Substituting means swapping a letter for a number and working out the value. Remember that a number written next to a letter means multiply: 3n means 3 × n, not 3 + n and not the digits stuck together. So if n = 4, then 3n + 2 means 3 × 4 + 2 = 12 + 2 = 14. Do the multiplying first (following the order of operations), then add the extra number. Say '3n' out loud as 'three lots of n' to keep the times sign in mind.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- substitute
- replace a letter with its number value
- expression
- a mix of numbers, letters and operations, like 3n + 2
- coefficient
- the number multiplying the letter (the 3 in 3n)
Worked examples
n = 4, find 3n + 2
- 1.3n means 3 × 4 = 12.
- 2.12 + 2 = 14.
= 14
n = 5, find 3n + 2
- 1.3n means 3 × 5 = 15.
- 2.15 + 2 = 17.
= 17
n = 3, find 4n + 1
- 1.4n means 4 × 3 = 12.
- 2.12 + 1 = 13.
= 13
For parents
Method: Turn the letter into a times sign first.
What to say: Ask 'what does 3n mean?' — three times n — before putting the number in.
Common mistakes:
- Reading 3n as 3 + n (n = 5 → 10 instead of 17).
- Sticking the digits together as 34, or forgetting the + 2.