Step 2:Think of a Plan

and

Step 3: Carry out the Plan

There are other strategies that can be used as you think through a plan for solving problems. They include guess and check and working backwards. You will look closely at these strategies in this activity.

As you practise these strategies, you will also carry out the plan and solve the problem.

This strategy follows these steps:

1. Guess a solution or way to see a problem.

2. Test the solution to see if it is correct. Use strategies such as calculating, researching, and asking questions.

3. If the guess is incorrect, you can guess again.

Here's an example of this strategy:

Three friends have been hired to help set up tables for a flea market.

Tui worked twice as many minutes as Joey.

Tara worked 10 minutes more than both Tui and Joey together.

In total, they worked 64 minutes.

How many minutes did each person work?

A table would help here:

Concluding Statement: Joey worked 9 minutes, Tui worked 18 minutes, and Tara worked 37 minutes.

You can check the answer by using information from the question.

• Tui worked twice as many minutes as Joey. 9 × 2 = 18

• Tara worked 10 minutes more than both Joey and Tui together. 9 + 18 = 27 + 10 = 37

• The total time worked was 64 minutes. 9 + 18 + 37 = 64

Some problems provide part of an end result and ask you to find other information.

To solve these kinds of problems, you can do the following:

Step 1: Begin with the information given in the problem.

Step 2: Work backwards to get an answer.

Step 3: Solve the problem.

Here's an example of this strategy:

Step 1: 38 students got off the bus at school.

Step 2: Work backwards:

• 38 – 9 = 29

• 29 – 6 = 23

• 23 – 5 = 18

• 18 – 1 (Sasha) = 17

Step 3: There were 17 students already on the bus when Sasha got on.