Reflection: Staircase of Complexity Doubles and Halves are Patterns Too - Section 2: What are Halves?


In math it is important to get students to explain their thinking. Young children do not think in mathematical terms (MP2) without some help in understanding those terms. As students were looking at patterns, I wanted them to understand how doubling is not the same as counting by twos. I could tell them that, but it was important for me to step back and let students discover this on their own. My goal is for students to be able to verbalize about what doubling is, but I wanted them to make that discovery. 

When I had them cut the paper in half, one piece doubled to two. Most students were really clear that if they cut those in half they would have four pieces, but when I asked them to cut the four pieces in half to double the amount, some students predicted that there would be 6 pieces and some predicted 8. Students are exploring halvesI listened to why students thought that there might be 6 or 8 and could see that some were using a skip count pattern instead of a doubling pattern. With a few more cuts, the students were grasping what the term of doubling meant so that they could explain it.

  Staircase of Complexity: Predicting from Patterns
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Doubles and Halves are Patterns Too

Unit 8: Numbers Have Patterns
Lesson 6 of 14

Objective: SWBAT use repeated patterns to solve problems with doubles and halves.

Big Idea: Can you double an odd number? Can you cut it in half? Patterns in doubles and halves help to answer these questions.

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