## The Complete Guide to Teaching Multiplication and Division

By Mary Montero

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Multiplication and division are major math skills for upper elementary. I have compiled FREE lessons, key skills, anchor charts, book recommendations, and several differentiated activities for teaching multiplication and division in this post for you.

## Download Everything You Need– for free!

This free PDF guide will allow you to have all of the resources you need for teaching multiplication and division right at your fingertips.

## Critical Elements When Teaching Multiplication and Division Skills

Because there are so many strategies to cover when teaching multiplication and division, the PDF includes this checklist to make sure you cover everything in your lessons.

## Teaching Multiplication Lesson Sequence

*Please Note: This skill sequence is ideal for 3rd grade+ and assumes students have had minimal exposure to the idea of arrays and equal groups.*

### Visualizing Multiplication

I always begin our multiplication unit with hands-on exposure to the concept of multiplication. I give my students a big handful of erasers (the fun shapes from the Dollar Spot) or any other manipulative. I either give them a multiple of 2 or 5, depending on the level of my students. I ask them to count how many they have in total. They usually start counting one by one, but there are always a few who will start separating them into groups to count – usually groups of 10. Once at least one student or group has put them into groups of ten, I ask them to model their thinking for all of us. Then, I ask all my students to discover another way to group the erasers to make them easier to count. Give them time to explore, and they will often come up with a variety of groupings. This is when I start to use verbiage like, “Oh, I see you have 7 **groups of **5. Let’s **skip count **by 5 to find how many you have in total.” I write down all of their different groupings (without the multiplication symbol for now). Every year, I’ve had students notice that this is multiplication (due to their prior knowledge) and point it out to the group, but if they didn’t, I would introduce it at this point.

**Amanda Bean’s Amazing Dream** (Amazon affiliate link) is one of my absolute favorite books for introducing multiplication. I read this book to my class, and then modify the activities at the back of the book as introductory lessons, based on your students’ skill level and prior knowledge. Even if you don’t teach the lessons in the back of the book, don’t skip this book! It sets such a great foundation!

### Ways to Show Multiplication

At this point, we start learning about all the different ways to show and model multiplication. I start with **repeated addition/skip counting**. This is when I begin emphasizing that you can replace the multiplication sign with “groups of” to help remember exactly what multiplication is showing. Then, I move to **equal groups**. Then, to jumps on a **number line**, and finally with **arrays**. (*I used to start with arrays, but I’ve found this to be slightly more abstract for students and now wait until they’ve grasped the other concepts first*.) After we’ve established these strategies for showing multiplication, I introduce a multiplication fact chart. I also create the “Ways to Show Multiplication” anchor chart as we are learning.

While we are learning different ways to show multiplication, I have them compile their strategies into a mini book for reference (I usually use the small books you can purchase at the Dollar Spot). Since this often occurs during the month of October, we usually end up doing a Halloween theme, but you can do any theme. I highly encourage you to have students draw strategies in their books or use stickers to show different strategies and groupings. You can **learn more about these reference books in my Instagram “multiplication” highlight**.

### Properties of Multiplication

After we have a solid understanding of the different ways to show multiplication, we start tackling properties of multiplication. The identity and zero property usually only take a quick lesson. Commutative Property and Associative Property take about a day. The distributive property is much more time-intensive and takes several days to truly understand and master, and I find that students who have a very solid understanding of arrays do best with this skill. While it’s a challenging skill, when students develop a true understanding of it, their conceptual understanding of multiplication grows immensely!

**Distributive Property Tips: **The best way I have used to show the distributive property is to use arrays and graph paper, as shown on my Properties of Multiplication anchor chart. You can also use a hundreds base ten block and separate it in multiple ways using a dry erase marker.

**Properties Mastery Tip: **I created this **Multiplication Masters resource** to help my students master WAYS to show multiplication and PROPERTIES of multiplication. It has become an absolutely critical component to my multiplication unit, and I have seen massive gains in understanding and math fact retention through its use.

### Factors and Multiples

While this resource is focusing on introductory multiplication skills, this is the point at which I would introduce factors and multiples. You can **learn more about teaching factors and multiples here**.

### Multiplying by Multiples of 10 and 100

This is such a fun and attainable lesson! I teach my students to find the basic fact, count the amount of zeroes in your factors, and attach the amount of zeroes to their product. We model extensively WHY this works, which you can l**earn more about in this post**.

### Multi-Digit Multiplication

After this, I start teaching **multi-digit multiplication strategies**.

## Teaching Division Lesson Sequence

*Please Note: This skill sequence is ideal for 3rd grade+ and assumes heavy exposure to and mastery of multiplication concepts.*

### Visualizing Division

We start our division exploration much like we start our multiplication exploration. I put my students in groups and give my students a small handful of erasers. I ask them to divide or split them equally among each person in their group. Once they are divided, I ask them to look at the groups they formed. Then, I ask them to use their multiplication skills to figure out how many erasers they have in total. This is usually when they get that glimmer in their eye and start to realize the connection between multiplication and division! Once they have found their total, I write the number down and ask them how many groups it has been divided/split into. Finally, I ask them how many are in each group.

