Teaching Math: Grades K-2: Representation

Reflect on each of the following questions about the Sampling Data problem, and then select "Show Answer" to reveal our commentary on them.

Question: Why is making a graph from the sample a good way for young children to represent their data?

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Our Answer: The graph is a visual means of representing what is in the sample. For young children, the graph helps them to begin to see the relationship between their sample and the chips in the jar.

Question: What conclusions do students draw from their graphs? What does this tell you about their thinking?

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Our Answer:

Benji concludes that there are only red and blue chips in the container. He does choose two numbers that add to 20, but the numbers in his estimate do not appear to be related to the number of each color in his sample. He may not see the relationship between the number of chips in his sample (10) and the number of chips in the jar (20).

Sasha doubles the number of chips of each color in her sample to predict the number of each color in the jar. She sees that since the number of chips in the jar is twice as much as her sample, it is reasonable to double the number of each color from her sample.

Question: What questions might the teacher have asked Sasha to help her predict the number of chips of each color?

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Our Answer: How many red chips did you draw? How many blue chips did you draw? What is the total number of chips that you drew from the jar? How many chips are in the jar? What do you notice about the number of chips you drew and the number of chips in the jar?

Question: How could you continue to help students determine the relationship between their samples and the actual number of each color of chip?

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Our Answer:

Students could take additional samples and represent their chips with the graph. Once students understand the relationship between the number of chips in the sample and the number of chips in the jar, they could represent their predictions by doubling the number of each color on their graphs.

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