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Session 10, Part C:
Problems That Illustrate Reasoning About
Number and Operations (55 minutes)
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As this course comes to a close and you reflect on ways to incorporate your new understanding of number and operations into your teaching, you have both a challenge and an opportunity: to enrich the mathematical conversations you have with your students around number and operations. As you are well aware, some students will readily grasp the ideas being studied, and others will struggle.
In Part C, you'll look at several problems that are appropriate for students in grades K-2. For each problem, answer these questions:
a. | What is the solution to this problem? |
b. | What is the number and operations content in this problem? |
c. | What skills do students need to work through this problem? |
d. | If students are having difficulty, what questions might help them work through this problem? |
e. | What questions might extend students' thinking beyond this problem? |
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Problem C1 |  |
You have the following cards:
How many different ways can you put two cards in the squares so that their sum equals 6?
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Problem C2 | |
The rectangles are all the same size, and the pieces within each rectangle are all the same size. Which rectangle has the most shaded? Which has the least shaded? How do you know?
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Problem C3 | |
I.
If you can trade 1 blue rhombus for 2 green triangles, how would you solve the problems below? Explain your reasoning.
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3. | Is 8 green triangles a fair trade for 4 blue rhombuses? How do you know? |
II.
If you can trade 1 red trapezoid for 3 green triangles, how would you solve the problems below? Explain your reasoning.
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3. | Is 10 green triangles a fair trade for 4 red trapezoids? How do you know? |
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Problem C4 | |
Using counters to represent numbers, we can observe the following:
Keeping this in mind, fill in the blanks below:
1. | An even number plus an even number gives an ________ number. (How did you decide?) |
2. | An odd number plus an odd number gives an ________ number. (How did you decide?) |
3. | An even number plus an odd number gives an ________ number. (How did you decide?) |
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Problem C5 | |
Consider one of the above problems. What kind of lesson could you generate around this topic? |
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