*Let me show you an effective way to teach multiplication when you first introduce it in 3rd grade.*

One of my most vivid school memories from childhood is learning to multiply in third grade. Yep, even back in the 70s, we learned multiplication in third grade. I can still picture Mrs. Bowman, my third-grade teacher introducing multiplication to us. On the chalkboard, she drew three circles to represent cows. Yep, cows. And, of course, cows give milk. If each cow produced five bottles of milk (which she drew in each circle), how many milk bottles would the cows fill? It was so exciting because I understood and knew the answer (the product)!

Meanwhile, I think back to how I came to understand this concept. Mrs. Bowman introduced multiplication to her 3rd graders by making it **visual**. She drew it on the chalkboard! If she had **NOT** drawn the cows and milk bottles, I doubt I would have understood multiplication. In short, her visual is the definition of multiplication (*which could be defined as a mathematical operation combining equal groups)*.

But why do we need to multiply – can’t we add? Students do not necessarily ask this question, but it’s how they tend to solve multiplication problems initially – by adding. In the second grade Common Core for Math, the students have learned to use repeated addition by arranging objects in columns and rows up to 5 by 5. We need to teach multiplication as not only another math operation but a more efficient way of adding. In this post, I’ll show you an activity to introduce your third graders to multiplication.

## What NOT to do first when introducing multiplication

To begin with, don’t start with an explanation of what multiplication is or is not. Instead, do what Mrs. Bowman did. Start with something kids can see. *Make it even better by starting with something they can do! *Here’s an activity to introduce multiplication. It has –

- has an entry point for all students
- involves students in problem solving from the start
- has various solutions
- includes and requires mathematical discourse
- emphasizes the process

Depending on your class size, you will need to select 12, 18, 24, 30, or 36 students. If you have an odd number of students, the “leftover” student can act as a recorder for the class.

What else shouldn’t you do? Drill and kill with endless worksheets. Give daily or weekly timed tests which build anxiety. Have a Margarita when the 4th-grade teachers tell you their students don’t know their multiplication tables. Ok, maybe the last one you can. Honestly, though, if kids are not multiplying during their summer breaks, they’re probably not going to remember their facts in the fall. You can tell the 4th-grade teachers I said so.

## Introducing multiplication with equal groups

One way to introduce multiplication is to represent it with equal groups. Firstly, pick a set number of students (12, 18, 24, 30, or 36) to come up to a designated spot in the class and stand together. Then, present this situation to the class. **Don’t tell the class ahead of time how many you’re picking. **

**Problem with Entry Point for All Students**

Students have signed up for an after-school art class. The students are waiting in the multipurpose room. The instructor is not sure how many students are waiting. How will the instructor know how many students are waiting?

Ask the students to turn to a partner (pair-share) to discuss how the instructor can determine how many students are waiting in the multipurpose room. Do you anticipate students will suggest the following?

- will count each student one by one
- or will count pairs of students
- or maybe count students in groups of (?)
- make estimate of a reasonable number

It’s important to anticipate how students will solve this problem. As you can see, by introducing multiplication this way, all students can discuss how to figure out the total number of students. Neither of the solution paths is wrong – but some are more efficient than others (which is important).

Each one of the anticipated solutions can lead to discussions and explorations of equal groups. The numbers 12, 18, 24, 30, and 36 can be grouped in many ways (*they have more than two factors*), so there is no single correct answer. In the beginning, learning about multiplication should stress conceptual understanding rather than focus solely on finding correct answers.

## Get visual with teaching multiplication

Do you remember how Mrs. Bowman launched multiplication with the bottles of milk? The visual cemented my understanding of multiplication. Let’s do the same for your students. In the previous activity, a recorder or yourself should be recording the different ways the students solved how many students waited.

For example, this visual can be something as simple as circles and dots. Make sure it’s all labeled. * What do the dots represent? What do the circles represent?* If you used 18 students as the example, you probably recorded all the different ways to group 18 students –

- 18 students in single groups or 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
- 2 students in 9 groups or 2+2+2+2+2+2+2+2+2
- 3 students in 6 groups or 3+3+3+3+3+3
- 6 students in 3 groups or 6+6+6
- 9 students in 2 groups or 9+9
- 18 students in one group or 18

In addition, notice labeling does NOT yet involve using the multiplication symbol (x or *) in a multiplication sentence. The symbols will be introduced later. Once you’ve recorded the different solution paths, you can on another day revisit to discuss them. ** Which is more efficient? Which takes fewer steps? **The discussion should lead students to understand learning multiplication is necessary to become more efficient at mathematics. Yes, you could say it’s a more efficient way of adding.

