For each problem, decide whether it is a JCU, SCU type, or CDU.
1. Shane blew up 3 balloons. How many more does he have to blow up to have 7 balloons?
Shane plans to blow up more balloons, so there will be are more at the end than at the beginning. This is a Join problem. The question asks for how much the number increases, so it's JCU.
2. Gwen has 9 video games. Lisa has 8 video games. How many fewer video games does Lisa have than Gwen?
This question describes two groups, and asks how much less is in one group than another (comparison). This is a CDU problem. There is no change over time in this problem (no groups change size--they are just compared to one another)
3. Jill had 8 markers. Some of her markers dried out. Now she has 3 markers left. How many of her markers dried out?
Some markers dry out so there are fewer markers at the end than at the beginning. This is a separate problem. The question asks for how much the number decreases (how many dried out), so it is an SCU problem
4. Marie made 8 bead necklaces. How many more does she have to make to have 10 bead necklaces?
Marie plans to make more neckaces, so there will be more neckaces at the end than at the beginning. The question ask how much the change will be, so this is a JCU problem.
5. John had 2 GI Joes. Luke had 5 GI Joes. How many more GI Joes did Luke have than John?
This question describes two groups, and asks how much more is in one group than another (comparison). This is a CDU problem. There is no change over time in this problem (no groups change size--they are just compared to one another)
6. Laura had 4 Webkinz. When she cleaned her room, she found some more Webkinz, and then she had 9 Webkinz. How many Webkinz did she find?
Laura found more Webkins, so the number of Webkins she had increased as a result of her action, which makes this a Join problem. The question asks for how many were foune--how much was the increase--so this is a JCU problem.
7. Sandy had 8 butterfly stickers. She gave some butterfly stickers to Ellen. Now she has 2 butterfly stickers left. How many butterfly stickers did she give to Ellen?
Sandy gave away some stickers, which reduced her number of stickers, so this is a separate problem. The question asks how many she gave away--how much the set was reduced by, so this is an SCU problem.
8. Michelle has 8 thick markers and 1 thin marker. How many more thick markers than thin markers does Michelle have?
This question describes two groups, and asks how much more is in one group than another (comparison). This is a CDU problem. There is no change over time in this problem (no groups change size--they are just compared to one another)
Decide for each statement whether it is true or false.
9. The difficulty for children in solving JCU and SCU problems is about equal
False. Unlike JCU problems, SCU problems do not have an easier entry point/way of phrasing to make problem solving easier, and the step where you either repeatedly count the remaining set or count backwards makes SCU direct modeling technically more difficult to carry out.
10. You should avoid teaching compare problems to children until upper elementary because they are so hard to understand.
False. Although compare problems are conceptually more difficult to understand, the structure of compare problems leads children to important understandings about the nature of subtraction that are not clear from the action (take-away) conception of subtraction. Thus, it's important that children learn about, and gain experience with, compare problems in the early elementary grades (grades 1 and 2)..
11. Childrens difficulty with solving SCU problems through direct modeling is mostly because they find the problems hard to understand.
False: While SCU problems are more difficult to understand than SRU problems, the most difficult part of solving SCU problems is keeping track of the diffent parts while repeately counting the set of counters remaining. Modeling SCU problems is almost a guess and check process, which makes it more cumbersome than either the modeling strategy for JCU or CDU problems.
12. Childrens difficulty with solving CDU problems through direct modeling is mostly because they find the problems hard to understand.
True: sentences describing comparisons of amounts (how many more than) have a unique and inherently numerical nature, and children need experiences with using and making comparisons of amounts of items that are already shown and modeled before they are ready to solve problems about comparisons. Some children will enter school with a familiarity with comparison language, and other children will not have experience with it.