Mastering Direct Proportion and Scale Factors

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Mastering Direct Proportion and Scale Factors

What do you already know about scale factors and proportion?

Learning Objective

At the end of the lesson you will be able to compare, represent, and reverse direct proportions and scale factors, including non-integer constants.

What is Direct Proportion?

When two quantities increase or decrease at the same rate, they are in direct proportion. If one doubles, so does the other.

How Do We Represent Proportion?

Using Equations

Using Scale Factors

y = kx, where k is the constant of proportionality.

Multiply by a scale factor to find the corresponding value. Not always a whole number!

Non-Integer Constants

Scale factors are not only integers. You might multiply by 1.5, 0.5, or 2.75. Practise using these in examples.

Comparing Scale Factors

If you know one value and the scale factor, you can find the other. Can you work backwards if you know the answer?

Using Reciprocals to Reverse

Multiply by the reciprocal to go the other way. Example: ×2 is reversed by ×½.

Reverse Process

Multiply by the scale factor to get from A to B.

Forward Process

Let’s Practise!

Work through these examples using scale factors that are fractions and decimals. Try reversing some too!

Reflect and Check

Can you now recognise and use non-integer scale factors, and find the reciprocal to reverse proportional relationships?

Write down 3 things you learned in this lesson.

Write down 2 things you want to know more about.

Ask 1 question about something you haven't quite understood yet.