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Lesson · Grade 9 · Mathematics

Scale Diagrams: Enlarging and Reducing with a Scale Factor

  • Grade 9
  • Mathematics
  • 2 min 8 s
  • British Columbia
  • BC9-MA-22

A 4 cm by 6 cm rectangle is enlarged with a scale factor of 2.5 to 10 cm by 15 cm and reduced with a scale factor of 0.5 to 2 cm by 3 cm. Each new length is checked by dividing it by the old one, the angles stay 90°, and the common mistake of adding the same amount to each side is shown to give a different shape.

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In one sentence

The question this lesson answers

How can we draw a shape bigger or smaller, and keep exactly the same shape?

Take a rectangle 4 centimetres wide and 6 centimetres tall.

Transcript

What the lesson says

How can we draw a shape bigger or smaller, and keep exactly the same shape?

Take a rectangle 4 centimetres wide and 6 centimetres tall.

In a scale diagram, every length is multiplied by the same number, called the scale factor. We will use 2.5.

The width: 4 centimetres times 2.5 is 10 centimetres.

The height: 6 centimetres times 2.5 is 15 centimetres.

The new rectangle is 10 by 15 centimetres. It is bigger, so it is called an enlargement.

Check by dividing each new length by the old one: 10 divided by 4 is 2.5, and 15 divided by 6 is 2.5.

The lengths change, but the angles do not: every corner is still a right angle, 90 degrees.

A common mistake is adding the same amount to each side: 4 plus 6 makes 10, and 6 plus 6 makes 12.

Check: 10 divided by 4 is 2.5, but 12 divided by 6 is only 2. The rectangle is too short, so it is not a scale diagram.

Now use a scale factor of 0.5: 4 times 0.5 is 2, and 6 times 0.5 is 3.

The new rectangle is 2 by 3 centimetres. It is smaller, so it is called a reduction.

Check: 2 divided by 4 is 0.5, and 3 divided by 6 is 0.5. The angles are still 90 degrees.

A scale factor greater than 1 gives an enlargement. Between 0 and 1, it gives a reduction. Exactly 1 keeps the same size.

To draw a scale diagram, multiply every length by the scale factor and keep every angle the same.

Curriculum

Where this fits

British Columbia, Grade 9

Mathematics, Geometry and measurement: spatial proportional reasoningBC9-MA-22

Next: Reading a Map Scale: From Centimetres to Kilometres

The outcomes and strands follow the British Columbia curriculum.

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