The value of teaching math problem solving is that students become involved at a deeper level. Are you teaching through how to solve math problems or just teaching for it?

Problem solving activities are part of every day life. Teaching these strategies provides students with:

- choices of how to solve for an unknown answer
- improved abilities to choose appropriate strategies
- scaffolded support for improving self-concepts about abilities to problem solve.

However, there should never be a prescribed “correct solution.” We must be careful not to give the impression that there is only one way to solve a mathematical problem.

Exercises are chosen with the goal of either teaching a strategy or practicing a technique to mastery. We also want to engage our students in real-life mathematical situations (problems they likely will encounter in everyday situations).

You must engage your students in *doing* mathematics and allow for multiple entry points to arrive at the same solution.

## 4 Steps for Math Problem Solving Activities

According to George Polya, there are always 4 steps that should be taken when attempting a new task:

**1. Understand the Problem**

Read and re-read. State the problem in your own words. Decide if there are multiple steps that will need to be taken to arrive at the final answer. Determine what the question is asking you to actually do.

Using the Model method, the students should draw what they know and what they are attempting to solve. Using a model to solve a problem is a necessary step for younger students who are not ready for more abstract methods (such are taught in algebraic equations).

If students can develop a mental image of the problem in their head, then they likely have a solid understanding of what the problem is asking.

**2. Make a Plan**

Choose your strategies. Think back to similar problem solving exercises and recall what was successfully used.

**3. Try It Out**

Go step-by-step with the problem solving strategies chosen. Draw pictures to show each step is correct if helpful. Self-talk your way through the problem.

**4. Look Back**

Always check your work. Did you actually answer the question? Did you use all relevant data? Does your answer make sense? Is there another way to solve the problem or show your answer differently?

To have a classroom that is truly focused on math problem solving, a teacher must let the students do the talking and take initiative in leading discussions. Teachers also share only relevant information and expect students to write and explain their solutions.

## Math Problem Solving Example

To solve math problems like this one, there are a multitude of strategies involved. I made it up on the spot with my class of second graders to demonstrate how to use Polya’s Problem Solving Steps.

**There were 20 dinosaurs. 1/2 of them were female. 1/2 of the females had 3 babies each. The rest of them had 2 babies each. How many dinosaurs are in the herd now?**

In order to understand it, we have to realize that the herd is much larger than at the beginning of the problem. That would signal the possibility to use addition or multiplication. However, there is an implied understanding of fractions and division as well.

This is a great example to use with children to model thinking out-loud about the steps required to solve this and how to draw models to show their thinking.

Two bars could be drawn: 1 representing 20, and the other in half. Then, that half could be divided into two and numbers written on each bar to represent the whole.

Groups can be drawn to show 5 groups of 2 and 5 groups of 3 (representing the babies).

How will your students pull all of it together to answer the final question? How would you show it?

## Fun Math Activities for Problem Solving

1. I have 6 coins that are worth 60¢ in my pocket. What coins might I have? Find multiple solutions and explain.

2. What helper facts could you use to solve these problems: 9 + 21, 4 x 5, 7 x 3, and 6 + 6?

3. Think about a square. Name three shapes that have at least one thing in common with a square and explain.

4. There are three ducks. Each duck is sitting on 4 eggs. How many eggs are the ducks sitting on?

5. Show 15 in at least 4 different ways.

6. I have a pocket full of silver coins. Could I have 65¢? Explain.

7. I am thinking of 2 numbers with a sum of 12 and a difference of 2. What numbers am I thinking of?

8. Joe has a pocket full of silver coins. Could he have 55¢? Explain.

9. There are 7 triangles. How many sides are there altogether?

10. Green books are twice as heavy as red books. There are 4 green books on one side of the scale. How many red books do we need to balance the scale?