Bar model word problems for kids

Short word problems with a bar picture that marks the unknown with a striped ? piece (some problems show several equal ? pieces). Part and whole, how many more, equal groups and two-step puzzles. Five levels, a daily set and printable sheets.

How it works

  1. Pick a level, or let the game raise it as you win
  2. Read or listen to the story, look at the bars, and find the ? number
  3. Print a worksheet with an answer key when you want a break from the screen

What this builds

A bar model is a drawing of a word problem in which each amount is a bar and the length of the bar matches the size of the number. It is a way of teaching word problems used in Singapore-style maths classes, and the same picture works for adding, taking away, comparing and sharing. A child who can see that the whole bar is made of two parts does not have to guess whether to add or subtract: the picture shows it. This game gives the story as short text that the speaker button reads aloud, draws the bars with striped question-mark pieces for the unknown (one piece, or several equal pieces when the problem is about equal shares), and asks for the number. It counts toward the word problems skill in the maths group of the kids games on this site. There is no timer by default, and a wrong answer gets a gentle Try again.

The five levels

Level 1, Parts, gives a whole and its parts: Ann has 4 apples and Ben has 3 apples, how many in all, or there are 9 apples and 5 are red, how many are green. Numbers stay within 12. Level 2, Pick the bar, shows the story and four bar pictures, and the child taps the picture that fits. The wrong pictures put the question mark in the wrong place, change one number, or draw a different kind of model, and each one would give a different answer from the right one. Level 3, More and fewer, asks for the number: how many more, how many does Ben have if he has 3 more, one friend gives some away, and equal groups such as 3 bags with 4 apples each, and routine two-step problems such as two friends together or a gift then a loss, with numbers to 25. Level 4, Work backwards, is the first contest-style level: a hidden start (after giving 5 away and getting 3 more, Mia has 9, how many at first), a total with a difference, and equal bars such as twice as many, with numbers up to 30. Level 5, Puzzle bars, adds three steps backwards, three friends in a row, twice as many plus extra, and a total over unequal bars, with numbers up to 50.

How every problem is made and checked

Each problem comes from one of 23 templates with names, objects and numbers drawn from small banks of 20 names, 12 objects and 5 containers. The numbers are chosen so that the answer is a whole number of at least 1, and the answer is worked out from the same numbers that appear in the story. Tests re-read the printed story at each level, work out the answer separately, and compare. For example, a total of 11 with one friend having 3 more means taking the 3 away to leave 8 and sharing it into 2 equal bars, so the smaller amount is 4, and the generator only uses totals where that comes out whole. Plurals follow the number, so a story says 1 apple and 2 apples, and describing words fit the thing described (red and green balls, never sweet books). The bars are drawn to scale, so a 10 piece is twice as long as a 5 piece. Level 2 pictures are checked so that exactly one fits the story and every other picture gives a different answer.

Daily set, adaptive levels and printing

The game moves up a level after 3 right answers in a row and down after 2 wrong answers in a row, and you or your child can pick a level yourselves. Each day there is a set of 5 problems, the same for everyone with the same date on their device. To print, choose a level, 4, 6 or 8 problems and Letter or A4 paper. Every print makes new problems, the bars are drawn in black and white with the unknown piece striped, and the last page is the answer key with a one-line reason for each answer. Stars and progress are saved in this browser only. This game does not teach the written symbols for adding and taking away, it does not mark the child's own drawings, and it is not a full maths course: it gives one kind of problem, done many times, in short sessions.

Frequently asked questions

What age are these word problems for?

Level 1 is meant for a 6 year old on the first day: two small numbers and a picture with a ? piece. Level 5 uses numbers up to 50 and is hard for a 7 or 8 year old. The levels adjust on their own, so a child lands at a comfortable one within about 10 problems.

What is a bar model?

A drawing where each amount is a bar and a longer bar means a bigger number. A whole is drawn as one bar over its parts. Two amounts to compare are drawn one above the other, and the gap between them is the difference.

Is the answer always a whole number?

Yes. Every problem is built so the answer is a whole number from 1 up, never a fraction or a negative. A total of 10 with a difference of 3 is never used because 7 does not share into 2 equal whole bars.

Why does level 2 show four bar pictures instead of asking a number?

Choosing the right picture is the hard part of a word problem. At level 2 the child decides what the story looks like, and from level 3 the child uses the same kind of picture to find the number.

Can I print the problems?

Yes. Pick a level, 4, 6 or 8 problems and Letter or A4. Each problem has its bars drawn with the unknown piece striped, and the last page is the answer key with a short reason for each.

Is my child's progress uploaded anywhere?

No. Stars, levels and streaks are saved in this browser on this device. The page counts visits with Google Analytics, never answers or scores.