Ownership, Agency, and Mathematical Properties

Intermediate: 9-10 year olds

CGI Math

A mixed-age classroom of kids is working on the second story problem of the year.  This multiplication problem is about our principal, Ms. Silva, and her many pizzas:

Principal Silva has 9 pizzas. Each pizza has 10 slices. How many slices does she have?

CHALLENGE: How many pizzas does she need to buy to have one slice for each of our 119 Intermediate students?

Today, there is a juicy scenario happening between two of the youngest children that I’ll call Nate and Kate. Nate solved the problem quickly and recorded his thinking with ease.

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Primary Classroom Doing Counting Collections

Primary: 6-8 year olds

CGI Math

Two students were sitting together, each counting his own collection, but working side by side. One student had counted and recorded marbles in groups of 10. The other had a very large basket of red and yellow tokens on his lap counting them by 1’s as he removed them from the basket. He was on 310 when I arrived. Our conversation went as follows:

Teacher: (to the 2 students) Can you each tell me about your strategies for counting?

Child 1: I counted the marbles and wrote groups of 10, then a 4. The total is 84.

Child 2: I am counting these tokens by ones. See….310, 311, 312…

Teacher: (to child 2) I am wondering what you might do if someone bumped into the desk and some of the tokens you have already counted fell back into the basket.

Child 2: I would start over at the beginning.

At this point, my assumption was that this child was not aware of the benefit of grouping the tokens. I decided to ask Child 1 more about his grouping technique to see if Child 2 might benefit from overhearing our conversation.

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