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Learning Math Home
Number Session 10, Part B, Grades 3-5: Classroom Case Studies
 
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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 young children's 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 B6

Solution  

Nicole and Photina were working together on a puzzle. Here are the two clues they were trying to put together:

Below is a snippet of their conversation:

Nicole: I think we could put them together in three ways. We could slide the left one over so that the E is below the cube, or slide it over more so that the square is on top of the E, or keep going so that the P is underneath the square.

Photina: I don't think that they all can work.

Nicole: Well, the first one has to work, because nothing overlaps.

Photina: In the second one, you can have a square number that is even. That's 4.

Nicole: Then the P is underneath the cube. That's okay, because 1 is a cube.

Photina: And the third one works, too, because 1 is a prime that is square.

Nicole: I guess now we have to look at another clue.

a. 

What does this conversation tell you about how the students are thinking about the problem?

b. 

How would you help them deal with any misconceptions they have?


 

Problem B7

Solution  

Shauna and Tony were working together on a puzzle. Here are the two clues they were trying to put together:

Below is a snippet of their conversation:

Shauna: I see that these two pieces could be put together in two ways. You could slide the right one over so that the top P is on top of the triangle, or slide it over one more square so that the bottom P is on top of the E.

Tony: Okay, for the first one, the only overlap is the P on top of the triangle. That works, because 3 is a prime and a triangular number.

Shauna: The second one works, too, because the bottom P is on top of an E, and 2 is an even prime number.

Tony: Are there any more overlaps for that one?

Shauna: I don't think so.

Tony: I think that the top P is on top of something. Let's cut it out and try.

Shauna: Yes, that P is on top of an E. But we said that was okay before.

a. 

What does this conversation tell you about how the students are thinking about the problem?

b. 

How would you help them deal with any misconceptions they have?


 
 

Join the discussion! Post your answer to Problems B6 and B7 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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