Criteria for Mathematical Problems
1. There is a perplexing situation that the student understands.
2. The student is interested in finding a solution.
3. The student is unable to proceed directly toward a solution.
4. The solution requires use of mathematical ideas.
Marilyn Burns, About Teaching Mathematics, A K-8 Resources, Third Edition
The goal of unpacking the problem is to support sense making around the context, not to help students come up with a strategy or an answer. (Carpenter, Fennema, Franke, Levi, & Empson, Children's Mathematics Cognitively Guided Instruction, Second Edition, 2015)
Join Problems
• Result unknown: NOTE: Simplest and found the most often!
There were 4 ducks in the pond. Three more ducks entered the pond. How many ducks are in the pond altogether?
• Change unknown
There were 4 ducks in the pond. Some more ducks entered the pond. Now there are 7 ducks in the pond. How many ducks entered the pond?
• Initial unknown
Some ducks were in the pond. Three more ducks entered the pond. Now there are 7 ducks in the pond. How many ducks were in the pond to begin with?
Separate Problems
• Result unknown: NOTE: Simplest and found the most often!
There were 7 ducks in the pond. Three ducks left the pond. How many ducks are left in the pond?
• Change unknown
There were 7 ducks in the pond. Some ducks left the pond. Now there are 4 ducks in the pond. How many ducks left the pond?
• Initial unknown
Some ducks were in the pond. Three ducks left the pond. Now there are 4 ducks in the pond. How many ducks were in the pond to begin with?
Credits:
Created with images by mikesween - "puzzle game solution"