Grade FG Use scale factors diagrams and maps
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Grade F/G Use scale factors, diagrams and maps (including geometrical problems) If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk
Key Vocabulary Scale factor Ratio Diagram Map Actual distance Enlargement
How to use scale factors Enlarge the line below by scale factor of 3. What will it measure after the enlargement? 20 cm 20 x 3 = 60 cm
How to use scale factors Enlarge the shape below by scale factor of 2. 4 cm 11 cm x 2 8 cm x 2 22 cm
How to use scale factors A rectangular field measures 20 m by 70 m. If the scale used to draw this on paper is 1: 100, what are the measurements of the field on paper? 1: 100 means 1 cm on paper is equivalent to 100 cm in real life 100 cm = 1 m If every meter in real life is 1 cm on paper, then: 20 m will be 20 cm and 70 m will be 70 cm on paper.
How to use scale factors Using the scale 1 : 1000, find the actual distance in metres, if the distance between two places is 6 cm on a map. Remember both parts of the ratio have the same units (centimetres) 6 x 1000 = 6000 cm is: 6000 ÷ 100 = 60 m
How to use scale factors B is an enlargement of A. Find the scale factor of the enlargement. 2 squares A 6 squares B Compare the widths 2 squares to 6 squares mean 6 ÷ 2 = 3. It is enlarged by a scale factor of 3.
How to use scale factors – Now you try … 1) A map uses a scale factor of 1 : 200 000. What does 2 cm represent in real life in kilometres? 2) The scale of a map is 1 : 2500. The actual distance between two towns is 20 km on the map. What is the map distance? 3) In a map, 8 cm represent 2 km. Write the scale of the map. 4) Copy the shape and enlarge it by scale factor 2.
How to use scale factors – Now you try … 1) A map uses a scale factor of 1 : 200 000. What does 2 cm represent in real life in kilometres? 1) 4 km 2) The scale of a map is 1 : 250000. The actual distance between two towns is 20 km on the map. What is the map distance? 2) 8 cm 3) In a map, 16 cm represent 2 km. Write the scale of the map. 3) 1: 12500 4) Copy the shape and enlarge it by scale factor 2.
Problem Solving and Reasoning a) b) c) d) Find the area of the shape below. Enlarge the shape by scale factor of 3. Then find the area again. What do you notice? Can you try more of these exercises to come up with a rule? a) 2 x 3 = 6 units 2 b) c) 6 x 9 = 54 units 2 d) Area of the second shape is 9 times bigger than the first.
Reason and explain • Look at the shape below. Can we say the shape is enlarged by scale factor of 3? A B • Do shapes always get bigger? • How can we represent a shape that was reduced in size?