Problem type solutions:
| JRU | JCU | JSU |
| SRU | SCU | SSU |
| PPW-WU | PPW-PU | |
| CDU | CQU | CRU |
1. Ann had 7 shells. Her mom gave her 5 more shells. How many shells does Ann have now?
JRU: There is an increase over time in this problem (with the last amount unknown)
2. Sarah has 4 marbles and Ann has 6 marbles. How many marbles do they have all together?
PPW-WU: There is no change over time in this problem, two known sets are being thought of as forming an unknown whole
3. John had 16 M&Ms, and he ate 9 of them. How many M&Ms does he have now?
SRU: There is a decrease over time (with the final amount unknown)
4. Alex has 16 toy cars, and Mark has 9 toy cars. How many more toy cars does Alex have than Mark?
CDU: There is no change over time, the amounts in two sets are being compared; the difference between them is unknown
5. Jan had some pencils, and then Matt gave her 3 more pencils. Now she has 10 pencils. How many did Jan have to begin with?
JSU: There is an increase over time (Matt gave her more) the start value is unknown
6. Mary had 9 erasers, and then her mom gave her 7 more. How many erasers does Mary have now?
JRU: there is an uncrease over time, with the final amount unknown
7. Sam had 8 crayons, and then Jack gave him some more. Now Sam has 12 crayons. How many crayons did Jack give him?
JCU: There is an increase over time (Jack gave him more), with the amount changed unkown.
8. Alex has 8 stickers. There are 12 places to put stickers on his sticker page. How many more stickers does Alex need to fill his sticker book?
JCU: This is a tricky one, but it's also one of the standard examples. The change over time is the perceived change from now until the future. This sort of change unknown problem is actually the easiest for children to solve.
All of 9-12 are compare problems
9. Alex has 8 stickers. Mike has 2 more stickers than Alex. How many stickers does Mike have? "more than Alex": so Alex is the referent; Alex has 8 , so the referent is known, and the compared quantity is not. CQU |
10. Alex has 8 stickers. He has 2 fewer stickers than Mike. How many stickers does Mike have? "fewer than Mike": so Mike is the referent; Mike's number is not given, so the referent is unknown. CRU |
11. Mike has 10 stickers. Alex has 2 fewer stickers than Mike. How many stickers does Alex have? "fewer than Mike": so Mike is the referent; Mike has 10 , so the referent is known, and the compared quantity is not. CQU |
12. Mike has 10 stickers. He has 2 more stickers than Alex. How many stickers does Alex have? "more than Alex": so Alex is the referent; Alex's number is not given, so the referent is unknown. CRU |
13. Karen had 12 colored pencils. 8 of them were sharpened, and the rest were not sharpened. How many pencils were not sharpened?
PPW-PU: There is no change over time, we just change the way we thing about the pencils from being one whole sets to two parts. One of the parts (the not sharpened part) is unknown.
14. Karen had 12 new crayons. Some of them broke. Now she has 8 crayons that are not broken. How many crayons were broken?
SCU: This is definitely a change over time, and the number of unbroken crayons decreased, so it is a separate problem. The amount that broke is unknown, and that is the change in the set of unbroken crayons
15. Jim's mom put some cookies in his lunch bag. He gave 3 to Paul, and had 4 left for himself. How many cookies did Jim's mom put in his bag?
SSU: The number of cookies Jim had decreased over time. The unknown is the amount he started with.