What is a bar model?

A bar model is a picture of a word problem. Each amount becomes a rectangle, drawn roughly to scale. Equal amounts get bars of the same length, and a bigger amount gets a longer bar. Once the story is drawn, you can see which part is missing.

Take this one. Ali has 3 times as many marbles as Ben, and they have 48 marbles altogether. Ben gets one block, called a unit. Ali gets three of the same blocks. The 48 covers all four blocks, so one unit is 48 ÷ 4 = 12, and Ali has 36.

In this game you build the model yourself. You add the blocks, put each number where it belongs and mark the ? for the answer. The game checks your picture against the story. A bar that does not match wobbles and tells you why. When the model is right, the sum is usually the easy part.

Why draw the problem?

Many word problems are hard because of the words. In a 2005 study of 151 Primary 5 pupils in Singapore, Ng Swee Fong and Kerry Lee found that most mistakes clustered around phrases like “more than”, “less than” and “times as many”. A bar model turns those phrases into lengths you can compare. That is why this game spends whole chapters on them.

A 2018 paper on the method by Berinderjeet Kaur notes that studies in Singapore and elsewhere have found it helps students with whole-number word problems, including students who find maths hard. It is one strategy among several. Some problems are quicker another way, and older pupils go on to algebra, where the unit block becomes a letter.

A short history of the bar model in Singapore

The method was developed in the early 1980s by a team of curriculum specialists at Singapore’s Ministry of Education. Their aim was to help young pupils who were struggling with word problems. Kho Tek Hong, who worked on the primary maths curriculum at the Ministry, is credited with developing the models and introducing them to teachers. He later co-wrote a book about the method.

Researchers date its place in the primary school curriculum to 1983. Singapore pupils have learned it ever since, and it is often described as a signature of Singapore primary maths. Schools in other countries have picked it up too. In Singapore it is usually called the model method, or model drawing.

How to play

• Read the story. Each person or thing in it has a row with its name.
• Pick Unit or Piece, then tap a bar to add one, or drag it there. Units are all the same size. A piece holds one number.
• Drag each number tag onto the model, or tap the tag and then tap its place: a block, the bracket over a bar, the tall bracket for “altogether”, the dashed gap for “how many more”, or a bracket under shaded units.
• Tap Check model. When the model is right, type 1 unit if you need it, then the answer.
• Stars: one for solving, one for a model that is right the first time, and one for no hints and no wrong answers.
• There are 54 levels in six chapters: part and whole, more or fewer, times as many, fractions, before and after, and harder problems. They follow roughly the order these ideas come up in primary school. The first level of every chapter is open from the start.

Tips for parents

Read it out loud first. Before anyone touches a block, ask who has more, and by how much or how many times.

Ask what one unit is. In most of these problems, finding one unit is the step that unlocks the rest.

Read the wobble together. If a bar wobbles, read its message and fix only that bar. A wrong check costs a star and nothing else, and every level can be played again.

Then try it on paper. The game practises one skill: turning a word problem into a bar model. On paper, rough bars are fine, as long as equal amounts look equal.

Your turn

Start with the roses in the garden. By the last chapter you will be lining up three bars and finding one unit on your own.