1. Generate and use simple formulae
Algebra
Generate and use simple formulae
Objectives
Day 1
Understand and use simple formulae.
Day 2
Make generalisations; Understand and use simple formulae.
Before teaching, be aware that:
On Day 2 you will need Function machine at
Year 6

2. Generate and use simple formulae
Algebra
Generate and use simple formulae
Starters
Day 1 1-step function machines (pre-requisite skills)
Suggested for Day 2 Times tables (simmering skills)
Choose starters that suit your class by dragging and dropping the relevant slide or slides below to the start of the teaching for each day.
Year 6

3. Generate and use simple formulae 1-step function machines
Algebra
Generate and use simple formulae
Starter
1-step function machines
Click here 
Pre-requisite skills – to use this starter, drag this slide to the start of Day 1
Click on-screen link ( Choose ‘1 step function machine, own step’ at Ask children to close their eyes while you enter × 5, + 11, – 20 and × 6 for the four function machines. Children open their eyes. Ask a pair to suggest an input. Click to show the output. Click on ‘store numbers’. Children discuss in pairs what they think the machine is doing. Ask a pair for another input, the other pairs guess what the output might be. Repeat several times. Then ask pairs to write on their whiteboards what they think the mystery function is. Reveal the function to check. Repeat with each function machine.
Year 6

4. Generate and use simple formulae
Algebra
Generate and use simple formulae
Starter
Times tables
Simmering skills – to use this starter, drag this slide to the start of Day 2
Children play in pairs. They each shuffle a set of 0–12 cards and place them face down. On the count of three, they each turn their top card over. The first child to say the product keeps both cards. Continue until all the cards are gone. Who won the most pairs? Play another round.
Year 6

5. Generate and use simple formulae
Algebra
Generate and use simple formulae
Objectives
Day 1
Understand and use simple formulae.
Year 6

6. Write a formula for the area of the turf.
Day 1: Understand and use simple formulae.
turf
patio
A company is building houses on different plots. The back gardens are 5m long, but they will be different widths.
Each will have a patio area, the width of the plot, and 2m deep. The rest of the garden will be turfed.
We can use ‘n’ to stand for the width of the garden, so the patio area is
2 × n metres squared, which we can write as 2n m2 for short.
Write a formula for the area of the turf.
3n square metres or 3n m2
Year 6

7. So what is the turf width now? So, what is the turf area now?
Day 1: Understand and use simple formulae.
They have decided to leave a 1m border along one side of the turf for a flowerbed.
So what is the turf width now?
n - 1
flower bed
turf
So, what is the turf area now?
patio
3 x (n – 1) square metres
or 3(n – 1) m2
Today would be a great day to use a problem-solving investigation – Stars and Crosses – as the group activity, which you can find in this unit’s IN-DEPTH INVESTIGATION box on Hamilton’s website.
Alternatively, children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download.
WT: Together, write and use formula to work out ages.
ARE/GD: Support children in writing formulae.
What would be the area of the turf if they left a border of 1m along each side?
3 times (n – 2) square metres
or 3(n – 2) m2
Year 6

8. The Practice Sheet on this slide is suitable for most children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT/ARE/GD: Write and use simple formulae.
Year 6

9. Generate and use simple formulae
Algebra
Generate and use simple formulae
Objectives
Day 2
Make generalisations; Understand and use simple formulae.
Year 6

10. Day 2: Make generalisations; Understand and use simple formulae.
This machine does two things, one after the other, to each input.
Each group in turn are going to suggest an input.
We’ll see the output and see if we can work out what the machine is doing…
Click on this picture of the function machine (at Choose ‘pairs to fit own rule of the machine’. Ask children to close their eyes while you select × 2, + 1 for the first machine, and × 10, – 4 for the second. Press ‘go’ and ask children to open their eyes.
Show the first machine. Explain that the machine does two things, one after the other, to each input. Each group in turn suggests an input. Click to get an output. Store the numbers.
After a while click on clue 1 to help children. Children must not shout out the answer, but suggest pairs of values which help the other groups to guess the function.
Record the rule of the first function machine: × 2, + 1. If n is the input, the number we put into the machine, we can write the output as 2n + 1, which means we double the input, then add 1.
Show the second machine. Input several values and look at the outputs. After a while click on clue 1 to help children. Again, children must not shout out the answer, but suggest pairs of values which help the other groups to guess the function.
Record the rule of the second machine: × 10, – 4. Ask children to work in pairs to describe the output using n. (10n – 4)
Year 6

11. Function machine rules
Day 2: Make generalisations; Understand and use simple formulae.
Function machine rules
The first function machine: × 2, + 1. If n is the input, the number we put into the machine, we can write the output as 2n + 1, which means we double the input, then add 1.
The second function machine: × 10, – 4. If n is the input, we can write the output as 10n – 4.
Children can now go on to do differentiated GROUP ACTIVITIES. You can find Hamilton’s group activities in this unit’s TEACHING AND GROUP ACTIVITIES download.
WT/ARE: Practise inputting numbers into a formula, then guess inputs for given outputs.
GD: Play ‘Guardians of the rule’ as a group. Pairs make up 2-step rules for others to guess.
Year 6

12. The Practice Sheet on this slide is suitable for most children.
Differentiated PRACTICE WORKSHEETS are available on Hamilton’s website in this unit’s PROCEDURAL FLUENCY box.
WT: Sheet 1: Identify functions and write outputs in terms of n (single-step and two-step machines).
ARE: Do sheet 1, and try Sheet 2 if they are able to complete Sheet 1.
GD: Sheet 2: Identify functions and write outputs in terms of n (two-step machines).
Year 6

13. Generate and use simple formulae
Algebra
Generate and use simple formulae
Well Done! You’ve completed this unit.
Objectives
Day 1
Understand and use simple formulae.
Day 2
Make generalisations; Understand and use simple formulae.
You can now use the Mastery: Reasoning and Problem-Solving questions to assess children’s success across this unit. Go to the next slide.
Year 6

14. Problem solving and reasoning questions
Algebra Unit 1
Problem solving and reasoning questions   
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 = 6.5 cm.
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 come to the same amount?
Year 6