Bar Model Method: In Problem Solving


This is the second unit of the special topic "The Bar Model Method". This is a pedagogical strategy widely used in Singapore to help students solve word problems. 

This unit Bar Models in Problem Solving, designed for students around Year 6, shows how to use the bar model method for handling multi-step problems involving four operations with whole numbers and fractions. The overall objective is to promote flexible thinking to solve non-routine tasks. Using a bar model provides a concrete approach for visualising the information in a mathematics problem and for organising it in a helpful way.

There are 8 lessons, which can be taught together or across the year.

Advice is given for using the unit with students who have not completed the first unit Introduction to Bar Model Method.

Read the Teachers' Guide (also included in the download) before using this resource.


Lesson 1: Part-whole Model - Division

In this lesson, students study multi-step problems which need a combination of whole number arithmetic operations for their solution. They make two different types of bar models for different division situations. They structure their problem solving by Polya’s four phases. Students then solve problems independently or in groups to consolidate their learning.

Lesson 2: Part-whole Model - Fractions

Students learn how to use the part-whole model to represent fractions in different real-world contexts. Solving the word problems is supported visually by the bar model and structured by Polya’s phases of problem solving. Students study examples and practise with further tasks.

Lesson 3: Part-whole Model - Fractions of Fractions

In this lesson, students encounter problems where the part-whole model is used to represent fractions, and fractions of those fractions. The bar models support an intuitive approach, building understanding of fractions and fraction calculations. Students study examples where either parts, parts of parts or the whole itself are to be found, and practise with similar tasks.

Lesson 4: Comparison Model - Whole Numbers

In this lesson, students use the comparison bar model to help solve multi-step word problems that include information about additive and multiplicative relationships between quantities. They study worked examples and practise with further tasks.

Lesson 5: Comparison Model - Fractions

In this lesson, students solve word problems that give information about fractions of different quantities that represent equal amounts. They use the comparison model for these problems, and solve them by identifying a common unit in the different quantities. Students see worked examples, then practise on several tasks.

Lesson 6: Stack Model – Whole Numbers

This lesson introduces the stack model. Students study problems where they compare two groups of quantities, with either a multiplicative or additive relationship given between individual items. Students work on two examples together, then practise independently or in pairs to consolidate learning.

Lesson 7: Change Model - Whole Numbers

In this lesson, students learn to use the change bar model, a variant on the comparison model. They construct visual representations of complex stories, usually involving multiple quantities that change over time, and use the representations to find a strategy for solving the problems. Students study examples, then practise the techniques on other tasks.

Lesson 8: Change Model - Fractions

In this lesson, students use the change model with word problems involving fractions. By working with the visual model, fraction calculations are replaced by intuitive steps. Students study problems where the quantities in a situation change either by a whole number amount, or by a fraction.


Last updated December 11 2018.