Problem-solving method
The bar model method, explained for parents
The drawing your child is taught in primary maths, before algebra. Here is what it is for, the words in a question that call for it, and how to tell whether it has actually landed.
- Used from
- P3
- Taught at
- P3–P6
What this method is
A bar model is a drawing of a word problem. Each quantity becomes a bar, drawn roughly to scale, and the thing you are asked for is the part of the picture left blank. It is the method MOE names first, and your child meets it from Primary 3.
Its job is to turn reading into seeing. Once the bars are on the page the arithmetic is usually obvious, which is why a child who can draw the question can nearly always finish it.
When to reach for it
These are the words in a question that point at this method. You do not need to be able to solve it to spot them.
“28 fewer pages than”
Any comparison wording means two bars, one shorter than the other, lined up at the left so the difference shows as the bit sticking out.
“3 times as many as”
Draw the smaller quantity as one unit and the larger as three of the same unit. Equal units are what make the bars readable.
“altogether”
A total. Draw it as a bracket across every bar rather than as another bar, so the parts and the whole stay visually different.
“How many were left”
Something has been removed, so the answer is the gap between the whole and the parts you can already draw.
Watch it work
Ben read 152 pages of his book on the first day. He read 28 fewer pages on the second day. The book had 410 pages, and he finished it on the third day. How many pages did he read on the third day?
Draw the day you know
day 1 = 152Start with the quantity the question hands you outright. Every other bar gets measured against this one.
Draw the comparison
day 2 = 152 − 28 = 124"28 fewer" is a shorter bar, not a new calculation to guess at. Line it up under day 1 so the missing 28 is visible at the right-hand end.
Bracket the whole book
day 1 + day 2 + day 3 → 410The total goes above all three bars. This is the step children skip, and it is the one that turns two facts into an answerable question.
Read the blank off the picture
410 − 152 − 124 = 134No new idea is needed here. The drawing has already told you the third day is whatever is left of the bracket.
The one it gets confused with
Every one of these still uses bars. What changes is what the bars are counting, and getting that wrong is more common than drawing them badly.
Does the question give amounts, or a ratio and a fraction? If nothing has a real value yet, count equal units instead of writing numbers in the bars.
Does something move or change partway through? Then one bar cannot hold it. You need a before picture and an after picture.
Does a fraction apply to what is left rather than to the whole? Then the bar splits twice, and the second split sits under the remainder only.
How can you tell it has clicked?
Ask your child to draw the question before solving it, and then cover the numbers. If the shape of the drawing still tells the story, they have understood it.
A child who draws bars of roughly equal length whatever the question is copying a format they have seen. That holds up until the numbers move, and then it stops.
One thing to try tonight
Read a question together and stop at the first comparison word. Ask one thing: which one is bigger, and by how much?
Have them draw only that much, then stop. Getting the two bars the right way round is the whole skill, and it takes a minute to check.
Where your child will meet it
Want the bigger picture on how these methods fit together? Maths heuristics, explained for parents
See which methods your child reaches for
StudyLah names the method in every worked solution, so you can see whether the problem was the method or the arithmetic.