Bar Model Word Problem Builder

Choose a model type, enter your numbers, and see a visual bar diagram with the solution. Bar models (tape diagrams) help you see the relationship between parts and wholes, compare quantities, and understand multiplication. Try a word problem preset or enter your own values.

Leave one field blank to find the missing value.

Word Problem Presets

Bar Model Diagram

Parts2418Total = 42

Solution

The total is the sum of all parts: 24 + 18 = 42

Reference Guide

Part-Part-Whole Models

A part-whole bar model splits a total into two or more parts. If you know the parts, add them up to find the total. If you know the total and some parts, subtract to find the missing part.

Example

Sam has 24 red marbles and 18 blue marbles. The bar shows [24 | 18] with a bracket showing the total = 42.

These models work for addition and subtraction problems. The bar always represents the whole amount.

Comparison Models

Comparison models stack two bars to show how much more (or less) one quantity is than another. The difference shows up as the gap between the bars.

Example

Mia has 45 stickers and Leo has 28. The longer bar (45) sits above the shorter bar (28), and the highlighted gap shows the difference = 17.

These are great for "how many more" or "how many fewer" word problems.

Multiplicative Comparison

Multiplicative models show "times as many" relationships. One bar is divided into equal segments, each the size of the base value.

Example

Ana read 4 times as many books as Ben (6 books). The product bar has 4 segments of 6, showing 4 × 6 = 24.

This model helps students understand multiplication and division as scaling.

Drawing Bar Models

Tips for drawing bar models by hand or on paper.

  • Read the problem carefully and identify known values.
  • Decide which type of model fits (part-whole, comparison, or multiplicative).
  • Draw bars proportional to the numbers.
  • Label each section and use a "?" for the unknown.
  • Write the number sentence and solve.

Bar models are also called tape diagrams and are a core strategy in Singapore math.