For each problem, decide whether it is a PPW-WU or PPW-PU.
1. Ellen has 2 toy animals. Shauna has 6 toy animals. How many toy animals do they have altogether?
PPW-WU. This problem tells the amounts in two part-sets, and asks for the amount in the whole-set.
2. There are 8 children swimming in the pool. 2 of the children are girls. How many of the children are boys?
PPW-PU. The set of children in the pool consists of the parts: girls and boys in the pool. The question asks for the number in one of the parts (boys), so it is a part unknown problem.
3. Paula has 10 green Jolly Ranchers and 3 purple Jolly Ranchers. How many Jolly Ranchers does she have in all?
PPW-WU. The set of Paula's Jolly Ranchers is made up of the parts: green and purple Jolly Ranchers. The question asks for the amount in the set of the combined parts.
4. There are 10 toy animals in the toy box. 7 of the toy animals are stuffed and the rest are hard plastic. How many of the toy animals are hard plastic?
PPW-PU. The set of toy animals is made up of the parts: stuffed animals and hard plastic animals. the question asks for the amount of hard plastic animals which is one of the parts.
5. There are 18 bouncy balls in the toy box. 9 of the bouncy balls are green and the rest are blue. How many of the bouncy balls are blue?
PPW-PU. The set of bouncy balls is made of the parts: green bouncy balls and blue bouncy balls. The question asks for the number of blue bouncy balls, which is one of the parts.
6. There are 10 crystal rocks in the collection, and 8 polished rocks in the collection. How many rocks are in the collection?
PPW-WU. The set of rocks in the collection is made of the parts: crystal rocks and polished rocks. The question asks for the number of rocks, which includes both parts, so it is asking for the amount in the whole set.
Decide for each statement whether it is true or false.
9. Part-Part-Whole problems can all be solved using the same direct modeling strategy as Join (result unknown) problems.
False. Part-Part-Whole-Whole Unknown problems can be modeled using a Join, result unknown strategy, but Part-Part-Whole-Part Unknown problems are modeled using the strategy of either a Separate, ResulWhole Unknownt Unknown, or Join change unknown.
10. Children figure out how to solve Part-Part-Whole problems later than Join and Sparate (result unknown) problems, because there isn't an action taking place in the problem to guide them on how to act out the problem.
True. The easily-modeled actions in the Join and Separate result unknown problems make them the easiest for children to understand and model. After gaining some sophistication with both language and mathematical problem solving, children can apply their knowledge to other problems, including Part-part-whole problems.
11. Some kindergarten aged children don't understand part-part-whole problems, and what the problem is asking for.
True. The notion of combining smaller sets into a larger set is one that takes a little time and practice to get used to for children at this stage.