Introducing Multiplication

Introducing Multiplication-Grouping Model

It’s easiest start with the grouping model, because it’s usually the easiest multiplication model for my students to understand. I spend a considerable amount of time teaching the difference between the number of groups and the number IN each group, which will later help with multiplication and division word problems. Be sure to give students a lot of multiplication problems in context, so that we can discuss which is the number of groups and how many are in each group. I write problems like the one below on the dry erase board and students model with their counters.

I’m careful to make sure to have students determine the number of groups they can create, rather than me telling them how many groups they can create with a given amount. This adds the element of problem based learning to instruction.

Introducing Multiplication-Repeated Addition

After teaching grouping models, show students how to use repeated addition to solve multiplication problems. I try to differentiate my lessons, so that some students may be working with a total of 12, others 24, others 36, and some up to 48. I always allow students to use snap cubes during these lessons to make this a hands-on learning experience.

Before I move on to arrays, I like to spend a little time reviewing grouping models and repeated addition with a game. I’ve found that it’s easy to go too fast in these beginning lessons, and some students will need a bit more time to develop a solid understanding of the two models.

Introducing Multiplication-Arrays

Since arrays and area models are incredibly important in fourth and fifth grade, it’s incredibly important to teach for deep understanding. As I teach arrays, I emphasize the importance of EQUAL groups. Once again, I use manipulatives to give my students more hands-on learning opportunities.

The book Amanda Bean’s Amazing Dream is awesome to use as you introduce arrays. The entire book is based around the use of multiplication situations, especially arrays. I made a recording sheet to go along with the book. You could either show the book on YouTube or you could read the book and show the pictures using a document camera.

Multiplication Games

Before students move on to more challenging multiplication concepts, I like to spend a little more time reviewing through games such the one below. It’s similar to the game War, but students must read grouping models in order to determine who has the highest product.  We also play games such as the classic Multiplication Bump.

I save multiplication on a number line for last, because this model the trickiest representation for my students. For extra practice, I enjoy this Representing Multiplication activity that you can download  here. I gave every student 24 snap cubes, and they had to find ways to place the cubes into equal groups. Once they placed the cubes in equal groups, they drew a model of the cubes. Then, students wrote a repeated addition number sentence and a multiplication number sentence that represented the equal groups. This is such a great task for introducing the concept of multiplication, especially the connection between multiplication and repeated addition.

Multiplication Problem Solving

Once I’ve taught each form of representing multiplication, we spend a bit more time working problem solving with multiplication. For instance, in this activity, students find all of the possible arrays to build the number 48. This could be differentiated by using many different numbers.

Another great way to incorporate math and literature is to read One Grain of Rice, which ties in perfectly to multiplication. After reading the book, let students try to find the total number of grains of rice that Raini gave the raja as an extension.

Another great book to tie in to multiplication is Spaghetti and Meatballs for All. In this book a family is having a get together and as more and more people arrive, they have to change their seating arrangements. In this activity, students develop a seating arrangement for 36 people, but they have to use different shaped tables. Each shape table holds a different number of people, which presents students with a bit of a challenge.

It’s also fun to have students use pattern blocks in a multiplication activity. In this lesson, students grab a handful of pattern blocks from the tub. Then students have to show how to use multiplication to find the total number of sides on all of the pattern blocks. This is fun, because everyone will have different answers. Naturally, some students will try to be cute and get a massive handful of blocks. It’s kind of funny when you see them realize how much more challenging that will make the activity.

When I teach multiplication word problems, I like to start with problems that include pictures. This allows students to visualize the problem.

Properties of Multiplication

Once students understand the concept of multiplication, the should become familiar with the properties of multiplication, which help students learn multiplication facts, as well as multiply larger numbers. You can read about teaching the distributive property here.

It’s important to teach conceptual lessons on the properties of multiplication. It’s not super important for students to be able to name the properties. Instead, students should understand the properties.

As someone who has taught fourth grade, I cannot emphasize enough the importance of the distributive property. It is the foundation of so many fourth grade multiplication and division standards. I begin these lessons with base-ten blocks. Students use their blocks to solve problems such as 3×15. Students will build an array to solve the problem. BUT, I don’t initially tell students how to build the array. Some may only use ones and some may use ones and tens. We look at the differences and compare the two arrays. This allows students to see HOW the distributive property works. We later move on to three digit numbers.

I like to spend several days on the distributive property to make sure that students really feel comfortable with this concept.

Multiplication Facts