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Year 6 Multiplication and Division: Scale Factor in Shapes

Solve problems using scale factor in areas of shapes in Year 6 math curriculum. Practice areas of triangles, rectangles, and parallelograms. Includes algebraic starter activities.

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Year 6 Multiplication and Division: Scale Factor in Shapes

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  1. Multiplication and Division Solve problems using a scale factor in areas of shapes Objectives Day 1 Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms. Day 2 Solve problems involving similar shapes where the scale factor can be found. Year 6

  2. Multiplication and Division Solve problems using a scale factor in areas of shapes Starters Day 1 Algebra: missing numbers (simmering skills) Day 2 Algebra: list pairs of variables (simmering skills) Year 6

  3. Multiplication and Division Solve problems using a scale factor in areas of shapes Starter Algebra: missing numbers Year 6

  4. Year 6

  5. Multiplication and Division Solve problems using a scale factor in areas of shapes Starter Algebra: list pairs of variables Year 6

  6. Multiplication and Division Solve problems using a scale factor in areas of shapes Objectives Day 1 Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms. Year 6

  7. Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms. • How can we find the area of this triangle? • Sketch a right-angle triangle with sides adjoining the right angle of lengths 4cm and 7cm. • Find the area of the rectangle and halve it to find the area of the triangle. • We can sketch a rectangle around the triangle like this. • Measure the longest side and compare with your neighbour. 1/2 × b × h Year 6

  8. Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms. • What do you think the area might be? • Work it out… • Is the longest side also twice the length? • Draw a similar-looking triangle but with each side next to the right angle twice the length of the first one. • We call these two triangles ‘similar’. • In maths, we use this word to describe shapes that might be different in size but have the same proportions. • The corresponding sides of similar shapes are a multiple of each other. • So, the lengths of the sides are double the original lengths, but the area is 4 times the original! Year 6

  9. Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms. 6cm 8cm To find the area of a parallelogram, we can ‘slide’ the triangle to the right to create a rectangle. • Work out the area of this parallelogram. Year 6

  10. Day 1: Solve problems involving similar shapes where the scale factor is known; Find areas of triangles, rectangles and parallelograms. • Whole class investigation • You will need a ‘Scaling up’ activity sheet. • Draw a similar rectangle on cm2 paper, such that the length of each side is double the original, and then another with triple the original length sides. • Find what has happened to the area of the rectangle. • Repeat for the triangle and parallelogram. • Be ready to feedback what you have found out. Year 6

  11. Challenge Year 6

  12. Multiplication and Division Solve problems using a scale factor in areas of shapes Objectives Day 2 Solve problems involving similar shapes where the scale factor can be found. Year 6

  13. Day 2: Solve problems involving similar shapes where the scale factor can be found. Similar shapes are identical in shape, but not in size. • So all circles, squares and other regular shapes are similar, but rectangles might not be. • Find two rectangles which look similar. Measure the sides of each. • Work out the scale factor, i.e. the number we need to multiply the side length of the first shape by to get the larger shape. • Repeat for the triangles. • It is useful to use a scale factor when producing a scale drawing of plans for a building or a model. The drawing would have the same proportions as the real building or model. Year 6

  14. Year 6

  15. Year 6

  16. Multiplication and Division Solve problems using a scale factor in areas of shapes Well Done! You’ve completed this unit. Objectives Day 1 Solve problems involving similar shapes where the scale factor is known. Find areas of triangles, rectangles and parallelograms. Day 2 Solve problems involving similar shapes where the scale factor can be found. Year 6

  17. Problem solving and reasoning questions True or false • If one triangle is scaled up to have sides 3x as long as another, the area is also 3x as large. • If two rectangles are similar and the scale factor is 4, then the area of the larger is 16 times that of the smaller. Calculate the area of the triangle whose sides are ½ the length of this one. Compare the two areas. What do you notice? Explain why the area of the smaller has this relation to the area of the larger. Year 6

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