Primary 6 · Mathematics

P6 algebra

Three more than n, and three times n, are not the same thing. Almost every child writes one when they mean the other in the first weeks of algebra. Here is the sentence it hides in.

Level
P6
Usually taught
Term 2
Covers
5 concepts

What changes at P6

At Primary 6, a letter arrives to stand for a number you do not know yet, not a label for the ribbon or the pencil. Adding, multiplying, collecting like terms, it is all arithmetic your child already does, with a letter where a number will later sit.

The marks are lost at the first step: turning the words into the expression. P6 keeps it linear with no brackets, but "3 more than n" and "3 times n" look so alike that the wrong one gets written without thinking.

The sentence that costs the mark

A blue ribbon is n cm long. A red ribbon is 3 cm longer than the blue one. Write the length of the red ribbon, in terms of n.

What the working usually does

3 timesn=3n

Puts the 3 and the n together into 3n. But 3n means 3 × n, which is three whole ribbons, not one ribbon that is a little longer.

What the question asked

3 more thann=n + 3

One ribbon, with 3 cm added on the end. "Longer" adds, so the 3 sits beside the n with a plus, not stuck to it.

Both look like real algebra, and 3n is the tidier answer, which is part of the trap. The only question is whether "longer" means add or multiply. It means add, and the two answers are far apart: if the blue ribbon were 10 cm, the red one is 13 cm, not 30.

Three more than n adds one box of 3. Three times n is three whole n boxes. Not the same thing at all.

The same question, worked properly

  1. Name the letter properly

    n = the blue ribbon's length

    n stands for a number of centimetres that is not known yet, not for "the ribbon". Reading it as a number is what makes the next step work.

  2. Read what "longer" does

    longer → add

    This is the step that fails. 3 cm longer means 3 added on, not 3 groups of the ribbon. This one word decides the whole answer, and it is the word that gets skimmed.

  3. Write the expression

    red ribbon = n+3n + 3

    One ribbon of length n, plus 3 more. The plus sign is the whole point.

  4. Check with a number

    if n=10n = 10: n+3=13n + 3 = 13, but 3n=303n = 30

    Substituting a number is the MOE check, and it settles it instantly: 13 and 30 are nowhere near each other, so 3n was never the same as n + 3.

How can you tell it has clicked?

You do not need algebra to check this. When your child writes an expression from a sentence, ask them to read it back to you in words, then read the question aloud too.

"Three times n" and "three more than n" sound different the moment they are said out loud, even when they looked the same being written. A child who spots the mismatch has understood. A child who reads 3n back as "three more than n" has found the exact gap.

One thing to try tonight

Pick a number for n at dinner, say 6, and ask two questions: what is 3 more than it, and what is 3 times it. Nine and eighteen. Two different answers from two different words.

Then show the writing: n + 3 and 3n. Same two symbols, 3 and n, arranged two ways that mean completely different things. Seeing the numbers move is what makes the letters stick.

What your child will meet in this topic

  • Algebra
  • Algebra Expressions
  • Finding the Value
  • Simplifying Algebra
  • Algebra Word Problems

Most Singapore schools introduce this in Term 2, 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

Turning words into expressions is the gateway to algebra word problems and simple equations, where a whole question is built from lines like this one and then solved.

A child who translates carefully, one phrase at a time, handles those. A child who mashes the numbers and letters together loses the marks before the solving even begins.

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 6

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.

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