# Exploring Ones, Tens, and Hundreds with Base Ten Blocks A Lesson for Third Graders

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4 On the board, I modeled for the children how to record this way of representing seventy-two. You and your partner are to build seventy-two with other combinations of the tens and ones blocks, the way we built one hundred in different ways. Record each way you find as I did for the example I showed. I continued, You ll work with your partner, but each of you will record on your own piece of paper. You ll have to share blocks with the other people at your table because there may not be enough for everyone to have his or her own. Write Seventy-Two as the title, and copy onto your paper the way we made seventy-two together. Record your ideas using a picture and with numbers. The exploration was accessible to all of the students but was more difficult for Karena. I gave her individual help while the others worked. I started by giving Karena smaller numbers to think about. We explored different ways to make twenty, then twenty-three, and finally thirtyfour. By the time we finished working on thirty-four, she wanted to work on seventy-two without my help. Arin, another student who often had difficulty, was thrilled with her work. She found three ways to make seventy-two using the base ten blocks. (See Figure 1.) Figure 1. Arin showed her growing understanding by making seventy-two in three ways. 4

5 As the students finished, I looked over their papers, asked for further clarification when needed, and then gave them the challenge of finding as many ways as possible to make 124 using base ten blocks. Vinay s work reflected how he systematically explored the possibilities by reducing the number of tens by one and increasing the number of ones by ten. He recognized that when he got to thirty-four ones and nine tens, he could no longer use a hundreds flat. (See Figure 2.) Figure 2. Vinay applied the pattern he noticed earlier to the more challenging problem of making 124. He also used expanded notation to represent his words and pictures. 5

### 118 One hundred Eighteen

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