For each problem, decide whether it is a PPW-WU type, or JRU.
1. Clara has 6 bouncy balls. Kallie has 4 bouncy balls. How many bouncy balls do they have altogether?
PPW-WU: the larger set of bouncy balls is made of the two smaller sets of Clara's bouncy balls and Kallie's bouncy balls. There is no change over time in this problem.
2. Briana had 8 bouncy balls. When she cleaned her room, she found 1 more bouncy ball. How many bouncy balls does she have now?
JRU: The number of balls Briana has changed (increased) when she cleaned her room.
3.Jeremy found 8 fossils by the stream. Later he found 2 more fossils. How many fossils did he find in all?
JRU: The number of fossils Jeremy found increased in the problem.
4. Blake has 2 red hats and 7 blue hats. How many hats does he have in all?
PPW-WU: the larger set of Blake's hats is made of the smaller sets of red hats and blue hats. There is no change in set amounts in this problem.
5. There are 8 large plates and 4 small plates in my cupboard. How many plates are in my cupboard.
PPW-WU: the set of plates in my cupboard is made of the smaller sets of large plates and small plates. There is not change over time in this problem.
6. Marissa had 4 fairies. For her birthday, she got 2 more fairies. How many fairies does she have now?
JRU: The number of fairies Marissa had increased in this problem.
Decide for each statement whether it is true or false.
7. Problems where there is a change over time (that would need to be represented by a movie) are harder for young children to solve than problems where you could just draw one picture to show everything.
False: Problems where there is a change over time are easier for young children to solve, because the change prompts the action needed to act out (direct model) the solution.
8. The phrases "in all" and "all together" are ones that some school aged children don't understand.
True: Children need experiences using these phrases in a context of telling "how many" are in different sets.
9. The best way to help children know what to do with PPW problems is to tell them that if they see the words "in all", it means you should add the numbers in the problem.
False: this works for the majority of problems, but it is misleading (leads to incorrect solutions) for some problems, and it does not increase the children's understanding of the problem situation.
10. JRU problems are easier for children to understand and solve than PPW-WU problems.
True: Some children find PPW problems siginificantly more difficult than JRU problems. This is most true of children in early elementary grades (K-1). This is a stage that most children move past fairly quickly with appropriate experiences and instruction.