We have mentioned that children solve addition and subtraction problems by focusing on the action in the problem. We illustrated joining problems where the action is a joining of two or more quantities (like 6 toy cars and 18 more toy cars).
The opposite of joining is separating. In many word problems the action involves separation of quantities. For example, Louise has 36 cookies and gives 12 to Henry (12 cookies are separated from the original quantity of 36). As with Join problems, there are three distinct quantities in Separate problems. There is a starting quantity, a change quantity (the amount removed), and the result. Any one of these quantities can be the unknown.
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? |
Generally, result unknown problems are easiest and start unknown problems are hardest. The reason for this is the types of strategies children use to solve these problems. Children solve separate problems in three distinct waysÑphysical (direct) modeling, counting, or using facts. We shall discuss each of these three strategies for each type of separate problem.
Mom and daughter solve separating
problems as they make a wreath