### 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 topmarks.co.uk. 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.