Bar Model - a Visual Problem Solving Strategy

The Bar Model (also known as the Model Method) is a visual problem solving strategy used to teach mathematics especially in primary and lower secondary levels. It helps students represent relationships between quantities using rectangular bars, making abstract problems more concrete and easier to understand. It is most famously used in the Singapore Math approach but has since been adopted worldwide.

What Is the Bar Model?

A bar model uses rectangular bars (drawn as boxes or strips) to represent numbers or quantities. Students draw bars to visualize parts and wholes, comparisons, or relationships in a math problem.

Example:

Ishant has 12 apples. Pawan has 8 apples. How many more apples does Ishant have than Tom?

Bar Model Representation:

Ishant	:  █ █ █ █ █ █ █ █ █ █ █ █ (12)
Pawan	:  █ █ █ █ █ █ █ █ (8)
? = Difference

Students can see clearly that the difference is the remaining part (4).

Types of Bar Models

1. Part–Whole Model

Used for addition and subtraction.

Example:

There are 5 red marbles and 7 blue marbles. How many marbles altogether?

[ Red 5 ] + [ Blue 7 ] = [ Total ? ]

2. Comparison Model

Used for comparing two quantities (differences).

Example:

Nidhi has 15 stickers. Arpita has 9 stickers. How many more stickers does Nidhi have?

Nidhi	: █ █ █ █ █ █ █ █ █ █ █ █ █ █ █ (15)
Arpita	: █ █ █ █ █ █ █ █ █       (9)
? = Difference

3. Multiplicative Model

Used for multiplication and division.

Example:

A packet has 6 sweets. There are 4 packets. How many sweets altogether?

[ 6 ] + [ 6 ] + [ 6 ] + [ 6 ] = [ ? ]

Or shown as a repeated bar model:

Packet: █ █ █ █ █ █ |  █ █ █ █ █ █  | █ █ █ █ █ █  | █ █ █ █ █ █

4. Fraction/Ratio Models

Used to visualize fractions, ratios, and proportions.

Example (Fraction):

¾ of a rope is 12 meters. What is the full length?

[ ? ] [ ? ] [ ? ] [ ? ]
   12 m = 3 parts
   1 part = 4 m
   Total = 16 m

Steps in Teaching with Bar Models

1. Read the problem carefully.

2. Identify known and unknown quantities.

3. Draw bars to represent the quantities and their relationships.

4. Label the bars (numbers, variables, or units).

5. Use the visual model to form equations or perform operations.

6. Solve and check your answer.

Benefits of the Bar Model Method

✅ Builds deep conceptual understanding.

✅ Encourages visual reasoning and problem-solving.

✅ Bridges arithmetic to algebraic thinking.

✅ Reduces reliance on rote memorization.

✅ Makes word problems less intimidating.

Example: Multi-step Problem

Jaswant has twice as many pencils as Anshul. Together they have 36 pencils. How many pencils does each have?

Bar Model:

Anshul	: █ █ █ █ █ █
Jaswant	: █ █ █ █ █ █  █ █ █ █ █ █ 
Total = 36

So, 3 parts = 36

1 part = 12

Anshul = 12, Jaswant = 24.

The Bar Model method is a powerful visual approach that helps students understand mathematical concepts in a clear and concrete way. By representing numbers and relationships through bars, learners can easily visualize addition, subtraction, multiplication, division, fractions, and ratios.