In this series of lessons, students learn a systematic strategy for analyzing and solving word problems based on either multiplication or division.

In this lesson, the concept of a unit relationship is introduced. It’s the multiplicative relationship in which there are a specified number of units of one type for each unit of another type.

Students learn to read text that describes a multiplicative relationship and describe it as a unit relationship. All of the situations used in this lesson can be described as “equal group” situations. Each group is part of a larger group.

In this lesson, the concept of a unit relationship is extended to a different kind of situation. In this lesson, a multiplicative relationship exists that can be described as a “multiplicative comparison.”

For multiplicative comparison situations, students learn to read text that describes the multiplicative relationship and describe it as a unit relationship.

In this lesson, students learn to represent a unit relationship as an array. The purpose of this lesson is to connect the student’s understanding of multiplication represented by a unit relationship to earlier understanding of multiplication as an array.

Students are given text that describes unit relationships and the student creates an array to represent the relationship.

In this lesson, students take multiplicative relationships presented as an array and use them to fill in the first column in a multiplication number family grid. The first column represents the unit relationship, so students are learning to recognize the unit relationship in an array and represent it in the number family grid. This reinforces the common understanding of multiplicative relationships as represented in arrays, unit relationships, and number family grids.

In this lesson, students extend what they learned in the prior lesson. They take multiplicative relationships like those in the prior lesson, presented in an array, and use them to fill out the second column of a multiplicative number family grid. All the problem situations in this lesson are “equal group” situations.

In this lesson, students extend what they learned in the prior lessons. They fill out both columns of a multiplication number family grid as in the prior lesson. The difference is that the problem situations in this lesson are “times a many” situations.

In this lesson, students extend what they learned in the prior two lessons. They read word problem situations for both “equal groups” and “times as many” situations and fill out a number family grid. They then find the missing value in the grid. Multiplication is used when the product is missing. Division is used when one of the factors is missing.

In this lesson, students complete the process of learning the systematic approach to solving multiplication and division word problems. They solve problems like those in the last lesson without using the graphic organizer – the number family grid.

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