# The Three-Store Problem A Lesson with Fifth Graders

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5 and checked, and then you used Alvin s idea. James returned to his seat to complete his paper. As the students worked, I started a T-table on the board, labeling the first column Start and the second column End. I recorded on the table the amounts that the students found as they worked, recording the end amounts as negative numbers when the man was in the hole and positive numbers when the man was ahead. After several entries, the table looked like this: Start End \$ \$10.00 \$ \$90.00 \$ \$ 2.00 \$ 7.00 \$14.00 \$ 8.00 \$ 6.00 \$ 7.75 \$ 8.00 Elissa decided to rewrite the table with the start numbers in order and in \$.25 intervals from \$5.00 up to \$ Several others did, too. I called the class back to the rug for a concluding conversation, and the interchange was lively. The general consensus was that guessing and checking, working backward, acting it out, and looking for a pattern were the most used problem-solving strategies. Elissa noticed that when the start amount changed by \$.25, the end amount changed by \$2.00. Alexandra wondered if the correct answer would double if you doubled the \$10.00 in the problem to \$ Not all of the students had the time to write about whether the problem was too easy, just right, or too hard. But our class discussion revealed that most of the students thought that the problem was just right for fifth graders. Scott said, It makes you think and it s a good challenge. And it s not boring, Gabriel added. I think it was hard, Michael said. For a long time everything I tried was wrong. Some students commented on their papers. George wrote: I thought this problem was just right for fifth graders because it doesn t take too long and you can t finish it in 1 min. Travon wrote: This was hard because there is no very helpful pattern that I know of. Cara wrote: I think it s just right and hard because you think a lot but it takes a long time. Kaisha had a different point of view. She wrote: I think it was pretty easy. 5

6 Figure 1. James s work. 6

7 The Three-Store Problem, continued Figure 2. Lauren s work. 7

8 The Three-Store Problem, continued Figure 3. Anthony s work. 8

9 Figure 4. Emma s work. 9

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