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Year 6 · Maths · SATs revision · Lesson 5

Reasoning: ratio, algebra and statistics

SATs reasoning practice on ratio and scaling, sequences, formulae and equations, the mean, pie charts and percentage discounts.

Whiteboard video lesson: Reasoning: ratio, algebra and statistics

23-minute video lesson

Teaching, worked examples and 20 practice questions solved step by step.

Watch free for a month

What your child will learn

  • Share in a ratio
  • Scale recipes
  • Solve equations
  • Use formulae and sequences
  • Find and use the mean
  • Interpret pie charts

The method

  1. Which topic?
  2. Draw it.
  3. Use the method.
  4. Check.

Key words: ratio, equation, formula, mean, pie chart.

Worked examples

The first three practice questions from the lesson, with every step.

Question 1

Share £45 between Cy and Di in the ratio 2 : 7.

  1. Step 1: Draw a bar model: Cy 2 boxes, Di 7 boxes
  2. Step 2: Total parts: 2 + 7 = 9
  3. Step 3: One part: £45 ÷ 9 = £5
  4. Step 4: Fill the boxes
  5. Step 5: Cy: 2 × £5 = £10, Di: 7 × £5 = £35

Answer: Cy £10, Di £35

Question 2

Share 84 stickers between Ed and Flo and Gus in the ratio 1 : 3 : 3.

  1. Step 1: Draw a bar model: Ed 1 box, Flo 3 boxes, Gus 3 boxes
  2. Step 2: Total parts: 1 + 3 + 3 = 7
  3. Step 3: One part: 84 stickers ÷ 7 = 12 stickers
  4. Step 4: Fill the boxes
  5. Step 5: Ed: 1 × 12 stickers = 12 stickers, Flo: 3 × 12 stickers = 36 stickers, Gus: 3 × 12 stickers = 36 stickers

Answer: Ed 12 stickers, Flo 36 stickers, Gus 36 stickers

Question 3

Girls : boys = 4 : 3. There are 28 girls. How many boys?

  1. Step 1: Draw a bar model: Girls 4 boxes, Boys 3 boxes
  2. Step 2: Girls: 4 parts = 28
  3. Step 3: 1 part = 28 ÷ 4 = 7
  4. Step 4: Boys: 3 × 7 = 21

Answer: 21