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Enlargement Scale Factors

Enlargement Scale Factors. Today we are learning how to: Identify enlargements Identify an enlargement scale factor Investigate the effect enlargement has on area and volume Investigate how to convert between different units of area and volume. Enlargements.

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Enlargement Scale Factors

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  1. Enlargement Scale Factors Today we are learning how to: Identify enlargements Identify an enlargement scale factor Investigate the effect enlargement has on area and volume Investigate how to convert between different units of area and volume

  2. Enlargements Which of the following are enlargements of the orange shape and why/why not?

  3. WHAT YOU NEED TO KNOW An enlargement is when a shape changes in size but the sides keep the same proportions as the original. An enlargement is drawn from a centre of enlargement by a given scale factor. A scale factor can be positive, negative or fractional.

  4. SHOW YOUR STRENGTH What information can you extract from the example below about the enlargement of the blue square? 7 0 0 15

  5. MAKE YOU THINK! Dave said he wanted to double the area of a rectangle. Dave did the following: Why is his example not an enlargement?

  6. MAKE YOU THINK! So what would happen to the area of a shape if you enlarged it by a scale factor of 2?

  7. DO NOW ACTIVITY Investigate what happens to the area of a shape when different scale factors are applied to it. Record your results in a table similar to the following:

  8. WHAT DO YOU NOTICE? The area of an enlarged shape can be found by multiplying the area of the original shape by the square of the scale factor. So what might happen with volume when different scale factors are applied?

  9. THINGS YOU NEED TO KNOW The area of a shape is changed by the square of the scale factor when an enlargement is applied. The volume of a shape is changed by the cube of the scale factor when an enlargement is applied.

  10. Confidence builder A square has side lengths of 4cm. The square is enlarged by a scale factor of 2. What is the area of the enlarged shape? 4 x 4 = 16cm2. 16 x 22 = 64cm2.

  11. Confidence builder A square has side lengths of 4cm. The square is enlarged by a scale factor of 3. What is the area of the enlarged shape? 4 x 4 = 16cm2. 16 x 32 = 144cm2.

  12. Confidence builder A square has side lengths of 4cm. The square is enlarged by a scale factor of -0.5. What is the area of the enlarged shape? 4 x 4 = 16cm2. 16 x 0.52 = 4cm2.

  13. Confidence builder A square has side lengths of ycm. The square is enlarged by a scale factor of 2. The enlarged shape has an area of 36cm2. What are the dimensions of the original square? y x y = y2cm2. y2 x 22 = 36cm2. So y2 = 9cm2. y = 3cm.

  14. Confidence builder A square has side lengths of ycm. The square is enlarged by a scale factor of 2. The enlarged shape has an area of 20cm2. What are the dimensions of the original square? y x y = y2cm2. y2 x 22 = 20cm2. So y2 = 5cm2. y = 2.4cm.

  15. Confidence builder A square has side lengths of ycm. The square is enlarged by a scale factor of 0.5. The enlarged shape has an area of 20cm2. What are the dimensions of the original square? y x y = y2cm2. y2 x 0.52 = 36cm2. So y2 = 144cm2. y = 12cm.

  16. DO NOW ACTIVITY The rectangle has dimensions 3cm by 4cm by 10cm. What is the area of the front face after an enlargement by a scale factor of 3? 4 Front 3 10 This prism has been enlarged by a scale factor of 6. If the new surface area is 72m2, what was the original surface area? The volume of cylinder 2 is 125 times the volume of cylinder 1. Cylinder 1 has a surface area of 40cm2. Calculate the surface area of cylinder 2.

  17. DO NOW ACTIVITY 4 40 x 3 = 120cm2 Front 3 10 y x 36 = 72m2. y = 2m2 Scale factor = 5 (cube root of 125). 40 x 52 = 1000cm2

  18. CREATIVE TIME Condense the learning of today’s lessons into some useful diagrams.

  19. MAKE IT HARDER! How might you use today’s learning to answer the following: Convert 16cm2 to mm2 Convert 95mm2 to cm2 Convert 7m2 to cm2 Convert 8400cm2 to m2

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