Primary and KS3Maths at school

Bar models in maths: a guide for parents

Written by A Dagdelen · Reviewed

A bar model is a rectangle drawn to stand for a number. It looks too simple to matter, but it is how many schools teach children to see what a word problem is asking before they choose a calculation.

Illustration: Quizo School

  • A drawingnot a way to calculate: it shows what to calculate
  • Part and wholethe most common kind of bar model
  • Comparisonbars side by side, for "more than" and "times as many"
  • Not namedin the National Curriculum, so the school decides when

What it is and when it appears

  1. A bar stands for a number. The child draws a long bar for the whole and splits it into parts, or draws two bars to compare amounts. The sizes don't need to be exact, just roughly right.
  2. It shows what to do, not how to calculate. Once the bars are drawn, the calculation is usually clear: if the whole and one part are known, the missing part is a subtraction. The child still adds, subtracts, multiplies or divides in the usual way.
  3. It runs from first sums to algebra. In many schools children start with bars made of cubes or paper strips, use drawn bars for fractions and word problems later in primary, and meet them again in secondary school for ratio and equations.
  4. The curriculum asks for pictures, not bars. The National Curriculum does not mention bar models. It asks for problems to be solved "using concrete objects and pictorial representations", and the bar model is one of the pictures many schools choose.
  5. It helps most with two-step problems. Problems with two steps, or with "times as many", are where bars help most. The drawing holds the information so the child can think about one step at a time.

Worked examples

Part and whole: Amira had 45 stickers. She gave some to her brother and has 28 left. How many did she give away?

A bar labelled 45 above a bar split into two parts, 28 and a question mark. Underneath: 45 − 28 = 17.4528?45 − 28 = 17
  1. Draw one bar for the whole: all 45 stickers.
  2. Underneath, draw the 28 she kept and leave the rest of the bar for the part we don't know.
  3. The missing part is the whole take away the part we know: 45 − 28.
  4. 45 − 28 = 17. She gave away 17 stickers.

Comparison: Ali has three times as many marbles as Ben. Together they have 48. How many does each have?

Two bars: Ben has one box, Ali has three boxes of the same size. A bracket shows that together they make 48. Each box is 12, because 48 ÷ 4 = 12.Ben12Ali1212124848 ÷ 4 = 12
  1. Draw one box for Ben. Ali has three times as many, so draw three boxes the same size for Ali.
  2. There are 4 equal boxes altogether, and they make 48.
  3. One box is 48 ÷ 4 = 12, so Ben has 12.
  4. Ali has three boxes: 3 × 12 = 36. Check: 12 + 36 = 48.

How to help at home

“That's not how I learnt it”

Many parents were taught to spot key words: "altogether" means add. Bars replace that guess with a picture, because key words can mislead: "how many more" is usually a subtraction. If drawing boxes feels slow, solve one problem your way and one with bars, and compare.

A 10-minute activity: draw the story

Make up a short problem from your day: "We had 30 biscuits and 12 got eaten." Your child draws the bars, then writes the calculation. Then they make one up for you to draw.

Ask, don't tell

Questions that help: what is the whole? Which part do we know? Which bar should be longer?

Use squared paper

Equal boxes are easier to draw on squares, and it keeps "three times as many" honest.

Common mistakes

  • Bars the wrong size. If Ali has more, Ali's bar must be longer. A quick "does this look right?" fixes most drawings.
  • The total in the wrong place. The total goes across the whole, not on one part. Ask your child to point to what the total covers.
  • Stopping at one box. In two-step problems, finding one box is only half the answer. Read the question again: who did it ask about?
  • Drawing the bar after the answer. A bar drawn at the end doesn't help. Encourage the drawing first, even a rough one.

Practise and explore on Quizo School

Questions parents ask

Does my child have to draw a bar model in a test?

Usually not, but it is a good habit for word problems. Teachers often ask for one in class to see how a child is thinking.

How exact do the bars need to be?

Not exact. Roughly right sizes are enough; the labels carry the numbers.

Can bar models help with fractions?

Yes. A bar split into equal parts is a clear picture of a fraction: three quarters of 20 is three of the four equal boxes in a bar of 20, which is 15.

My child finds the bars harder than the sum.

For a one-step problem, that is fair: skip the bar. Bring it back for problems with two steps or "times as many".

Practise problem solving in short bursts

Build your quiz lets your child pick maths units and 10, 20 or 30 questions for a quiz of their own. It is part of the Family plan. New families get the Family plan free for 14 days, with no card needed.

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