# Bar Model Method: Introduction

This is the first 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 *Introduction to Bar Model Method* introduces students to two types of bar models for solving word problems: part/whole models and comparison models, each applied to addition, subtraction, multiplication and division.

There are 8 lessons, which can be taught in one block or across several terms, intended for around Year 5.

Students learn to visualise and represent the mathematical quantities and relationships in a problem, thus improving their ability to solve problems. Three lessons include addition and subtraction of fractions, supporting an intuitive approach.

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

### Lesson 1: Addition of Whole Numbers

Students are introduced to the bar model method with the part-whole bar model through this lesson. Students learn how to construct the part-whole bar model and how it can help to represent addition contexts through worked examples with simple numbers and tasks with larger numbers. Three types of addition contexts are used: (1) one set of items made up of 2 parts; (2) the whole being formed from two distinct sets of items; and (3) another set of items “adding on” or “joining” to form a new whole.

### Lesson 2: Subtraction of Whole Numbers

In this lesson, part-whole bar models are used to represent subtraction problems involving whole numbers. Students study various different subtraction situations (e.g. ‘take away’, compare) through five examples. Students then practise with further problems to consolidate this learning

### Lesson 3: Multiplication & Division

Students learn how the bar model can help represent multiplication and division contexts by studying examples and practising with further tasks. The tasks encountered involve equal groups multiplication and partition and quotition variations of division problems. The examples use very simple numbers. Consolidation tasks have larger numbers and contain more mathematical information to sort through.

### Lesson 4: Addition of Fractions

In this lesson, students learn how to use bar model as a tool to represent a variety of worded addition problems involving fractions, by studying worked examples and practising with further tasks. They encounter situations where the bars that make up a bar model may simultaneously represent an absolute number (e.g. $50) and a fraction of a specified quantity (quarter of a cost).

### Lesson 5: Subtraction of Fractions

Students learn how the part-whole bar models can represent subtraction contexts involving fractions. Students study examples and practise with further tasks, individually or in groups. The bar models provide support for intuitive methods of solving these problems, which supports the development of fraction concepts and skills.

### Lesson 6: Comparison Model for Addition

Students are introduced to a new type of bar model, the comparison model, through two very simple examples. Problems, for individual or group solving, involve quantities with known differences (e.g. one quantity is 10 more or less than another; one quantity is one fifth larger than another). Drawing the bar model supports an intuitive approach to the fraction calculations involved.

### Lesson 7: Comparison Model for Subtraction

This lesson introduces the comparison model for subtraction problems. The examples use only whole numbers. In a comparison context, variation comes from changing which of the three relevant quantities (larger, smaller and difference) are known or to be found, and by expressing the comparison using different language (e.g. fewer than, increased to). Consolidation problems use larger numbers and contain more information.

### Lesson 8: Comparison Model for Multiplication

Through this lesson, students learn how the comparison bar model can display the mathematical relationships in problems involving multiplication and division. The calculations only involve whole numbers. Examples demonstrate bar models for problems solved by multiplying and problems of two visually different types solved by division. Students then complete tasks, individually or in groups, to consolidate and extend their learning.

Last updated September 8 2022.

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