Introducing Multiplication

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

Introducing Multiplication-Repeated Addition

After I teach grouping models, I then show students how to use repeated addition to solve multiplication problems. You can differentiate your lessons, so that some students may be working with a total of 12, others 24, others 36, and some up to 48. You can absolutely 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

I know my students had experience with arrays up to five by five in second grade, but I know how important arrays are in fourth and fifth grade, so I try 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.

I love using the book Amanda Bean’s Amazing Dream as I 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 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.

I love incorporating math and literature, and this lesson is one of my favorites! I read One Grain of Rice, which is really a neat book, and it ties in perfectly to multiplication. After reading the book, I 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 a bit more easily.

Properties of Multiplication

Once my students understand the concept of multiplication, I begin teaching the properties of multiplication, which help students learn multiplication facts, as well as with the multiplication of larger numbers. I made a set of task cards for the properties of multiplication, so we could practice this in class.  I tried to make the emphasis of the task cards the distributive property, since that property is typically the trickiest for third graders. However, it is essential for students to understand and apply the distributive property as they move to fourth grade math standards.  I’ve added these task cards to my math work stations.

I also make sure to add plenty of conceptual lessons to my multiplication instruction on the properties of multiplication. It’s not super important for students to be able to name the properties. Instead, it’s important that students understand the properties. However, keep in mind that multiplication situations are not necessarily commutative.

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