Bar Model Problem Generator

What this generator does

Chooses the size of one unit of the model first and builds every number from it, so each answer is whole. The answers are then found again from the question's own words — the total, the difference or multiple, the fraction and the given amount — by trying every whole number up to 2,000, and a question is used only when exactly one answer fits.

How to use this tool

1. Choose a level, the kinds of problem and how many questions.
2. Tick the hint box to draw an empty bar model under each question.
3. Press Make the sheet, then Show the answers to see each finished model.
4. Print the questions and the answers, or type a sheet code to make the same sheet again.

Understanding the controls

Level

Gentle uses small numbers and halves, thirds and quarters; standard goes to a few hundred with thirds to sixths; stretch uses larger numbers and fifths to ninths.

Kinds of problem

Total and difference, times as many, fraction of a whole, and fraction spent with an amount left. The sheet cycles through the kinds ticked.

Hint

Draws the empty model under each question, with the numbers the question gives and a question mark for each unknown part.

Sheet code

Leave empty for a fresh sheet from the browser's secure generator; with a code, the same code and settings make the same sheet again while the generator is unchanged.

Worked examples

Code harbour, standard, question 1

Ezra and Chidi have 45 stickers altogether. Ezra has 9 more than Chidi. Two equal parts are 45 − 9 = 36, so Chidi has 18 and Ezra 27.

Code harbour, standard, question 4

Lena spent 2/3 of their money on a game and had £11 left. The one third left is £11, so the game cost £22.

Common use cases

• Introducing bar models with problems that need them
• Practice with fractions of an amount and what is left
• Comparing a pupil's drawn model with a finished one

How this generator works

For a total and a difference, the shorter bar is one unit and the longer bar is one unit plus the difference, so two units are the total minus the difference. For times as many, the bars are k units and one unit, so one unit is the total divided by k + 1. For fractions, the bar is cut into as many equal parts as the denominator: the given amount covers the numerator's parts (or the parts left over), which gives one part and then the whole. The check does not reuse any of this: it reads the relations the question states and tries every whole-number answer.

Randomness and fairness

Names, items and numbers come from the browser's secure generator, or a seeded one when you type a code. A code repeats a sheet while the generator is unchanged. Codes are deterministic, not cryptographic, and not a secret.

For how randomness is produced across the whole site, see how Generate Random works.

Assumptions this tool makes

• Fractions are in lowest terms, and every answer is a whole number of things or pounds.

Limitations and good to know

• Four problem shapes only; ratio problems with three bars and before-and-after problems are not made.
• Fractions are written as a/b on one line rather than stacked.
• Money is in whole pounds.

Common mistakes

Halving the total in a difference problem

Take the difference off first; only what is left splits into two equal bars.

Answering with the whole when the question asks for the part

In a fraction-left problem, the bar gives one part; the question asks for the parts spent, not the whole amount.

Privacy and your data

Questions are built in your browser. With analytics consent, a count records how many questions a sheet had; the problems and any code are not sent.