Box 6–6 A Third-Grade Class Finds 54+48

The students had worked on the problem at their desks for about 15 minutes and were sharing their procedures with the class. The teacher, Ms. G., called everyone over to look at Ellen’s solution strategy.


[Makes 54 and 48 with tens and ones blocks.] I knew this was 54, so I went 64, 74, 84, 94,…[She moves one 10 block for each count. Then she counts the single cubes, moving a cube with each count.] Ninety-five, 96,…, 102.

Ms. G:

Now class, what question am I going to ask her? Norman?


You didn’t use the 54. Did you have to make it?

Ms. G:

Good, Norman, that’s just what I was going to ask her. Ellen, did you need to make that 54?

Ellen: No.

Ms. G: [Pulls the 54 away and covers it with her hand.] OK, now show me how you can solve the problem without the 54.


Sixty-four, 74,…[She repeats the above strategy, counting on without the 54.]

Ms. G:

OK, now you told me that you could do this without us moving to your desk. How would you have done that?


OK, I just put 54 in my head, and then I go 48 more. I go 54 [slight pause], 64, 74, 84, 94. [She puts up a finger with each count to keep track of the four tens in 48. At this point she has four fingers up. She puts down her fingers and puts them up again with each count as she continues counting by ones.] Ninety-five, 96, 97,…, 102.

SOURCE: Adapted from Carpenter, Fennema, and Franke, 1996, p. 11.

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