# Multiplication/Division Relationships

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Our Multiplication/Division Relationships lesson plan teaches students about the relationships between multiplication and division. Students learn the “repeated addition” and “repeated subtraction” methods and use it to solve practice problems.

Included with this lesson are some adjustments or additions that you can make if you’d like, found in the “Options for Lesson” section of the Classroom Procedure page. One of the optional additions to this lesson is to make the activity more interactive by hidind the cards with numbers on them around the classroom and have students search for them.

# What our Multiplication/Division Relationships lesson plan includes

Lesson Objectives and Overview: Multiplication/Division Relationships lesson plan helps your students understand the relationships between multiplication and division. Multiplication and division are inverse operations. The lesson reinforces this concept for students by having them list fact families. The lesson also suggests students consider multiplication as repeated addition, and division as repeated subtraction. At the end of the lesson, students will be able to multiply and divide up to 100 using strategies that reinforce the relationship between multiplication and division. This lesson is for students in 2nd grade, 3rd grade, and 4th grade.

### Classroom Procedure

Every lesson plan provides you with a classroom procedure page that outlines a step-by-step guide to follow. You do not have to follow the guide exactly. The guide helps you organize the lesson and details when to hand out worksheets. It also lists information in the blue box that you might find useful. You will find the lesson objectives, state standards, and number of class sessions the lesson should take to complete in this area. In addition, it describes the supplies you will need as well as what and how you need to prepare beforehand. The supplies you will need for this lesson are cards with number sets. To prepare for this lesson ahead of time, you can copy the materials and gather the cards.

#### Options for Lesson

Included with this lesson is an “Options for Lesson” section that lists a number of suggestions for activities to add to the lesson or substitutions for the ones already in the lesson. To make the activity more interactive, you could hide the cards with numbers on them around the classroom and have students search for them. Your students can also generate their own sets of numbers as a class. If you have more advanced students, you can have them write the fact families for multiples of 11 and 12. Finally, you can have any student who’s struggling with the lesson draw or use modeling to help them grasp the lesson concepts.

### Teacher Notes

The teacher notes page includes lines that you can use to add your own notes as you’re preparing for this lesson.

## MULTIPLICATION/DIVISION RELATIONSHIPS LESSON PLAN CONTENT PAGES

### Multiplication/Division Relationships

The Multiplication/Division Relationships lesson plan includes one page of content. The lesson begins by stating that multiplication and division are inverse operations. This means that they are opposite operations, and “undo” each other.

We can think about multiplication as repeated addition and division as repeated subtraction. For the problem 4 x 3, we’re just adding 4 three times (4 + 4 + 4 = 12). For the problem 12 /4, we subtract the number 4 s many times as we can (12 – 4 = 8, 8 – 4 = 4, and 4 – 4 = 0; we subtracted 4 three times, so the quotient is 3). It’s easier to multiply or divide, instead of doing repeated addition or subtraction, because it’s faster.

We can also look at these problems as models. The lesson includes a helpful example of a model, which shows two rows of four symbols. For multiplication, we can look at the model and think 2 groups of 4 equals 8 or 4 groups of 2 equals 8. For division, we can look at the model and think 8 divided by 2 equals 4 or 8 divided by 4 equals 2.

Next, students will learn about fact families, which are groups of related facts that use the same set of numbers. For the example set using 2, 4, and 8, we can make four related facts: 2 x 4 = 8, 4 x 2 = 8, 8 /4 = 2, and 8 / 2 = 4. We can switch around the order of the numbers without changing the solution because of the commutative property. The lesson then includes examples of other fact families.

## MULTIPLICATION/DIVISION RELATIONSHIPS LESSON PLAN WORKSHEETS

The Multiplication/Division Relationships lesson plan includes three worksheets: an activity worksheet, a practice worksheet, a homework assignment, and a quiz. You can refer to the guide on the classroom procedure page to determine when to hand out each worksheet.

### FACT FAMILY ACTIVITY WORKSHEET

For the activity worksheet, students will draw a set of numbers out of a pile and use them to create a fact family. They will then show the multiplication as repeated addition ad the division as repeated subtraction.

### MULTIPLICATION/DIVISION RELATIONSHIPS PRACTICE WORKSHEET

The practice worksheet asks students to solve the given multiplication and division problems. They will also show various multiplication problems as repeated addition and division problems as repeated subtraction.

### FLASH CARDS HOMEWORK ASSIGNMENT

For the homework assignment, students will have an adult ask them multiplication facts from the multiplication table shown on the worksheet. The adult will highlight or circle the ones that the student does not get correct. Next, the student will create multiplication and division flash cards with the problems that they got incorrect, using them to practice.

### QUIZ

This lesson includes a quiz to test students’ knowledge and understanding of the lesson material. The quiz asks them to make a fact family using the provided number set.