How the Model Method Works
In a bar model, every amount in the story is drawn as a bar. Bars that are the same length stand for the same amount, so the drawing shows at a glance which person has more, what makes up a total, and which part is unknown. The unknown is marked with a question mark. Teachers in Singapore introduce the method in Primary 1 and Primary 2 with simple part-whole stories, and by Primary 6 it is used for ratio, fractions and before-and-after problems.
How to Use This Page
- Pick the school year and the number of problems, then press Start. Three or five problems make a good daily session.
- Read the problem, then draw the model. For simpler problems, your child picks the right model out of three. For problems with units, they build the model: press + and − to give each bar the right number of units, or tap the boxes to shade the fraction.
- Find 1 unit. For unit problems, your child works out what one box is worth before answering.
- Answer the question. A wrong step shows the correct model and the working, and your child carries on from there.
- Fix the ones you missed. At the end, only the problems with a wrong answer come back.
Problem Types by Level
| Level | Problem types | Example |
|---|---|---|
| P2 | Part-whole (altogether, missing part); comparison (more, fewer, how many more), within 100 | Mei Ling has 26 shells. Wei Jie has 9 fewer. How many does Wei Jie have? |
| P3 | The same within 1000; times as many, with the total or the difference given | Priya has 4 times as many stamps as Daniel. Priya has 36 more. How many does Daniel have? |
| P4 | Comparison with a total; times as many; fraction of a whole | Aisha gave 2/5 of her marbles to Farid. She gave away 18. How many did she have at first? |
| P5 | Fractions; ratio with the total or the difference; times as many with larger numbers | The ratio of Ben’s cards to Siti’s cards is 3 : 5. They have 96 altogether. |
| P6 | Ratio; before-and-after (giving some away until both are equal); fractions with larger numbers | Raju had 3 times as many beads as Hui Min. After Raju gave her 15, they had the same number. |
Why Draw Before Calculating
Children who go straight to the numbers often pick the operation from a key word: “more” means add, “left” means subtract. That works until a question says “Ben has 17 more than Ali. Ben has 52. How many does Ali have?”, where “more” needs a subtraction. A model doesn’t rely on key words. Ben’s bar is drawn longer than Ali’s by 17, Ben’s bar is labelled 52, and the drawing shows that Ali’s amount is 52 take away 17.
Units extend the same idea to multiplication and division. Once both bars are drawn as equal boxes, every times-as-many, fraction and ratio problem turns into the same three moves: count the units that match the number you know, divide to find one unit, then multiply for the amount you want. That is why this page asks for 1 unit as its own step.
Tips for Parents and Teachers
- Ask “who has more?” first. Before drawing, decide which bar is longer. Most wrong models come from getting this backwards.
- Draw the same model on paper. After a problem on screen, ask your child to copy the model into an exercise book with the labels. Exams expect a drawn model as part of the working.
- Label everything. Names at the left, numbers on the parts they belong to, and a question mark on what is asked.
- Check with the story. Once the answer is found, put it back into the problem: does Ben really end up with 17 more than Ali?
- Practise the prerequisites. Fraction and ratio models need fraction sense: our interactive fractions page covers it, and the worksheet generator prints word problems with answer keys.
Nothing to Install, Nothing Stored on Our Server
The bar model practice runs entirely in your browser on any phone, tablet or computer. There is no account and no download. The last level you chose is remembered on this device, and nothing about your child’s answers is sent to us.
Frequently Asked Questions
The bar model (or model drawing) method is how Singapore primary schools teach word problems. Each quantity is drawn as a rectangle, a bar, so the child can see how the numbers in the story are related: parts that make a whole, one amount that is more than another, or amounts made of equal units. Once the model is drawn, the arithmetic usually becomes obvious.
When one amount is a number of times another, or the amounts are in a ratio, each bar is cut into equal boxes called units. If Ben has 3 times as many stickers as Ali, Ali’s bar is 1 unit and Ben’s is 3 units. If they have 48 stickers altogether, 4 units are 48, so 1 unit is 12. Every answer then comes from multiplying the value of 1 unit.
Choose your child’s school year. P2 has part-whole and comparison problems within 100. P3 adds numbers to 1000 and times-as-many problems. P4 adds fractions of a whole. P5 adds ratio. P6 adds before-and-after problems where one person gives some to another. Dropping a level for a few rounds is a good way to build confidence.
The page shows the correct model straight away and explains it, then lets your child carry on to the next step with the right model in front of them. Only the final answer decides whether the problem counts as right, and the “Fix the ones I missed” button brings back the problems that went wrong at the end of the round.
Yes. There is no account, no download and no limit on rounds. It works in any browser on a phone, tablet or computer, and nothing about your child’s answers is sent to us.