Difference Unknown: One type of compare problem involves finding out how many more are in one set than another. For example, James has 6 mice. Joy has 11 mice. How many more mice does Joy have than James?
Set Unknown Problems: Another type of compare problem involves finding out how many are in the one set by knowing both the number of items in one set and the difference between the two sets. For example, James has 6 mice. Joy has 5 more mice than James. How many mice does Joy have? or Joy has 11 mice. She has 5 more mice than James. How many mice does James have?
| Join: 7 + 9 = ? | 7 + ? = 16 | ? + 9 = 16 | ||
| Result Unknown | Change Unknown | Start Unknown | ||
| Byron has 7 shells. Then Melissa gave him 9 more shells. How many shells does Byron have now? |
Byron has 7 shells. Melissa give Byron some shells. Now Byron has 16 shells. How many shells did Mellisa give him? |
Byron has some shells. Melissa gives him 9 more. Now Byron has 16 shells. How many shells did Byron start with? |
| Separate: 8 - 3 = ? | 8 - ? = 5 | ? - 3 = 5 | ||
| Result Unknown | Change Unknown | Start Unknown | ||
| Colleen has 8 guppies. She gave 3 guppies to Roger. How many guppies does Colleen have left? |
Colleen has 8 guppies. She gave some guppies to Roger. Then she had 5 guppies left. How many guppies did Colleen give Roger? |
Colleen has some guppies. She gave 3 guppies to Roger. Then she had 5 guppies left. How many guppies did Colleen have to start with? |
| Compare: | ||||
| Difference Unknown | Set Unknown | |||
| James has 6 mice. Joy has 11 mice. How many more mice does Joy have than James? |
James has 6 mice. Joy has 5 more mice than James. How many mice does Joy have? |
Joy has 11 mice. She has 5 more mice than James. How many mice does James have? |
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Compare-Difference-Unknown problems can be solved by a physical (direct) modeling strategy involving matching. For the problem involving the unknown difference (James has 6 mice. Joy has 11 mice.), children use a matching strategy. Here children count out a set of six cubes for James, and another set of 11 cubes for Joy. Then they put the 6 cubes in a row, followed by making another row of 11 cubes next to the row of 6 cubes. Children then count the 5 cubes not matched with a cube in the first row. These 5 cubes represent the difference.
Compare-Set-Unknown problems are solved with a variety of counting strategies. For the problem involving the unknown larger set ( James has 5 mice etc.) children will count up: "6 (pause) 7 (1), 8 (2), 9 (3),10 (4), 11 (5). For the problem involving the unknown smaller set (Joy has 11 mice. She has 5 more mice than James.), children may count down to find the smaller set: "11 . . . 10(1), 9(2), 8(3), 7(4), 6(5). James has 6 mice." For example, to solve the problem with the unknown larger set (James has 6 mice. Joy has 5 more mice than James), children will count up.
Her dad asks her to compare the scores