Review Answers from Lessons 1-4

Practice identifying problem types. For each problem (1-15) decide if it is JRU, JCU, SRU, SCU, PPW-WU, PPW-PU or CDU. Explain how you know what the problem type is.

1. Seth had 4 Bionicles. When he cleaned his room, he found some more Bionicles, and then he had 7 Bionicles. How many Bionicles did he find?

JCU: This problem has an action (finding more) that results in a change over time, so it is a Join or Separate; the action joins more to the set, so it is a Join problem. The question asks for the amount of the change (how many found), so it is a Change Unknown problem.

2. Sandy had 8 Silly Bandz. She gave some Silly Bandz to Ellen. Now she has 6 Silly Bandz left. How many Silly Bandz did she give to Ellen?

SCU: This problem has an action (giving some) that results in a change over time, so it is a Join or Separate; the action takes some away from the set, so it is a Separate problem. The question asks for the amount of the change (how many given), so it is a Change Unknown problem.

3. There are 2 red pens in the desk, and 3 blue pens in the desk. How many pens are in the desk?

PPW-WU: There is no action in this problem (no change over time) , so it is not a Join or Separate problem. This problem relates two part sets (red and blue pens) to a whole (pens in teh desk) so it is a Part-Part-Whole problem. The problem asks for the amount in the whole, so this is a Whole Unknown problem.

4. Mark had 12 crayons. He lost some of his crayons. Now he has 9 crayons left. How many crayons did he loose?

SCU: This problem has an action (losing some) that results in a change over time, so it is a Join or Separate; the action takes some away from the set, so it is a Separate problem. The question asks for the amount of the change (how many lost), so it is a Change Unknown problem.

5. John saw 5 birds at the bird feeder in the morning. At lunch, he saw 3 more birds. How many birds did John see in all?

JRU: This problem has a change over time (some in the morning, some at lunch) that changes the total. This counts as an action, so this is a Join or Separate problem. The change over time is an increase, so this is a Join problem. The question asks for the result of the change (in all), so this is a Result Unknown problem.

6. There are 12 gum balls in the drawer. 7 of the gum balls are purple and the rest are white. How many of the gum balls are white?

PPW-PU: This problem has no change over time, so it is not a Join or Separate. This problem uses the relationship between two parts (purple and white gum balls) and a whole (the gum balls in the drawer), so this is a Part-Part-Whole problem. The problem asks for the amount of one of the parts (white gum balls), so this is a Part-Unknown problem.

7. Shauna had 10 pencils. 3 of her pencils broke. How many pencils did she have left?

SRU: There is an action (change over time) in this problem (pencils breaking), so this is a Join or Separate problem. The action decreases the number of pencils, so it is a Separate problem. The problem asks for the result of the action (how many are left), so this is a Result Unknown problem.

8. Sarah had 4 apple slices. Her mom gave her 3 more apple slices. How many apple slices does Sarah have now?

JRU: There is an action (mom gives her more) which results in a change over time, so this is a Join or Separate problem. The action increases the amount Sarah has, so this is a Join problem. The question asks about the result of the action (how many now), so this is a Result Unknown problem.

9. There are 13 children playing an instrument in the band. 5 of the children are boys. How many of the children are girls?

PPW-PU: There is no change over time in this problem, so it is not a Join or Separate. This problem involves a relationship between two parts (boys and girls) a a whole (children) so this is a Part-Part-Whole problem. The question asks for the amount in one of the parts (how many girls), so this is a Part Unknown problem.

10. There are 3 glow in the dark toy bugs in the drawer, and 6 colored toy bugs in the drawer. How many fewer glow in the dark bugs than colored toy bugs are in the drawer?

CDU: There is no change over time in this problem, so it is not a Join or Separate problem. This problem involves two sets, and there is not a part-whole relationship between the sets, instead the sets are compared to see which is larger and by how much, so this is a Compare problem. The question asks how many fewer are in one set than the other, so it is asking for the difference in size between the two sets, so this is a Difference Unknown problem.

11. David has 3 dollars. How many more dollars does he need to earn to buy a 7 dollar video game?

JCU: There is an action (earning money) that is a planned for/hoped for change over time, so this is a Join or Separate problem. The proposed change over time is an increase, so this is a Join problem. The question asks for the amount of the increase (how much does he need), so this is a Change Unknown problem.

12. Mark had 16 Pokemon cards. He gave 7 Pokemon cards to Luke. How many Pokemon cards does Mark have left?

SRU: There is an action (giving cards) that yeilds a change over time, so this is a Join or Separate problem. The change over time is an decrease in the amount of Mark's cards, so this is a Separate problem. The question asks for the resulting amount at the end (how many left), so it is a Result Unknown problem.

13. Ellen made 2 bead necklaces. How many more does she have to make to have 6 bead necklaces?

JCU: there is an action (making necklaces) that is a planned/hoped for change over time, so this is a Join or Separate problem. The change over time is an increase in the number of necklaces, so it is a Join problem. the question asks for the size of the change (how many more should she make), so this is a Change Unknown problem.

14. Gus has 7 toy cars. Ethan has 3 toy cars. How many toy cars do they have altogether?

PPW-WU: There is no action (change over time) so this is not a Join or Separate problem. This problem has two parts (Gus's cars and Ethan's cars) and a whole (altogether), so it it a Part-Part-Whole problem. The problem asks for the amount of the whole (how many altogether), so this is a Whole Unknown problem.

15. Ethan has 5 toy trains. Mark has 8 toy trains. How many more toy trains does Mark have than Ethan?

CDU: There is no action (change over time) so this is not a Join or Separate problem. The sets in the problem (Ethan's trains and Mark's trains) do not have a part-whole relationship, and the problem does ask for how many more are in one set than another so this is a Compare problem. The problem asks for the difference in size between the two groups, so this is a Difference Unknown problem.

Answer each of the following in complete sentences.

16. In what way are Join and Separate problems similar?

Both Join and Separate problems have an action that results in a change over time in the amount in the set described in the problem.

17. What makes Part-Part-Whole, whole unknown problems more difficult for some children than Join, result unknown problems?

The lack of an action makes it hard for children to know what they should do with the amounts represented in the problem. They also may not be used to the idea of looking at sets in terms of parts and wholes and the idea of combining sets.

18. How (what manipulative steps) does a child direct model to solve a Join Change Unknown problem?

A child puts out counters to show the number of objects in the set when the problem starts, then they count out more counters (showing the amount of the change) and add them to the first set, and then they count all of the counters to find how many there are at the end.

19. How (what manipulative steps) does a child direct model to solve a Compare Difference Unknown problem?

The child counts out the counters to represent the amounts in the two sets. The child then pairs up the counters (side by side) in a 1-1 correspondence, and counts the counters that do not have a partner to find the difference.

20. When children direct model PPW-PU problems, which other problem type's direct modeling strategy do they usually use to solve the problem?

Children usually use the SRU strategy to solve PPW-PU problems, though occasionally they will use a JCU strategy.

21. Give 2 examples of where learning vocabulary and language is important for solving the word problems discussed in this section.

The word "altogether" in part-part-whole problems, and the mental joining process it represents is a vocabulary meaning children may not understand; also compartive sentences telling a how many more than or lesson than may be unfamiliar to kindergarten children. It's important to understand these words and sentences, so children can understand what the problems are asking for.