## Problem Solving“I did then what I knew how to do. Now that I know better, I do better.” ― Maya Angelou

Research supports that problem solving is not only about applying mathematics but also to learn new mathematics. (Van de Walle, 2007)

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?

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