# How To Teach Multiplication and Division Together.

Teaching multiplication and division together - *right from the start* - can **save time and tears**. Who would turn down such a bargain? It's like buying one and getting one free. Or getting two for the price (*in this case, the effort*) of one.

**Learning** multiplication facts and **immediately applying** that knowledge to related division facts is one step on the path to success in getting the facts memorized.

Keep reading to see WHY and HOW.

### Why Teach Multiplication and Division Together?

The sad fact that **so many students do not have basic facts at their command** speaks to the problems that exist. The way basic facts are traditionally taught obviously is not effective for a large number of students.

## Traditional Teaching Order

The order in which basic facts is typically taught is often ineffective.

**Traditional Sequence**

**Typical Results**

Teaching multiplication and division together right from the start helps to avoid those erroneous paths of thinking. Some students inherently grasp this similarity in basic multiplication and division facts, and for them memorization is a breeze.

**The fact that many children do not possess this inherent ability has nothing to do with intelligence or lack thereof.**

It has to do with learning styles. Everybody can learn and learn well. That’s part of what makes teaching so exciting!

**How To Teach Multiplication and Division Together.**

There’s no compelling reason for separating multiplication and division.

Why is that? **The same numbers are used in learning both operations.**

Using correct mathematical terminology will enhance conversations and instructions about basic facts, helping to cement that relationship. Experience confirms that children have no trouble learning and using proper mathematical terminology.

Posting those relationships in a prominent place during the early stages of learning will also help.

**Children have no problem with the vocabulary that connects the two when correct terminology is used in instruction.**

*This poster is included in our printable lesson plan: A Fun Way to Show the Multiplication and Division Relationship.*

When students understand the multiplication/division for themselves, they won't have to remember two different sets of facts. On the contrary, they will be getting ‘*Two-for-the-price-of-one’*. The work they did for multiplication will automatically transfer over to division.

This will certainly save time and tears.

**A Fun Way To Show The Multiplication & Division Relationship.**

Here's a fun and simple exercise you can do with your child to either:

### Video and Printable Lesson Available

The exercise below has been created as an instructional video and printable lesson to use with your learner.

Start with a pile of about 24 counters1 from which the child will draw.

Using counters from the pile, can you show me 3 sets of 4? (*Wait for the child to demonstrate.*)

Q: How many counters is that? *(12)*

That could be written as **3 x 4 = 12**. - (*Write the example out*). That means 4, 3 times, a **multiplication example**.

Put the counters back in the pile - and this time show me 4 sets of 3.

Q: How many counters? *(12)*

That could be written as **4 x 3 = 12**. **Again, multiplication**.

Q: What is the product of 3 x 4? *(12) *

Q: What is the product of 4 x 3? *(12)*

So it makes no difference which order we write the factors, or whether we have 3 sets of 4, or 4 sets of 3. As long as we have the same number of counters in each set, we can express it as **a multiplication example**.

Put the 12 counters back together in front of you. Beginning with exactly 12 counters, separate them into 4 sets.

Q: How many in each set? *(3)*

When we start with the total amount and divide it into equal sets, **that's division.** **12 / 4 = 3** (*You will probably want to write this in the 'little house' form with the quotient on the 'roof.'*)

Put the 12 counters back together in front of you. Beginning with exactly 12 counters again, this time separate them into 3 sets.

Q: How many in each set? *(4)*

We started with the total amount, 12, and divided it into equal sets; again **that's division**. **12 / 3 = 4**.

Put the 12 counters back together in front of you.

Suppose I asked you to tell me:

Q: How many sets you can make with 3 counters in each set.

Show me that, but I'll bet you already know how many sets that will make. Exactly, that's 4 sets. **12 / 3 = 4**. We can find how many in each set or how many sets.

**That's division.**

We can find how many in each set or how many sets. **That's division!**

We've used the same number of counters for multiplication and division.

Q: Can you tell me how multiplication and division are different?

In multiplication, you start with the smaller amounts, **factors**, and put them together to make a larger amount, **product**.

In division, you start with the total amount, **dividend** (*which is the same as the product in multiplication*). You see how many equal groups you can make from it.

The **divisor** in division is the same as one of the **factors** in multiplication, and the answer or **quotient** in division is the same as the other **factor** in multiplication.

So to make life easier for ourselves, we're going to learn and practice multiplication and division together. We'll start with the easy tables, learn the multiplication facts for a table, and immediately we'll practice the division facts for the same table. We won't consider the table mastered until both multiplication and division of that table are mastered.

Easy enough!

1Note: Counters are not just for primary grades. Upper elementary students can benefit from manipulating counters and, thus, creating visual images in their heads.

A variety of items can be used for counters:

I use caps from plastic water bottles. They are readily available and a good size. Allow students to use counters as long as they need the support. They will stop on their own when concrete support is no longer needed.

### I would love to hear from you! ❤️

Have a question? Idea for a resource you might find helpful?

Be so kind and leave a comment below.

I like this idea. It makes sense. I started teaching my daughter multiplication and she’s mastered some facts but we kind of stalled so I introduced division and right from the very first lesson, I made sure to connect the two and go back and forth between them. So now I am going back over the math facts she has mastered and teaching the related division facts and then as we move on, I plan on having her memorize both the multiplication and division ones at the same time.

Thanks for your comment, Sherrie. Teaching multiplication and division together does make learning the facts so much simpler. You might want to change the order of the tables also so that all the easy facts are mastered first–that makes the supposedly difficult facts easy too!

Considering where you and your daughter are now, you might want to take a look at this blog post Multiplication Facts – Finally Master Them This Year!

What a fantastic idea. I can’t believe I never thought of this!

I’m now teaching my child to write even pure multiplication in both regular and division form too. This further enhances an understanding how how the numbers are linked. It could even be written in fraction format, to show that fractions are really just a form of division. In fact the division symbol is actually just a blank fraction.

Hello Edward. Thanks for your comment. I’m always encouraged when I hear about parents and teachers who are helping their learners understand that math really does make sense. Best wishes to you and your child.

Very simple and extremely effective method.

Thanks for sharing Brenda!!

Thanks for your comment, Sujatha. I’m always encouraged when I hear about parents and teachers who help learners to understand that math really does make sense. Best wishes to you and your learner.

Very helpful! I will definitely try to use this strategy.

Thank you, Joan. I’m always encouraged when I hear about parents and teachers who are helping learners to see that math really does make sense. Best wishes to you and your learner.

you are a great teacher ,you make it so easy , I enjoyed every second listening to you , thank you

Nesreen, thank you so much for your encouraging remarks!

Thank you so much Grandma Bee, I have a fourth grader grandson who is struggling with division and I want to help because it is really frustrating for him. This concept makes so much sense and is really easy to understand and visual that I can’t wait to begin to help. Thank you again.

Hello, Anita. Thanks so much for your encouraging remarks. Sometimes mastery of multiplication and division facts can indeed be frustrating. Here is a link with more tips and strategies for helping your son. http://www.grandmabee.com/make-math-facts-stick. Blessings to both of you.

I find it easy way to teach; excellent, good job

Thanks for your encouraging remarks, Sangeetha.