Unit 3: Subtraction
Topic F: Problem Solving
Why are you studying mathematics?
Some of you are taking math because you have to, but we hope you all want to have math skills to help you in your jobs, in job training, and in your everyday life. Numbers are an important part of our lives – we are surrounded by numbers.
Numbers are not often by themselves or set up neatly on a page for us to add or subtract. Numbers are usually in the middle of sentences and mixed in with other numbers. Sorting out the numbers you want and deciding what to do with those numbers is called problem-solving.
You are going to learn five problem-solving steps that will be useful in all your math work in courses, in jobs, and in your everyday life.
Problem Solving Steps
Step 1: Read or listen to the problem carefully. Understand the problem. Are there words that help you imagine what is happening? Can you draw a picture or diagram to show what is happening? Can you say the problem in your own words? What is the question? Underline it.
Step 2: What does the problem tell you? What do you know? Write down or circle the information you have. Often you have more information than you need. Think about the question you need to answer, and use only the information that will help you answer that question. What do you want to find out?
Step 3: What must you do with the information to answer the question? What arithmetic operation should you use addition, subtraction, multiplication or division? You will be learning keywords and patterns that will help you choose the correct operation. Write an equation for the problem, An equation is a number sentence such as
12 + 5 =
Step 4: Estimate the answer.
- Round the numbers so you can work with them quickly.
- Use the operation you chose in Step 3 and come to a quick answer.
- Does this estimated answer make sense? Does it answer the question in the problem? THINK about this before you do Step 5.
Step 5: Solve the problem using the actual numbers.
- Check your arithmetic calculations.
- Compare your result to your estimated answer.
- Reread the problem. Does your answer make sense?
- Write a sentence answer to the problem.
You must always say what the numbers are counting. He has 4, means nothing. We need to know 4 what… 4 children? 4 dogs? 4 dollars? These are called the units.
Some abbreviations used with numerals:
kilometre km
metre m
centimetre cm
kilogram kg
gram g
litre L
hour h
minute min
Now study the three example problems that show the five steps.
Example A
Jorge earned $165 last week and $142 this week in his job pumping gas at the service station. He spent $15 on his girlfriend’s gift. How much did he earn pumping gas?
Step 1: Read. Understand the problem. Find the question. Underline it.
How much did Jorge earn pumping gas?
Step 2: Find the Needed information. circle it.
Jorge earned $165 and $142.
The information about his girlfriend’s gift has nothing to do with finding out how much he earned.
Step 3: What Arithmetic operation