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Number Session 10, Part B: Classroom Case Studies, Grades 6-8
 
Session 10 Session 10 6-8 Part A Part B Part C Homework
 
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Session 10, Part B:
Reasoning About Number and Operations

In This Part: Exploring Standards | Examining Students' Reasoning

Here are scenarios from two different teachers' classrooms, each involving students' developing ideas about number and operations. Snippets of students' discussions are given for each scenario. For each student, consider the following:

• 

Understanding or Misunderstanding: What does the statement reveal about the student's understanding or misunderstanding of number and operations ideas? Which ideas are embedded in the student's observations?

• 

Next Instructional Moves: If you were the teacher, how would you respond to this student? What questions might you ask so that the student would ground his or her comments in the context? What further tasks and situations might you present for the student to investigate? Note 3


 

Problem B5

Solution  

Ming Hui and Kenneth were working to translate the base five number 1234 to a base ten number. The teacher has asked them not to use manipulatives. Below is a snippet of their conversation:

Ming Hui: We can't use the tiles this time, so let's try to remember what tiles are put under each place.
Kenneth: Okay, put the 1 tiles under the 4. That's 4.
Ming Hui: And then the 5s are under the 3. That's 15 more.
Kenneth: And then the 25s are under the 2. That makes 50 more.
Ming Hui: So far we have 4 plus 15 plus 50. That's 69.
Kenneth: And then we have one more. That must be the 100s. We've got 169 in all.
Ming Hui: Yes, the base ten number is 169.

a. 

What methods did the students use to solve the problem? What do these methods tell you about how the students are thinking about the problem? What mistake did they make in their conversion process? Why do you think they made this common error?

b. 

How would you help the students deal with any misconceptions they have?


 

Problem B6

Solution  

Brad and Kent were working to translate the base ten number 342 to a base five number. Below is a snippet of their conversation:

Brad: That's three 25s and four 5s and two more.
Kent: No, we're going the other way.
Brad: Oh, you're right. Then the three 100s are twelve 25s. That's two 125s and two 25s.
Kent: And the four 10s will make eight 5s, or one 25 and three 5s.
Brad: Okay. So far we've got two 125s, three 25s, and three 5s. All we need is two more. So the number is 2332.

a. 

What methods did the students use to solve the problem? What do these methods tell you about how the students are thinking about the problem?

b. 

How would you help the students deal with any misconceptions they have?


 
 

Join the discussion! Post your answer to Problems B5 and B6 on Channel Talk; then read and respond to answers posted by others.
 

Next > Part C: Problems That Illustrate Reasoning About Number and Operations

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