Algebra in P6: Why the Letters Trip Children Up, and How to Check

24 September 2026 · by Larry

A child who can work through a three-step fraction problem without blinking is told that y is 4 and asked for the value of 3y. She writes 34.

It looks careless, and it is not. For six years, two symbols written side by side have always been digits in one number. In algebra, 3 next to y means 3 × y, and nobody made a point of telling her the rule had changed.

That is the heart of P6 algebra. The ideas in it are small. The notation is new, and almost every mark lost in this topic comes from a child reading the notation the old way. Once you know which old habit is getting in the way, most of the slips below take one conversation to fix, not a term.

What your child is actually being asked to do

Algebra is one of only two properly new topics in P6 (the other is circles; the rest continues earlier work, as set out in what actually changes from P5 to P6). At this stage it is a first taste, not the algebra you may remember from secondary school. The questions she meets mostly come in a few shapes:

• Write an expression. "A pen costs p cents. What is the cost of 3 pens?" The answer is 3p cents.
• Find its value. "Find the value of 2y + 3 when y = 5." The answer is 13.
• Tidy it up. y + y + y is 3y, and 4k + 2k is 6k.
• Find the missing number. "x + 5 = 12. Find x." The answer is 7.

Schools differ in exactly how far they go and in what order. If you want the official list for your child's year, MOE publishes the primary syllabuses on its site, and your child's own textbook chapter is the best guide to the wording her teacher uses.

The one idea underneath every one of those questions: a letter stands for a number. Not a thing, not a word, not a digit. A number we have not been told yet, or a number that could be different each time. Nearly every slip below is a child forgetting one part of that sentence.

Slip one: reading 3y as a two-digit number

This is the 34 from the opening. The fix is to make the hidden multiplication visible again, for a while, before taking it away.

Ask her to write every expression with the × sign put back in: 3y becomes 3 × y. Then y = 4 turns it into 3 × 4, which she has known for years. After a week or so of writing the sign in, she can start leaving it out, because she now knows what the gap means.

A useful companion question is "what is y + y + y?" If she says 3y without pausing, the notation has landed. If she writes y3 or looks lost, stay here before moving on. (The number is written first by convention: 3y, not y3.)

Slip two: treating the letter as a label, not a number

This one is quieter and does more damage later. Many children learn "a stands for apples" or "p stands for pens". It sounds harmless, and it produces answers that read like shorthand instead of mathematics: 3p for "three pens" rather than "three times the cost of one pen".

The trouble shows when the question moves on. If p stands for pens, then p + 5 means nothing at all: a pen and five what? But if p stands for the cost of one pen in cents, then p + 5 is simply a price 5 cents higher, and 3p is what three pens cost.

So when she writes "let p be…", push for the full sentence: "p is the number of…" or "p is the cost of…". If her sentence has "number of", "cost of", "mass of" or "age of" in it, the letter is a number. If it is only a noun, it is a label, and the next question will trip her up.

Slip three: joining things that do not join

Asked to simplify 3y + 4, a child writes 7y. It feels finished, and 3y + 4 feels like a sum she has abandoned halfway. Children find it genuinely uncomfortable to leave an answer with a plus sign in it.

Arguing about "like terms" rarely helps at this age. Letting her test it does. Pick a number for y and try both:

If y = 2, then 3y + 4 is 3 × 2 + 4 = 10. But 7y is 7 × 2 = 14. They are not the same, so 3y + 4 cannot be turned into 7y.

One warning worth passing on: do not test with 1. If y = 1, then 3y + 4 is 7 and 7y is also 7, and the wrong answer seems to pass. A test with 2, 3 or 10 gives the honest result. That little trap is worth showing her deliberately, because it teaches that a check needs a fair number to mean anything.

The same test settles the questions that do combine. 4k + 2k with k = 3 gives 12 + 6 = 18, and 6k gives 18 too. Same answer, so they really are the same thing.

