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Learning Math Home
Number Session 10, Part C Grades 3-5: Classroom Case Studies
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
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Session 10, Part C:
Problems That Illustrate Reasoning About
Number and Operations
(55 minutes)

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 3-5. 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?


Problem C1

Solution  

John, Sarah, and Mary Beth each threw three beanbags at this target. All the beanbags landed somewhere on the target. Each person's score was the sum of the numbers in the rings where that person's three beanbags landed.

1. 

What is the greatest possible score?

2. 

What is the lowest possible score?

3. 

How many different possible scores are there?

4. 

John and Mary Beth got the same score but didn't hit the same rings. What was their score?


 

Problem C2

Solution  

1. 

Which is greater, 5/6 or 5/8? How do you know?

2. 

Which is greater, 2/3 or 3/4? How do you know?

3. 

Which is greater, 5/8 or 2/3? How do you know?

4. 

Put these fractions in order from smallest to largest, and explain your reasoning:
1/2, 5/6, 2/5, 5/8, 2/3, 9/10, 5/3, 3/4


 

Problem C3

Solution  

1. 

What is the smallest number of blocks you can remove so that there are 3 red blocks for every 4 green blocks left in the box? Which blocks did you remove? How did you figure it out?

2. 

What is the smallest number of blocks you can remove so that there are 3 red blocks for every 2 green blocks left in the box? Which blocks did you remove? How did you figure it out?


 

Problem C4

Solution  

One, 2, and 3 are consecutive integers. If you add 1 + 2 + 3, you get 6, which is 2 • 3.

Two, 3, and 4 are consecutive integers. If you add 2 + 3 + 4, you get 9, which is 3 • 3.

1. 

What is the sum of 3 + 4 + 5? Does it follow the pattern?

2. 

What is the sum of 7 + 8 + 9? Does it follow the pattern?

3. 

What can you tell about the sum of any three consecutive integers?


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