Y10 Foundation: Topic 25: Ratio and proportion and scale factors

Objectives:

    • Understand what is meant by ratio
    • Write a ratio in its simplest form; and find an equivalent ratio
    • Share a quantity in a given ratio
    • Understand and use examples in direct proportion
    • Interpret map/model scales as a ratio
    • Use integer and non-integer scale factors to find the length of a missing side in each of two similar shapes, given the lengths of a pair of corresponding sides
    • Know the relationship between linear, area and volume scale factors of similar shapes
    • Deduce the areas and volumes of similar shapes after they have been enlarged by simple scale factors
    • Read and construct scale drawing, eg work out the real distance if the map distance is 6 cm and the scale is 1:25000

Prior Knowledge:

    • Using the four operations
    • Ability to recognise common factors
    • Knowledge of fractions
    • Use ruler and compasses to construct triangles with given dimensions
    • Some concept of enlargement (magnification)

Key Vocabulary:

  • Copy and paste here.

Differentiation & Extension:

    • Similar triangles
    • Share quantities in a ratio involving fractions, and decimals
    • Use a map to plan a journey, eg how long will the journey take travelling at average speed of 40 km/h (or mixed speeds for different roads)
    • Deduce areas and volumes of similar shapes for harder scale factor enlargements (including fractions)
    • Further problems involving scale drawing, eg find the real distance in metres between two points on 1:40000 map

Using & Applying ideas:

  • Collaborate here.

NOTES
    • Students often work well with ratios of two quantities
    • They have greater difficulty with ratios of three quantities and particular attention needs to be given to this

Teaching & Learning Resources:


3D Shapes Resources