**The Doorbell Rang** (Amazon affiliate link) is a GREAT book for introducing division and equal shares AND introducing the idea of fact families with multiplication and division.

### Multiplication or Division?

Once students have a basic understanding of division, I pause instruction on division strategies and ask them to start thinking about the connections and differences between multiplication and division. I use my **multiplication OR division task cards** and have students practice determining which operation is appropriate with given scenarios. This is also a great time to teach **quotative vs. partitive **division.

### Ways to Show Division

At this point, we start learning about all the different ways to show and model division. We discuss: Using an **array**, **repeated subtraction, creating equal groups**, **using a number line**, creating a **strip diagram**, and using a **fact family**.

## Division Properties

For Division, I teach students these key property concepts:

- When zero is divided by a number, the quotient is zero.
- Any number divided by one is the number itself.
- If we divide a number by itself, the quotient is one. (Not applicable to zero)
- We can’t divide a number by zero.

### Inverse Operations

Teaching multiplication and division as inverse operations is critical in developing conceptual understanding of division and helping students master their math facts. We create this interactive anchor chart together.

### Interpreting Remainders

After they have a solid grasp of division, I teach students about interpreting remainders. They have already had exposure to remainders before this lesson, but they LOVE the ”mystery” of figuring out what a remainder represents. I have included several documents that include “Remainder Reminders” that I teach my students. Here are different ways remainders can be used:

**Use the remainder**— This happens when the remainder is actually the answer.**Round Up**– When you use the remainder to round up your answer. The quotient is not your answer, but it’s one greater because you have a remainder. (For example: when you are splitting children among cars to go to a summer camp. You can’t simply leave two students out, so you need to add another car to transport everyone)**Ignore**– Sometimes we ignore the remainder. This usually happens when we are finding truly equal groups.**Share the Remainder as a Fraction or Decimals –**I MAY give my students a little blurb about this option, particularly students ready for this information, but in general, I do**not**teach this to 4th graders as it begins to muddy their understanding.

### Long Division

After this, I start teaching long division strategies to 4th grade+. This **division blog post is packed with tips**.

## Mastering Multiplication and Division Math Facts

Here are a few of my favorite ways to reinforce math facts. The PDF includes several more!

### My Favorite Math Fact

I know it sounds silly, but I have a favorite math fact! It’s 6 x 6 = 36 and every student I’ve ever taught knows this fun fact about me. Naturally, I embed it into my math fact practice and have my students pick a favorite math fact. I print it out on a label and let them wear it to proudly display their favorite math fact WITHOUT the answer… Then we play a game where we walk around and say, “Hi! Your favorite math fact is 6 x 6 is 36!” It’s a hoot!

### Run a Row

My students LOVE practicing their math facts with this fun relay race! The kids are in two lines and have to compete relay-race style to get all of the facts correct. The numbers 1-12 are on each team’s side of the board and then they have a number (in this case it was +7, but you can adapt it to other operations very easily) to add or multiply by each number. SO easy to adapt to addition, subtraction, and multiplication! You can **watch a video of this game in action here.**

### Mental Math Practice

I start each math session with a quick 2-3 minutes of mental math cards. I give students a VERBAL, multi-step problem that they must solve. Using these **mental math task cards** makes it simple to prep.

## More Multiplication and Division Practice Activities

After extensively teaching multiplication and division, here are a few additional ways we practice our skills.

### Flipbooks

I created these **multiplication flipbooks** as a way to consolidate our learning and as an alternative to interactive notebook foldable activities. The left-hand side is designed for teaching and reviewing the concept and the right-hand side is perfect for practicing the skill. We have an entire section in our binder for these so they can go back and reference them all year.

### Go on a “Field Trip” for Arrays

This is always a favorite of my students, and I often assign it as homework! Send students to the store to find all of the items that have been arranged in arrays (cookies, donuts, sausages, displays, etc.). Have them take pictures and bring them back to class. No time for a field trip? No problem! Just have them use everyday items to create arrays that match expressions. **Click here for a free home arrays template**.

### Multiplication and Division Task Card Carnival

There are SO many different skills, properties, and strategies to practice with multiplication and division that we spend about two months on the operations! Throughout those two months, I always focus on allowing my students to interact with these skills in a variety of ways. Over the years, I have created **dozens of task cards that practice ALL properties and strategies**. They are a staple in my class. I use them:

- As a whole group warm up
- To play SCOOT as a whole class
- In small groups, independently or with me
- On a scavenger hunt around the room or outside
- For Jeopardy-style review

## Multiplication and Division Book Lists

I created an **Amazon Affiliate List of my favorite multiplication and division picture books**. The free PDF includes the specific titles and activity suggestions to make teaching your lessons easier.

## Related Blog Posts

- Mastering Multiplication
- More Multiplication Ideas
- Multiplication Facts
- Teaching Long Division
- Long Division Strategies

## Related Resources

## Mary Montero

I’m so glad you are here. I’m a current gifted and talented teacher in a small town in Colorado, and I’ve been in education since 2009. My passion (other than my family and cookies) is for making teachers’ lives easier and classrooms more engaging.