Lesson 9 — Activity 1: The 4-Step Method


Getting Ready:


The next lessons in this theme will focus on problem solving.

The remaining lessons in this theme focus on solving math word problems. You will learn about and practise using strategies to work through problems you will come across in math work.

You may have come across some of these strategies in previous courses and some of them may be new to you.


Think about This:


Think of a time when you experienced a problem that you had to solve. It might not be a math problem, but a problem at school or outside of school.

How did you go about solving it?

Did you have a plan of action?

Did it involve following steps ?

Did having a plan make it easier to solve the problem?


Sometimes you might come across a math word problem and have no clue how to even start it. It is important to have a plan for approaching problems. We call such a plan the 4-Step Method.


Step 1: Understand the Problem

To understand a word problem, you need to be able to answer some questions:


  • What information is given?
  • What are you asked to find?
  • Does the question need an exact or approximate answer?

You can use one or more of the following strategies to help you answer these questions. You might:

  • interpret visuals such as pictures, charts, tables, or graphs
  • identify the keywords in the problem
  • identify which information is important and which is unimportant


Step 2:Think of a Plan


The keywords in a problem and the important information given will help you develop a plan for solving problems. You may decide to:

  • look for patterns
  • draw a picture or use manipulatives
  • make the problem simpler
  • practise using guess and check
  • work backwards
  • organize information


 

Step 3: Carry out the Plan


You can solve the problem using a pencil and paper, manipulatives, a calculator, a computer, or by using another strategy that you identified in your plan.

Remember to always state the solution to the problem in a statement.








Step 4: Look Back and Verify

You can choose one or more of these strategies to check your answer for reasonableness:

  • Use the information and/or numbers in the problem to estimate a solution. Then compare your answer to this estimate to help you determine if your answer is reasonable.
  • Check that decimals are placed correctly.
  • Use a calculator.
  • Use the opposite operation (subtract if you added, divide if you multiplied, etc.).
  • Compare your answer with others.


A further thing to do when looking back:

  • Think if another strategy that might have worked just as well or better than the one you used.
  • Think about what other kinds of problems you can solve using the strategies you employed.





Here's how to use the 4-Step Method:

Look at this problem:
Read this problem about preparing for a birthday party.

Sage was hosting a birthday party. She invited 14 girls and 12 boys.

She made 1 dozen pink cupcakes and 2 dozen blue cupcakes.

When the party was over, there were 4 cupcakes remaining.

How many cupcakes were eaten?

Click on the tabs to follow the steps.


In this problem, we are given quite a bit of information. Let's identify which information is most important and what you are asked to find:


Sage was hosting a birthday party. She invited 14 girls and 12 boys.

She made 1 dozen pink cupcakes and 2 dozen blue cupcakes.

When the party was over, there were 4 cupcakes remaining.

How many cupcakes were eaten?


The most important information and what you are asked to find has been highlighted above. It is interesting how many people Sage invited, but it is not important information. So now we understand the problem.

There are many strategies you can use in this step. For this problem, it would be best to make it simpler. That is, we must first figure out the total number of cupcakes made, then determine how many were eaten.

We could write an equation to do this: (1 dozen + 2 dozen)  – 4 = number of cupcakes eaten


Now we will begin to solve our equation:

(1 dozen + 2 dozen) – 4 = cupcakes eaten

First, we must remember that a dozen = 12. Our new equation would look like this:

(1 x 12 + 2 x 12)  – 4
(12 + 24) – 4 =
36 – 4 = 32


This means that the number of cupcakes eaten was 32.


This final step is very important. Does the answer make sense? In the problem, we wanted to know how many cupcakes were eaten. Our answer was 32, which is less than the total number made (36), so that answer makes sense.


We can check our answer further by using the opposite operation. (32 + 4 = 36), so our answer checks out!


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