Bar Models: What Your Child Is Being Taught and How to Help

21 August 2026 · by Larry

Your child brings home a worksheet with rectangles drawn all over it. You read the question, work the answer out in your head in about four seconds, and tell her. She writes it down. It is correct, and she still loses most of the marks.

That is usually the moment a parent first goes looking for what a bar model actually is — and the honest answer is that it is not a way of getting the answer at all. It is a way of seeing the problem before any arithmetic happens.

What the rectangles are for

A bar model is a picture of how the quantities in a question relate to each other. A rectangle stands for an amount. Its length shows roughly how big that amount is compared to the others. A question mark marks the bit you are being asked for.

The reason this is taught so early is simple: a child in primary school does not have algebra yet. Without it, a word problem is a guessing game about which operation to use. With a drawing, the operation becomes visible — once the picture is right, the child can usually see whether to add, subtract, multiply or divide without being told.

So the drawing is not a hoop to jump through before the real work. It is the real work, which is why the marks live there.

Nearly every model is one of two shapes

This is worth knowing, because it makes the whole thing far less mysterious.

Part and whole. Two or more bars sitting end to end, with a bracket over the top showing the total. This covers everything of the form "she had some, she got some more" or "there were this many altogether, some were red".

Comparison. Two bars drawn one above the other, lined up at the left, with the extra bit at the end of the longer one labelled. This covers "how many more", "twice as many", "he has 12 fewer than her".

Most questions are one of those two. The harder ones in P5 and P6 are usually one of them sitting inside the other, which is why it pays off to get comfortable with both early rather than treating them as a lower-primary chore.

The four things parents do that make it harder

I have done at least three of these.

Solving it your way and handing over the answer. The answer was never what was being marked. Worse, a child who is given answers stops attempting the picture, and the picture is the skill.

Drawing the model for her. Very tempting, especially at half past nine. But deciding what the bars represent is the entire thinking step. Drawing it for her leaves her with the easy part.

Insisting the bars are measured. They need to look roughly right — a bar for a bigger amount should look bigger — but they are not meant to be accurate to the millimetre. A lot of homework tears come from a child with a ruler trying to make a sketch exact.

Using algebra language. "Let x be the number of apples" works, and it collides head-on with what she is being taught this year. She will meet letters soon enough, and the bar model is the thing that will make them make sense when she does. Introducing them now mostly produces a child who can follow neither method.

What actually helps

Two questions, asked before anything is drawn:

• "What do we know?"
• "What are they asking for?"

Then, if she is stuck, one more: read one sentence and draw only that sentence. Most children who freeze on a long problem are trying to hold all of it in their head at once. Taking it a sentence at a time gets a picture started, and a started picture is usually enough.

When the model is wrong, resist correcting it. Ask instead: "does that picture match what the sentence says?" Reading the sentence again with her own drawing in front of her is what teaches her to check her own work — and checking is a separate skill from solving, which I wrote about in the answer was right and the marks still went.

When it feels like extra work

There is a stage, usually around P4 or P5, when a child can see the answer instantly and finds drawing the model insulting. That frustration is reasonable and worth naming rather than arguing with.

Two things are true at once: she is right that she does not need it for this question, and she will need it for the ones coming. The same picture handles fractions, ratio and percentage later, and those are the questions where nobody sees the answer instantly. A child who abandons the model at P4 tends to meet it again at P5 under much worse conditions.

If the sums inside the problem are the sticking point rather than the picture, that is a different problem with a much easier fix — the arithmetic just needs to become automatic enough to stop stealing attention. Our bar models guide goes through the shapes step by step, and word problems: when the sums are fine but the story is not covers the case where the numbers were never the issue.

The short version

• The drawing is the thinking, not a formality before it
• Almost every model is part-and-whole or comparison
• Ask what we know and what is being asked, before drawing anything
• One sentence at a time when she is stuck
• Do not draw it for her, do not measure the bars, and leave the letters until school introduces them

Bar models tend to arrive just as the questions become multi-step. That shift, and the rest of it, is in what actually changes from P2 to P3.