Primary 5 · Mathematics
P5 number and shape patterns
The rule for the 10th term of a pattern is one line, and most children get it slightly wrong the same way: they multiply by 10 when the answer needs a 9. Here is where the missing one goes.
- Level
- P5
- Usually taught
- Term 1
- Covers
- 2 concepts
What changes at P5
At Primary 5, patterns stop being about spotting what comes next and start being about jumping straight to a far term. Your child finds the common difference between terms, then uses a rule to reach the 10th or the 50th without listing every one.
The rule is short: the nth term is the first term plus (n − 1) lots of the common difference. Every part is easy except the (n − 1), which is the one place the marks are quietly lost.
The sentence that costs the mark
Look at the pattern 5, 8, 11, 14, … What is the 10th term?
What the working usually does
5 +10 × 3=35
Multiplies by the term number, 10, so it counts ten jumps of 3 from the start. But the first term is already there before any jump is taken.
What the question asked
5 +(10 − 1) × 3=32
Takes 10 − 1 = 9 jumps, because the 10th term sits after nine steps from the first. The first term costs no jump.
Both start at 5 and add a run of 3s, and both land on a term-shaped number. The only difference is whether you jump 10 times or 9, and the 10th term is nine jumps along, not ten.
| Point | Value |
|---|---|
| Point 1 | 5 |
| Point 2 | 8 |
| Point 3 | 11 |
| Point 4 | 14 |
The same question, worked properly
Find the common difference
each term is + 3Look at the gap from one term to the next. Here every step adds 3, so the common difference is 3.
Count the jumps, not the terms
10th term = 10 − 1 = 9 jumpsThis is the step that fails. To reach the 10th term you take 10 − 1 = 9 jumps, because the first term is already there before any jump. Using 10 here is the whole error.
Apply the rule
5 + 9 × 3 = 5 + 27 = 32First term, plus nine jumps of 3. The 10th term is 32.
Check on a term you can see
4th term = 5 + 3 × 3 = 14Test the rule on a near term: the 4th term is 5 + (4 − 1) × 3 = 14, which matches the list. If it works there, it works at the 10th.
How can you tell it has clicked?
You do not need to know the rule to check this. Ask your child how many jumps it takes to reach the 10th term from the first. The answer is 9, not 10, and a child who says 10 has found the exact slip.
A child who understands counts the gaps between terms, not the terms themselves. A child who multiplies by the term number lands one step too far, on every pattern, at every term.
One thing to try tonight
Stand at the bottom of a staircase and count up to the 10th step. You take 9 steps, because you were already on the ground before the first. Reaching the 10th of anything is 9 moves from the start.
That is the same − 1 the pattern rule uses. Try it on any pattern in the homework: how many jumps to the term they want? Always one fewer than the term number.
What your child will meet in this topic
- Shape Patterns
- Pattern Rules
Most Singapore schools introduce this in Term 1, though schools do differ by a term either way. If your child’s school runs a different order, you can set it in the schedule on your dashboard.
What it leads to
The (n − 1) rule is the first taste of a general formula, which is where algebra begins in secondary school: a rule that works for any term, not just the ones you can list. The same off-by-one waits there too.
A child who counts gaps, not items, carries that habit into sequences and formulae later. A child who forgets the − 1 keeps landing one term too far, now inside longer algebra.
The methods your child will use here
Each one is the same method wherever it turns up, so it is worth learning once.
More in Primary 5
Other topics in the same year, so you can see what sits either side of this one.
Struggling with the working rather than the topic itself? How to help your child with problem sums
See how your child is doing on this topic
StudyLah marks each step separately, so you can see whether it was the setup or the arithmetic that cost the mark.