Short Blocks

Maths Year 6 Autumn Algebra

Each unit has everything you need to teach a set of related skills and concepts.

Generate and use simple formulae (suggested as 2 days)

Planning and Activities

Day 1 Teaching
Show the garden problem about area. Show how we can use a letter, n, to stand for the width of the garden so the area of the patio is 2n or (2 × n) metres squared. Children then use this to write a formula for the area of the turf. Then alter the width to (n – 1) metres. So, the area of the turf is 3 times (n – 1) or 3(n – 1) square metres. Alter the width again so the area is 3 times (n – 2) or 3(n – 2) square metres
Group Activities
-- Together, write and use formula to work out ages.
-- Support children in writing formulae.

Day 2 Teaching
Choose ‘pairs to fit own rule of the machine’ from Ask children to close their eyes while you select × 2, + 1 for the first machine, and × 10, – 4 for the second. Each group choose several inputs and study the outputs. Show children how to record a generalisation using n, e.g. 2n + 1.
Group Activities
Use the ‘Stars and Crosses’ in-depth problem-solving investigation below as today’s group activity.
Or, use these activities:
-- Practise inputting numbers into a formula, then guess inputs for given outputs.
-- Play ‘Guardians of the rule’ as a group. Pairs make up 2-step rules for others to guess.

You Will Need

  • Garden sketch (see resources)
  • ‘Write a formula’ sheet (see resources)
  • Function machine from
  • Flipchart and pens
  • 1–10 cards

Mental/Oral Maths Starters

Day 1
1-step function machines (pre-requisite skills)

Suggested for Day 2
Times tables (simmering skills)

Mastery: Reasoning and Problem-Solving

  • If the perimeter of a regular shape is 5 × n, where n is the length of a side, what is the shape? Find the perimeter when n = 6.5cm.
  • Darren draws a function machine. It trebles a number and then subtracts 6. Sophie sees that one of the outputs is 15. What was the input? Then Darren inputs 11. What output will Sophie see? Write the formula for Darren’s machine.
  • Formula A is 3n.
    Formula B is n + 6.
    What number can n represent which will make these two formulae equal the same amount?

In-depth Investigation: Stars and Crosses
Children find totals of the numbers in shapes on a 1-100 grid, make generalisations and then write a formula to find the total of any similar shape on the grid.
The PowerPoint can be used to guide your class through this investigation.

Extra Support

This unit has no separate Extra Support activities.