Scale and similar shapes (age 11+)

Activities to try

1. 1

   Measure, scale and convert on a map

   Why it works: Scale is a consistent multiplier: going from a map measurement to the real distance means multiplying by the scale denominator for this reduced map; the reverse means dividing. Track the units at each step and express the answer in the units requested, here kilometres.

   1. Read the scale ratio aloud before calculating, e.g. 'one centimetre on the map is 25000 centimetres in real life' — emphasise that both sides share the SAME unit.
   2. Measure the map distance between two points (e.g. two villages 8 cm apart on a 1:25000 map). Optionally, drag a ruler on a map and use a live panel that unfolds measured map-cm, multiplication by25000, then the cm-to-m-to-km conversion, with the scale bar alongside for checking.
   3. Before calculating, estimate: real life is bigger than the map, so map→real MUST multiply — predict roughly how big the real distance should be.
   4. Multiply: 8 × 25000 = 200000 cm.
   5. Do the unit conversion as a deliberate final step, tracking units: 200000 cm ÷ 100 = 2000 m, then ÷ 1000 = 2 km.
2. 2

   Draw a room to scale (the divide direction)

   Why it works: Going from real distances to a scale drawing requires dividing by the scale factor; seeing the room come out the wrong SIZE against a familiar reference makes the direction error concrete.

   1. Choose a scale (e.g. 1:100) for drawing your own bedroom.
   2. For each real wall length, work out the line to draw: divide the real length by the scale factor (e.g. a 4 m wall at 1:100 → 4 m = 400 cm, 400 ÷ 100 = 4 cm on the diagram).
   3. Draw the walls at the computed lengths and compare the result against a reference object of known size (e.g. a doorway) to sanity-check.
   4. Say aloud why this is a divide: 'the diagram is smaller than real life, so real→map DIVIDES.'
   5. Check: if the drawn room looks absurdly large, you probably multiplied instead of dividing, so revisit the direction rule. If it shrinks to a dot, check your units. For example, dividing 4 m by 100 without first converting to centimetres gives 0.04, which is far too small to draw.
3. 3

   Direction and conversion practice with sharp distractors

   Why it works: The common errors — leaving the answer in cm, and dividing instead of multiplying — produce predictably wrong magnitudes that a sense-check would have caught.

   1. Answer targeted items such as: '8 cm on a 1:25000 map → ___ km' (correct: 2 km).
   2. Identify and reject the error value 200000 (the real distance left unconverted, in cm).
   3. Identify and reject the error value ≈0.00032 (the result of dividing instead of multiplying).
   4. Decide which operation (multiply or divide) applies when drawing a room to scale versus reading a real distance.
   5. Choose a sensible scale for a given object and justify it.