This activity can be repeated over several days when launching multiplication by simply changing the number of students (12, 18, 24, 30, 36) and the problem or situation. I would NOT use all the numbers but instead reserve at least two of them for the next step. ** What is the next step?** Have students use concrete materials to represent the same situation.

## Hands-on learning multiplication with equal groups

My favorite math tool to use with multiplication is foam tiles. These foam tiles can make equal groups and work well with constructing arrays (and later on for finding area and perimeter!). You can learn more about how I used these math tools in my post about 3 methods for building a conceptual understanding of multiplication.

Again, use the numbers (12, 18, 24, 30, and 36) to present a new situation/problem but pick a number you haven’t used. For now, students will be familiar with the routine. The difference this time is you will ask them * How many different ways can the number (12, 18, 24, 30, 36) be grouped?* Let them use their foam tiles (or whatever math tool you have) to figure it out. They also need to record their findings and include labels for their visuals.

Once the findings have been recorded, they can share with a partner to compare and discuss. Or you can have them work from the beginning in partner groups or cooperative groups.

The next step is to present the same task but now with products having only 2 factors (other than the number itself multiplied by 1).

- Pick 9, 14, 15, 21, or 27.
- Have them try to find all the different ways to group them to count.
- They’ll discover other than one group of (9, 14, 15, 21, or 27), there is only one other way (i. e., 3 x 3; 2 x 7; 5 x 3 3 x 7; 3 x 9).
- Play devil’s advocate and ask why can’t 9 be put into groups of 2 or 4? Why can’t 15 be put into groups of 2 or 4 or 6?

The point is for students to learn that with multiplication, it’s a fact groups have to be equal in quantity to multiply.

## Are your students now understanding how multiplication works?

Great! Now is the time to start introducing the multiplication symbols. Instead of writing 3 groups of 6 or 6+ 6 + 6, we can explain to students mathematicians prefer efficiency. So mathematicians would write 6 + 6 + 6 as 6 x 3. You can then help students make the connections.

* What does the first number represent*? It’s the quantity in each group.

*It’s the number of groups. Don’t forget to now formally introduce the academic vocabulary of factors and products. You could make an anchor chart for students to reference as they continue to learn multiplication.*

**What does the second number represent?**So is that it? Nothing else to do? We only wish! But we know introducing multiplication is not the only step. We know multiplication also involves learning strategies for improving fluency, learning and applying the Properties of Multiplication, and teaching multiplication all year long.

## What are your next steps for teaching multiplication?

Once equal groups are understood, it’s time to move into constructing arrays. Think of arrays as a more efficient method of arranging equal groups. A set of tiles or a group of tiles is easier to unitize (make the same quantity in each group) if they are in a row. In a previous post, I have a student video showing him making an array is efficient!

Two other ways to keep emphasizing the equal groups (or equal rows/columns with arrays) are to use subitizing cards and the Notice and Wonder routine.

Firstly, for the subitizing cards, make your own! Using PowerPoint or Google Slides, create a slide with 4 circles. In each circle, put 5 objects (you can select icons or shapes from either program). Customize it with color, and it’s ready to go! Use them as digital slides or print out the slide. Either way, use the multiplication subitizing cards as a number talk.

Secondly, for the Notice and Wonder routine, select photos showing a quantity of an item. No more than 50 items preferably in an array. Show the picture and ask what students notice and wonder. If they wonder how many, then it’s a good time to discuss solution paths to * how many*? I have put together a packet of 6 pictures for use in this routine with instructions.

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## Need resources for introducing multiplication?

Before moving into my current role as a district math coach, I taught 3rd grade for many years. So introducing and teaching multiplication is a passion for me. I have created many resources to help teachers with multiplication. Check out the previews below. Then, visit my TpT store to find out more!

I developed this animated PowerPoint to teach the concept of multiplication using equal groups, arrays, and number lines. It includes detailed Presenter’s Notes on the animation sequence and questions to ask. It’s also interactive with follow-along worksheets.

Another way to develop a deeper understanding of multiplication is to know and apply the Properties of Multiplication. This PowerPoint covers the Identity Property of Multiplication, the Zero Property of Multiplication, the Commutative Property, and the Associative Property of Multiplication. It’s also interactive with follow-along worksheets.

Fluency involves more than memorization or a quick response. Students need to learn fluency strategies when memory and recall fail. I developed this resource to teach multiplication fluency strategies such as halving, doubling, using squares, and adding/subtracting a group. Check out the preview below, then head on over to my store for more detailed information.

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**How do you introduce multiplication to your students? **

**Share in the comments below!**