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Reasoning and ProofSession 04 OverviewTab atab btab ctab dtab eReference
Part A

Observing Student Reasoning and Proof
  Introduction | Completing Patterns #1 | Problem Reflection #1 | Completing Patterns #2 | Problem Reflection #2 | Classroom Practice | Observe a Classroom | Questions and Answers | Your Journal

 
 

The next pair of students has been given the following pattern to continue:


Shape Pattern


They are having some difficulty coming to agreement on their solution.


Caleb thinks this is the correct answer:


Caleb's Solution

Martina thinks this is the correct answer:


Martina's Solution

Let's look at the conversation that follows.



Teacher: You have come up with two different ways to add more blocks to my pattern. Caleb, describe your pattern.
Caleb: Big square, little square, big square, little square, big square, little square, big square, little square.


Teacher: Martina, describe your pattern.
Martina: Red, red, blue, blue, red, red, blue, blue.


Teacher: Now, that's interesting; you both seem to have different patterns. Caleb, can you continue Martina's pattern?
Caleb: I think so . . .
Caleb places the following pieces:


Caleb Places Pieces


Teacher: Martina, can you continue Caleb's pattern?


Martina places the following pieces:


Martina Places Pieces


Caleb: That's not my pattern!


Teacher: Let's listen to what Martina is thinking.
Martina: I saw that there was a big piece and then a little piece, so the pattern is big, little, big, little, big, little.


Teacher: Do your pieces fit that pattern?
Martina: Yes.


Teacher: Caleb, was that your pattern?
Caleb: No, my pattern was big square, little square, big square, little square, big square, little square, big square, little square, so a big square should be next.


Martina: There weren't any big squares left, so I just added a big piece.


Teacher: Could Martina's answer be another pattern chain?
Caleb: Yes, but that's a different pattern.


Teacher: Let's get another set of blocks so you can find the pieces you need to complete Caleb's pattern.
Martina: Big square, little square, big square, little square, big square, little square, big square, little square . . . I need a big square and a little square (she continues with Caleb's pattern):


Martina Continues Caleb's Pattern

Next  Reflect on the Completing Patterns problem

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