Drawing Part-Part-Whole Bar Models

Introduction

From partitioning numbers to solving word problems, bar models provide learners with a tangible way to understand and solve problems. They are especially useful for showing part-part-whole relationships between numbers. In this lesson plan, your learner will explore strategies for drawing part-part-whole bar models.

Before beginning the lessons, your learner should know how to partition numbers up to 5.

Key Concepts for Partitioning Numbers with Bar Models

Just as with cherry models, bar models serve as visual tools to represent the part-part-whole relationships between numbers. They essentially show how a number can be split into smaller parts.

Bar models can be categorized as proportional or non-proportional. In proportional bar models, the size of the bar directly corresponds to the magnitude of the number it represents. This means that larger numbers are represented by longer bars, providing a clear visual indication of their relative sizes.

Your learner may already be familiar with the concept of relating the size of a bar to the number it represents if they have previously worked with bar graphs.

Teaching Plan

The following activities will help your learner become confident in representing part-part-whole relationships with bar models. Remember to work at a pace that is comfortable for your learner.

Examples and visuals to support the lesson:

1. Drawing Bars to Represent Groups

This activity serves as an introduction to bar models by relating them to groups of up to 5 objects.

• Begin with a picture depicting 5 items arranged in a row, and align cubes alongside to match each item. Progress to drawing connected squares to represent the cubes, then remove the dividing lines between the squares to form the bar.
• As your learner advances through these representations, prompt them to consider what the cubes, squares, and bar represent in the context of the whole. Encourage them to articulate this relationship in complete sentences, such as "There are 5 objects, so 5 is the whole."
• Use your learner's understanding of partitioning to establish the connection between the number of objects in the picture and the size of the bar.

Skill Check
I can draw a bar that represents the "whole" of a number.

2. Drawing Bars for Partitioned Groups

In this activity, learners will further develop their understanding of bar models by partitioning the whole into two parts.

• Begin with a picture depicting 5 objects split into two parts, such as 3 red birds and 2 blue birds. Then, arrange block cubes to represent the group accordingly, with 3 red blocks and 2 blue blocks.
• Next, draw 3 connected squares for the 3 red blocks and 2 connected squares for the 2 blue blocks. Erase the dividing lines to create two bars, each representing a part with lengths of 3 and 2.
• Finally, connect the two bars to form one partitioned bar. Notice that this forms the bottom row of the bar model.
• Encourage your learner to describe the part-whole relationships using complete sentences, emphasizing understanding such as "There are 3 red birds and 2 blue birds. 3 is a part, and 2 is a part."

Skill Check
I can draw a bar that represents the "parts" of a number.

3. Part-Part-Whole Bar Models

In the previous activities, we established the foundation for bar modeling by representing the whole group of 5 and partitioning it into two parts. Now, we can integrate these concepts to form a complete bar model.

• Guide your learner in combining the bars to create the full bar model, illustrating it alongside a cherry model with the same numbers. Prompt your learner to identify similarities and differences between the two models to facilitate connections.
• Next, use the bar model to showcase all the different ways of partitioning the number 5. Emphasize that the bar model offers unique visual information compared to the cherry model, with the size of the bar providing insights into the numbers. Continue relating each bar model to the cubes (or pictures) it represents to reinforce understanding.
• Note that while the bar model is effective for representing various partitions, it may not be suitable for cases where one of the parts is 0.

Skill Check
I can draw a bar model that represents the "whole" and "parts" of a number.

4. Ongoing Practice

Provide your learner with practice exercises where they partition numbers up to 5 using the bar model. The objective is for them to adeptly transition between a given context, such as a story problem or a group of items, and both the cherry and bar models.

You can provide grid paper to assist your learning with drawing bars. However, at this stage, they don't need to create perfectly proportional bar models. Instead, focus on the concept of representing the part-part-whole relationships.

Summary

Bar models offer a structured and visual method for representing part-part-whole relationships in mathematics. Throughout this lesson, we have explored the fundamentals of bar modeling, including its use in partitioning numbers and solving mathematical problems. By mastering the art of bar modeling, learners can develop a deeper understanding of math concepts and enhance their problem-solving skills.

Teaching Plan adapted from NCETM under OGL license v3.