KS2 Maths reasoning (SATs) textbook

Chapter 3: Ratio and proportion reasoning

  • Strand Ratio and proportion
  • Level Year 6
  • Practice 96 questions with step-by-step solutions

KS2 SATs practice for reasoning (Year 6). Original questions in the style of the national tests. Content: Solve problems involving the relative sizes of two quantities where missing values can be found by integer multiplication or division (Year 5-6), Use the ratio language a:b and the link between ratio and fractions (Year 6), Solve problems of unequal sharing and grouping using fractions and multiples (Year 6), Use the unit method for proportion, including percentages of a whole (Year 5-6), Solve problems involving similar shapes where the scale factor is known or can be found (Year 6), Use proportional reasoning to compare prices and quantities, and explain why a comparison is or is not fair (Year 5-6).

Open Year 6 chapter

By the end of this chapter you will be able to

  • Simplify a ratio and find a missing amount from a ratio
  • Share an amount in a given ratio and write each share
  • Use the unit method to scale a recipe or a rate
  • Compare the price of one item to decide which is better value
  • Find a scale factor and use it to find a missing length

You should already know

  • Multiplication and division facts, and equivalent fractions (Year 4 and Year 5)
  • Fractions of amounts and percentages (Chapter 2 of this book)

Where this leads

  • Measures in context (Chapter 4 of this book)

Lessons in this chapter

  1. 3.1 Ratio language and simplifying ratios
  2. 3.2 Sharing in a ratio and fractions of a total
  3. 3.3 The unit method and percentages
  4. 3.4 Best value and fair comparisons
  5. 3.5 Similar shapes and scale factors
  6. Summary and key words
  7. Check-up and practice test questions

Read the whole chapter on one page (good for printing).

Practise with real exam questions

The DfE publishes every past KS2 test, with mark schemes, for free.

KS2 Maths reasoning (SATs) past papers