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4. Place-Value Centers
First-graders develop an understanding of the numeration system by relating counting, grouping, and place-value concepts. Activities include measuring with Unifix cubes and using base-ten blocks. NCTM standards: number sense and numeration, measurement, connections.

5. Pumpkin Seeds
A grade 1-2 class, working in groups, develops their sense of larger numbers by estimating and counting the number of seeds in pumpkins. NCTM standards: number sense and numeration, estimation, communication, reasoning.

6. Animals in Yellowstone
Fourth- and fifth-graders develop number sense and meaning for large numbers by estimating how many bison, elk, and pronghorn they saw on a field trip to Yellowstone National Park. Students debate and justify their estimates verbally and in writing. NCTM standards: number sense and numeration, estimation, problem solving, connections.

7. Cubes and Containers
Kindergarteners sort Unifix cubes in various ways, focusing on the properties of the objects’ similarities and differences. By creating patterns, children develop an early understanding of geometry. NCTM standards: concepts of whole number operations, number sense and numeration, communication, reasoning.

8. Amazing Equations
Using the day of the month, first- and second-graders investigate the concepts of addition and subtraction as they share story problems that relate to the date. Teams use everyday language and experiences to connect to the mathematical language and symbolism for operations. NCTM standards: concepts of whole number operations, whole number computation, communication, connections.

9. Domino Math
First- and second-graders investigate number relationships and explore the concept of addition in a part-whole model using dominoes. They develop mathematical communication as they represent mathematical ideas with physical materials, words, diagrams, and symbols. NCTM standards: concepts of whole number operations, whole number computation, problem solving, communication.

10. Marshmallows
Second-graders create and discuss a bar graph based on the number of marshmallows they estimate each person in their class would eat on a camping trip. After discussing their results, students determine how many bags of marshmallows to take. NCTM standards: concepts of whole number operations, statistics and probability, reasoning, problem solving.

11. What’s the Price?
Third-graders use problem-solving approaches--such as role playing or drawing pictures—to investigate and understand division. They make connections to everyday life and use calculators as they determine unit costs for two different boxes of cereal. NCTM Standards: concepts of whole number operation, fractions and decimals, problem solving, communication.

12. Dino Math
Kindergarteners team up in buddy pairs to explore addition combinations using a "dinosaur math" mat. They work with basic addition facts and use a part-whole concept to perform the addition. NCTM standards: whole number computation, number sense and numeration, communication.

13. Window Puzzle
First-graders investigate number combinations by working with a window puzzle (a square divided into four equal squares). In this task students explore both addition and subtraction employing physical materials to aid in computation as well as using mental math. NCTM standards: whole number computation, communication, reasoning.

14. Wheel Problem
First-graders are asked how many vehicles could be in a parking lot if the total number of wheels is 24. Students review each step of the problem-solving process before they decide on which materials to use and develop strategies. NCTM standards: whole number computation, concepts of whole number operations, problem solving, communication.

15. Bean Sprouts
Pairs of second-graders explore subtraction, based on the number of plants sprouting from the bean-seeds they have planted. The importance of context for student understanding, and various approaches to problem-solving, are exemplified. NCTM Standards: concepts of whole number operations, reasoning, problem solving, communication.

16. This Small House
Second- and third-graders use calculators, paper and pencil, and mental math within a realistic task. Students plan the decorating of their milk carton houses using spatial sense to select appropriate furnishings while staying within their allocated budget. NCTM standards: whole number computation, geometry and spacial sense, connections, communication.

17. Choose a Method
A fourth-grade class shares their reasoning in evaluating the appropriateness of different computational methods (base-ten blocks, calculators, mental math, or paper and pencil) to specific problems. NCTM standards: whole number computation, estimation, communication, reasoning.

18. Thanksgiving Quilt
Creating quilt squares from construction paper, first graders develop spatial sense as they discuss and handle different shapes. They connect geometric ideas to number ideas as they cut squares into congruent triangles. NCTM standards: geometry and spacial sense, patterns and relationships, communication, connections.

19. Pattern Blocks
Second-graders learn the mathematical terms for pattern-block pieces: hexagon, trapezoid, square, triangle, and rhombus. Ideas about fractions emerge as students spot size relationships between shapes. NCTM standards: geometry and spacial sense, number sense and numeration, reasoning, connections.

20. Shapes From Squares
A second/third-grade class develops spatial sense as they subdivide and change squares to create different shapes. The language of geometry—square, trapezoid, hexagon, etc.—grows naturally from their explorations. NCTM standards: geometry and spacial sense, communication, reasoning.

21. A Rocket Shape
Second- and third-graders experiment to subdivide a square to recreate a rocket shape. After completing their rockets, they reconvene as a class to discuss their difficulties and problem solving strategies. NCTM standards: geometry and spacial sense, measurement, problem solving, reasoning.

22. Circumference/Diameter
After reviewing the meaning of radius, diameter, center, and circumference, fourth-graders working in teams measure circular objects throughout the room. They are then challenged to find the relationship between the circumference and the diameter. NCTM standards: geometry and spatial sense, measurement, connections, reasoning.

23. Windows, Dinos, and Ants
First-graders are engaged in problem solving and measuring with both standard and nonstandard units. Students work in groups to measure three different distances: ant farm tunnels, dinosaurs, and the length from their classroom window to the playground below. NCTM standards: measurement, number sense and numeration, problem solving, reasoning.

24. How Long Is a Minute?
Having already studied the concept of an hour, first-graders investigate time as a measure of duration. They list activities, such as writing their name, that could be accomplished within a minute, then estimate how many times in one minute they could do it. NCTM standards: measurement, estimation, reasoning, connections.

25. Balloon Travel
In an integrated math/science lesson, second- and third-graders collect data to answer questions such as, "What is the farthest a balloon can travel before falling?" To answer the question, they must understand distance, volume, capacity, and time. NCTM standards: measurement, estimation, connection, problem solving.

26. Meter Cords
Third- and fourth-graders use linear measurement in learning about decimals. Students measure different items with a meter divided into 10 parts then learn to write their measurements using decimal notation. NCTM standards: measurement, fractions and decimals, connections, communications.

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