food Court, Who Owns the Most Land? Pattern Block Thinking

CDIII
Pyramid of Crunchkins

Volume 9
Right-Equilateral Triangle? A Pyramid of Crunchkins

Volume 10
Follow My Lead, Barnum's Animal Cracker Circus
Name That Portion
  • Use fractions to describe how many in a group share a characteristic; represent fractions, percents on number line; find, order equivalent fractions, percents; interpret common uses of percents; build on unit fraction knowledge
  • Represent fractions as rotation around a circle; mark strips into fractional parts; find equivalent fractions; order, add fractions
  • Represent decimals on grids; read, write, order, add decimals; divide to find decimal equivalents of fractions; compare fractions using different models, notations; make sense of word problems using fractions, decimals
  • Plan, conduct surveys; organize, represent data as fractions, percents, circle graphs; interpret common uses for fractions, decimals, percents
CDI
Checkerboard Investigation, Two-Inch Square, Deluxe Birthday Cake, Equal Snacks, Is Dan Losing His Marbles? Portfolio Pizza Party, Shopping for Shoes, Should We Burst Their Bubble? Shovel, Shovel, Shovel, Zeno the Xylophone Maker

CDII
Book Club, Dependable Parent Volunteers, Feverish Freddy, Fun Night, Taco Spread, Who Owns the Most Land?

CDIII
Lugging Water

Volume 9
Spilled Milk

Volume 10
Lugging Water, Fishing Worms
Between Never and Always
  • Associate verbal descriptions of probability with numeric descriptions; repeat probability experiments; use probability to predict; estimate probabilities from results of actual trials; predict, analyze features of distribution; learn to add probabilities of simple events
  • Interpret fairness of game; develop systematic ways to generate a list; distinguish between games of chance/skill; analyze group data in terms of general features-center, spread; understand variability in results
CDI
New Year's Party, Necco® Mania, Making a Fair Decision, Miss Amico's Birthday Bash, Valentine Candy Challenge

CDII
Fair's Fair, A Lucky Draw, The Price is Right, But Are You? Pattern Block Thinking
Building on Numbers You Know
  • Relate repeated add to mult; use skip-counting patterns; develop, explain, compare strategies for subtracting larger numbers; record computation strategies in numbers, words, symbols
  • Develop, record, compare strategies for solving mult, division problems; make sense of remainders; understand relationships between mult, division; model situations with mult, div, and other operations
  • Develop, explain, record, compare strategies for estimating, finding exact answers; solve mult, division problems in more than one way
  • Work on developing sense of quantities up to 100,000s; use rectangular array model to represent factor pairs of large numbers; develop a sense of 1 million
  • Apply computation strategies to more difficult problems; develop strategies for estimating answers to difficult problems; read, write, sequence multiples up to one million' develop sense of one million; understand relationships among four basic operations
CDI
Carpet Caper, Filling the Pool, Great Pizza Dilemma, I-Did-A-Read, Portfolio Pizza Party, Shovel, Shovel, Shovel, What's the Problem? Winning Ticket

CDII
Chick-a-dee-dee, Feverish Freddy, Fun Night, "M&M® Cookie Combos

CDIII
Jeff's Marbles, Raising Chicks, Lunch at the Hot Dog Hut, Saving Money

Volume 10
Bird Watching, Jeff's Marbles, Raising Chicks, Snack Shopping, Kate's Flower Garden, Lunch at the Hot Dog Hut, Over in the Meadow, Saving Money
Measurement Benchmarks
  • Use tools for measuring length, weight, volume, time; recognize different units of measure; use benchmarks to estimate; decide when precise measurement is required; keep track of, calculate total measurements; compare distances; use scale on maps
  • Order items by measures of weight, liquid quantities; compare relative sizes of standard, metric measures; measure weight with balance; distinguish between quantity and weight; use graphs to organize data; develop benchmarks for larger weights
CDI
Theodore Bear, Necco® Mania, Blue Print, Busy Day, Sandbox for Geoffrey, Should We Burst Their Bubble? Shovel, Shovel, Shovel, Terrific Tiles

CDII
The Beaver Olympics, Bridge Building on Lake Champlain, Galaxy Araca, Getting Ready, Got Milk? Ollie Owl's Food Court, "Planely" A Problem, A Stinky Situation

CDIII
Celebrating My Birthday

Volume 9
Spilled Milk, Celebrating My Birthday

Volume 10
Making Candles, Kate's Flower Garden
Patterns of Change
  • Build designs that change in regular way, according to number patterns; predict later steps of number patterns, designs; make tables, graphs to display number patterns; use language of speed, motion to describe number patterns
  • Explore relationships among distance, time, speed; explore irregular increases, decreases; explore ways that speed, time, distance can be represented with tables, graphs, stories; interpret intervals in a table; interpret steepness in a distance vs. time graph; associate tables, graphs, stories
  • Develop vocabulary to discuss motion; represent motion with tables, graphs, verbal descriptions; explore relationships among distance, time, speed; connect slope in a graph with rate of change; relate number patterns to graph shapes
CDI
Portfolio Pizza Party, Zeno the Xylophone Maker, Blue Print, Busy Day, Pedal Power

CDII
Chick-a-dee-dee, To the Detail, Don't Let the Bedbugs Bite

CDIII
Picture Frames, Ls for Linda, Improving His Aim, A Pyramid of Crunchkins, Help - I'm Melting

Volume 9
Spilled Milk, Picture Frames, Counting Sheep, L's For Linda, Improving His Aim, A Pyramid of Crunchkins, Help - I'm Melting!!!

Volume 10
Bobsled Blunders, Barnum's Animal Cracker Circus, Collections
Containers and Cubes
  • See 3-D arrays of cubes as congruent layers; explore volume
  • Understand the relationship between dimensions of a box and how many rectangular packages fill the box
  • Work on understanding volume; describe, justify methods for determining volume
  • Compare volumes; understand structure of solids through building them
CDI
Spring Seeds
Data: Kids, Cats, and Ads
  • Use line plots to represent data sets; compare two data sets; find medians; make hypotheses make statements based on data
  • Collect, examine data; make representations of numerical, categorical variables; use fractions, percents; explore how two variables might be related; learn to enter, analyze data
  • Learn what a sample is; compare data; learn why a larger sample is preferable
  • Choose strategy to find a representative sample; compare data; analyze single data set in more than one way
  • Define question, sample; test, refine survey questions; collect and collate data; develop theories based on data; make recommendation based on interpretation of data
CDI
Equal Snacks, M&M® Mini-Bus Challenge, Making a Fair Decision, Miss Amico's Birthday Bash, New Year's Party, Portfolio Pizza Party, Should We Burst Their Bubble? Spring Seeds, Theodore Bear

CDII
Bridge Building on Lake Champlain, Don't Let the Bedbugs Bite! "M&M® Cookie Combos

CDIII
Playing Checkers, Lost Spinner, Should Hannah Play?, Calling All Students, Picture Frames, Ls for Linda, Improving His Aim, A Pyramid of Crunchkins, Help - I'm Melting, Pumpkin Character Challenge, Batting Practice, Bobsled Blunders, Barney's Bakeries

Volume 9
Calling All Students, New Equipment, Picture Frames, Counting Sheep, L's For Linda, Improving His Aim, A Pyramid of Crunchkins, Help - I'm Melting!!! Pumpkin Character Challenge, Pavich Raisins

Volume 10
Batting Practice, Bird Watching, Bobsled Blunders, Barney's Bakeries, Collections, Hiking

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