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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 6-8. 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 |  |
The points are all equally spaced on the number line. Identify the four points that represent the following:
1. | 3/4 - 1/6 |
2. | d • f |
3. | e - a |
4. | b  d |
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Problem C2 | |
The yearly changes in the enrollment in your school for the last four years were, respectively, a 20% increase, a 20% increase, a 20% decrease, and a 20% decrease.
1. | What is the net change over the four years, to the nearest percent? |
2. | Would the answer change if the decreases came before the increases? |
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Problem C3 | |
The sum of nine consecutive integers is 63. What is the smallest positive integer that could be part of the sum? |
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Problem C4 | |
Lucky Edgar has been hired by a movie star to be his assistant on the set of a new film. For his salary, Edgar has been given a choice: He could get paid either $1,000 per day for 20 days or $1 on the first day, $2 on the second day, $4 on the third day, and so on, doubling each day for 20 days. Which salary should Edgar choose? |
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