KS2 Mathematics: Scale Factors, Similar Shapes and Percentages

Ratio and proportion in Year 6 goes beyond sharing sweets and scaling recipes. The national curriculum asks pupils to solve problems involving similar shapes where the scale factor is known or can be found, and to use percentages for comparison, not only to calculate them. Both ideas rest on the same insight: when things grow or shrink in proportion, every length is multiplied by the same number, and when groups have different sizes, you compare them fairly by turning each into a number out of 100.

The twelve quiz questions cover enlarging a rectangle by a scale factor, finding the scale factor between two similar rectangles, finding a missing side of similar triangles, finding a missing side when the scale factor has to be worked out first and is less than 1, shrinking a square by a scale factor of one quarter, and seeing that the perimeter is multiplied by the scale factor too. Two questions use scale in real life: a floor plan at 1 cm to 2 m and a model car one twentieth of the real size. The last four compare with percentages: two test scores out of different totals, two classes of different sizes, a plant whose height increases by 15%, and a percentage discount against a money-off offer. The wrong options are the classic traps, such as adding instead of multiplying, using a scale factor the wrong way round, or comparing raw numbers instead of percentages.

The flashcards give the key ideas: what similar shapes and scale factors are, why angles stay the same when a shape is enlarged, how lengths and perimeters change, what a scale drawing is, what a scale factor less than 1 does, and how percentages make fair comparisons possible.

The printable written work has eight problems: enlarging a rectangle and comparing perimeters, completing a pair of similar triangles, deciding whether two rectangles are similar, a garden plan and the length of fencing it needs, a model aeroplane used in both directions, a survey comparison, three shop offers on the same coat, and explaining why adding the same amount to every side does not give a similar shape.

In the oral exam an examiner asks one question at a time and asks you to explain whether you multiplied or divided by the scale factor, and why.

The material is aimed at Year 6 pupils preparing for the reasoning papers of the end of Key Stage 2 tests, and it follows on from the category's ratio and proportion material on sharing, recipes and map scales.

• Enlarge and reduce shapes by a given scale factor, including scale factors less than 1
• Find the scale factor between similar shapes and use it to find missing lengths
• Recognise that adding the same length to every side does not make a similar shape
• Use scale drawings and models to find real and scaled lengths
• Compare quantities from groups of different sizes using percentages
• Solve problems with percentage increases and compare percentage and money-off offers

Practice material written by Zestly, based on the Year 6 mathematics programme of study in the national curriculum for England (DfE, 2013): ratio and proportion (solve problems involving similar shapes where the scale factor is known or can be found; solve problems involving the calculation of percentages and the use of percentages for comparison).