Math in Focus:  Chapter 9 - Bar Modeling with Multiplication & Division

Math in Focus: Chapter 9 - Bar Modeling with Multiplication & Division

Author: Sara Levine

Bar Models can be used to solve different kinds of multiplication and division word problems.

In Grade 2 and early in Grade 3, students learned to use bar models to solve two-step problems involving addition and subtraction. This is extended in this chapter to include multiplication and division.

Both multiplication and division are based on the concept of equal groups, or the part-part-whole concept, where each equal group is one part of the whole. In Grade 2, students showed this with one long bar (the whole) divided up into equal-sized parts, or units. This unitary bar model represents situations such as basket of apples being grouped equally into bags. 

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A bar model can also show two steps, where some amount might be subtracted from the whole, or added to equal groups. Here, a basket of apples had some apples removed from it and the rest of the apples were divided equally into bags.

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Finally, two separate sets might be compared, showing one whole being a multiple of another whole. Here the number of apples is three times the number of oranges.

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Drawing bar models provides students with a means of organizing information and determining the calculations needed to solve a problem. Bar models simplify the problem by showing clearly what steps need to be taken to answer the question.
-Math in Focus

New Vocabulary:
twice: two times
double: two times

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Chapter 9 - Multiplication

In this video, you will see how to use bar models to show multiplication problems. It also goes over what to do when you see the words "twice" and "three times" in a problem. There is a problem at the end of this video for you to solve. On your paper, please copy down the bar model and solve the problem using a method that is efficient and that you are comfortable with.

Source: Math in Focus

Multiplication with 2 steps (multiplication & subtraction)

A bookshelf had 4 shelves of books.
Each shelf had 116 books.
The store owner sold 382 books.
How many books are left?

We solved this problem together in class. We needed two separate bar models to show the problem.

Source: Math in Focus

Bar Models with 2 Steps: Part-Part-Whole and Multiplication

A student explains his group's strategy.

Megan makes a necklace with 12 red beads and 15 yellow beads.
She makes a total of 3 necklaces.
How many beads does she use in all?

This problem uses a Part-Part-Whole bar for addition, then multiplication (we know the number of groups and how many in each group)

Source: Math in Focus

Bar Modeling (division) with a picture

In this video, we take a word problem, model it out with a picture (apples) and then draw the bar model that goes with the problem.

Division - How many in each group?

In this video, a student solves a division problem where we know the total and how many groups. He has to figure out how many go into each group.