Slip four: putting the numbers the wrong way round

Addition and multiplication forgive the order: y + 5 and 5 + y are the same. Subtraction and division do not, and word problems love them.

• "5 less than y" is y − 5, not 5 − y. The words say "5" first, so children write it first.
• "y sweets shared equally among 3 children" gives each child y ÷ 3 (often written y/3), not 3 ÷ y.

Again, a number settles it faster than a rule. Say y is 20. Five less than 20 is 15. Which expression gives 15? 20 − 5 does; 5 − 20 does not even give an answer she has learned to work with. Or say y is 12 sweets among 3 children: each gets 4, and 12 ÷ 3 is 4, while 3 ÷ 12 is a quarter of a sweet. The wrong version gives an answer that is obviously silly as soon as a real number is put in.

Slip five: putting a value in, and then losing the order

"Find the value of 2y + 3 when y = 5." The right answer is 2 × 5 + 3 = 13. The two common wrong answers are 28, which comes from reading 2y as the number 25 (slip one again), and 16, which comes from doing 5 + 3 first and then doubling.

The second is not really an algebra mistake at all. It is the order of operations: multiply before you add, unless brackets say otherwise. If this is where the marks are going, the problem sits one step back, and why 3 + 4 × 2 is not 14 is the place to start. Algebra only makes that gap easier to see, because the multiplication sign is invisible.

A habit that prevents both: when putting a value in, rewrite the whole line with the number in brackets first. 2y + 3 becomes 2 × (5) + 3. It is one extra line and it removes both ways of going wrong.

Where the bar model comes in

If your child has spent years drawing bar models, algebra is closer to what she already knows than it looks. The letter is simply a bar she has not been told the length of. "Ali has y stickers. Ben has 4 more than Ali. How many do they have altogether?" Draw it: one bar for Ali labelled y, one bar the same length plus a short extra piece of 4 for Ben. Together that is two y-bars and a 4, so 2y + 4.

And the check still works. If Ali has 10, Ben has 14 and together they have 24. With y = 10, 2y + 4 is 20 + 4 = 24. The picture, the expression and the numbers all agree. If you have read the piece on bar models, this is the moment it was preparing her for: the drawing is the reason the letters make sense.

Finding the missing number without tricks

For "x + 5 = 12", parents who learned algebra at secondary school often reach for "move the 5 across and change the sign". It gets the answer, but it is a rule with no picture behind it, and at P6 the questions are simple enough to reason out directly: what number, add 5, makes 12? That is 7. Then check: 7 + 5 = 12.

The same question works for the other shapes. "3 × x = 21" is "what number, three times, makes 21?" It is 7, and 3 × 7 = 21. Reasoning this way keeps the letter meaning a number, which is the whole point. The shortcuts will come later, when she can see why they work.

A five-minute check at the kitchen table

No worksheet needed. Ask these one at a time, and listen to how she answers as much as what she answers:

• "If y is 4, what is 3y?" 12. If she says 34 or 7, it is slip one.
• "A pen costs p cents. What does p + 5 mean?" A price 5 cents more than one pen. If she says "a pen and five", the letter is a label (slip two).
• "Is 3y + 4 the same as 7y? Prove it with a number." Watch which number she picks. If she picks 1 and says "yes", show her 2.
• "Write 5 less than y." y − 5. If she writes 5 − y, ask her to try it with y = 20 (slip four).

Most children get some of these right and stumble on one. The one she stumbles on is worth ten minutes. Another page of mixed algebra questions mostly gives her more practice at the slip she already has.

What does not help

Drilling definitions ("a term is…") before the idea is secure. And being alarmed when a strong child struggles here. Algebra catches fluent children precisely because they read 3y at speed, the way they have read numbers for six years. Slowing down on the notation is not going backwards.

StudyLab's Primary 6 Algebra game asks two kinds of question: putting a value into an expression such as y = 3x + 2, and finding x in a sum like x + 6 = 13. It is deliberately small. Those two moves, and the habit of checking with a real number, are what every harder algebra question is built on.