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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.

27. Pencil Box Staining
Fourth-graders are faced with the task of finding out how much stain to buy from the hardware store and encounter problems as they work with many mathematical ideas in the context of a real application. Students work in groups with pencil box pieces, a ruler, calculator, and instruction sheet. NCTM standards: measurement, fractions and decimals, problem solving, reasoning.

28. Ladybugs
First-graders choose ladybugs as a topic for learning. Based on their observations, students make bar graphs and a class chart to record the number of heads, wings, feet and antennas ladybugs have. They make connections among real objects, diagrams, and numerals. NCTM standards: statistics and probability, number sense and numeration, connections, communication.

29. Woodpecker Habitat
First- and second-graders apply probability and sampling techniques to their study of the habitat of the endangered red-cockaded woodpecker. Using colored cubes to represent elements in the environment, students simulate factors that might harm or help the birds. NCTM standards: statistics and probability, whole number computation, reasoning, connections.

30. Bubble Gum Contest
Third-graders stage a bubble gum blowing contest using sampling to determine the ratio of winners to entrants. They enlarge their sample, collecting data from all the third-graders in their school and use fractions to interpret the data. NCTM standards: statistics and probability, fractions and decimals, connections, communication.

31. Dice Toss
Fourth-graders work with statistics, probability, fractions and decimals while conducting an experiment to see which sum comes up most often when rolling two dice. Once the groups complete their experiments, they compile their findings on a class bar graph and analyze the graph. NCTM standards: statistics and probability, fractions and decimals, communication, reasoning.

32. Questioning Data
A fourth- through sixth-grade class takes data collected from surveys on questions of personal interest. They then represent the data in a graph, and write about what the graph interprets and the questions they still have about the survey subject. NCTM standards: statistics and probability, connections, communication, reasoning.

33. Fraction Strips
First- and second-graders make fraction pieces from paper strips and play a game that involves covering a whole strip with fractional pieces. As they play they informally add fractions and make connections from objects and actions to symbols. NCTM standards: fractions and decimals, number sense and numeration, reasoning, communication.

34. Arrays and Fractions
A first- through third-grade class investigates fractional parts of a set by building arrays that represent wholes of different sizes. In their task they use mathematical language and symbols and form mathematical connections among concepts of addition, area, multiplications, division, and fractions. NCTM standards: fractions and decimals, number sense and numeration, reasoning, communication.

35. Everyday Decimals
Second- and third-graders extend their understanding of common fractions to notation for decimal fractions and to the numeration system. They interpret the use of decimals in the real world by bringing to class items that have decimals or fractions written on them. NCTM standards: fractions and decimals, number sense and numeration, connections.

36. Cookies To Share
Through a story about sharing cookies, fourth-graders investigate a the problem of dividing eight cookies among 12 children. It helps them develop meaning for the concept of division and leads to the use of fractions. NCTM standards: fractions and decimals, number sense and numeration, communication, connections.

37. Fractions With Geoboards
Fourth- and fifth-graders investigate the concept of halves using the geoboard as an area model. They learn that one-half means two equal-sized parts with equal areas, but that are not necessarily congurent. NCTM standards: fractions and decimals, geometry and spacial sense, reasoning, problem solving.

38. People Patterns
One of several lessons on patterns, individual kindergarteners are lined up to represent different patterns to the class. In groups they create their own patterns from simple two-element patterns or more complex six-element patterns to share with the class. NCTM Standards: patterns and relationships, number sense and numeration, communication, reasoning.

39. All Sorts of Buttons
Kindergarteners and first-graders hear a story about buttons, then sort their own collection of buttons to develop skills of classification--observing likenesses and differences. Students see that objects can be looked at in a number of ways and develop a sense of pattern and regularity. NCTM standards: patterns and relationships, number sense and numeration, reasoning, connections.

40. Story-Based Centers
Second-graders work at learning centers around their classroom that are based on the story "Caps for Sale." At the centers students construct graphs, figure out coin combinations to equal 50 cents, use a computer to explore patterns, and write story problems and number sentences. NCTM standards: patterns and relationships, whole number computation, connections, communications.

41. Products and Sums
Exploring relationships between addition and multiplication, fourth-graders represent numbers, sums, and products with symbols and with geometric patterns on paper. NCTM standards: patterns and relationships, number sense and numeration, reasoning, communication.

42. Valentine Exchange
A bilingual fourth-grade class uses a Valentine’s Day card exchange problem to explore mathematical relationships and share problem solving strategies. NCTM standards: patterns and relationships, number sense and numeration, problem solving, reasoning.

43. Beans, Beans, Beans
Kindergarteners sharpen their estimation skills and number sense as part of a unit on plants and seeds. Using three known quantities for reference, student groups must estimate the number of an unknown quantity of beans, and then count the beans by tens. NCTM standards: estimation, number sense and numeration, reasoning, communication.

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