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iGCSE (2021 Edition)

1.07 Solving contextual problems with whole numbers

Lesson

Not all mathematics questions come in the form of an equation. Sometimes we are presented with a real world problem and we want to translate the words into mathematics, so that we can solve the problem

Part of solving word problems comes from understanding the information we are given by reading it carefully, and correctly deciding which mathematical operations to perform. In this lesson we will look at how to turn word problems into a mathematical statement.
 

Worked example

A guitar teacher charges $\$28$$28 for every one hour lesson. How much would it cost for $12$12 lessons?

Think: Let's start by figuring out which steps to perform to solve the problem, then translate those steps into a mathematical statement.

Do: We know that the guitar teacher charges $\$28$$28 for every $1$1 hour. We want to figure out how much it would cost for $12$12 lessons.

If we know every lesson is $1$1 hour, that means we have $12$12 hours' worth of lessons. Every hour is worth $\$28$$28, so we have $28$28 groups of $12$12.

This is the same as $12$12 times $1$1 times $28$28. Translating this into a mathematical sentence gives: $12\times1\times28$12×1×28.

We can now solve to get:

$12\times1\times28$12×1×28 $=$= $12\times28$12×28
  $=$= $336$336

We can now conclude that it would cost $\$336$$336 for twelve lessons.

Reflect: We want to be able to translate the question into mathematical language that makes it easier to follow. We can then identify which operations to use, in order to solve the question. Once that's done, we follow the correct order of operations. In this example the only operation used was multiplication, but in other situations we may need to use a combination of different operations.

 

Practice questions

question 1

On Grace's farm, there are $6$6 cows and $9$9 goats. How many animals are there altogether?

Question 2

I scored $7$7 goals in my netball match. Eileen scored twice as many as me. How many goals did Eileen score?

Question 3

The number of motor accidents at a particular intersection was reported by traffic police to be $45$45 last year. The local council then decided to put up warning signs for motorists approaching this intersection. The following year the police reported only $29$29 accidents there.

How many fewer accidents were there after the signs were introduced?

Outcomes

0580C1.1A

Identify and use natural numbers and real numbers.

0580E1.1A

Identify and use natural numbers and real numbers.

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