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

They are having some difficulty coming to agreement on their solution. Caleb thinks this is the correct answer: Martina thinks this is the correct answer: 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:

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

Martina places the following 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):

  Reflect on the Completing Patterns problem