Meaningful Engagement with Multiplication and Division


Teaching the four operations (addition, subtraction, multiplication, and division) is my absolute favorite thing about math.

You heard that right. It outweighs fractions, measurement, place value… you name it. Before I get into engaging ways to teach multiplication and division in your upper elementary classroom, let me prove it to you why teaching the operations in math is the best (and quite possible the most important.) The ideas in this article can also be said for addition and subtraction.

top 3 reasons why teaching operations is the

Child manipulating multiplication equation in a classroom.

1. We use the four operations constantly! Addition, subtraction, multiplication, and division can be related to just about any “real world” situation. Students buy into concepts much easier when the why is clear. We use the operations while grocery shopping, playing sports, cooking, and so much more.

2. Mastering these concepts sets students up for success in future math units. Once a student understands single-digit multiplication, double-digit multiplication is much more obtainable. A student can’t multiply fractions or find the area of a room without having already mastered basic multiplication.

3. They are closely related and can be used by students as a gateway to finding an answer. If a student initiatively finds division difficult, you can use the concept of repeated subtraction to help division become more attainable. You can also do the same with multiplication and repeated addition. Relating multiplication and division (and addition and subtraction) as inverse operations also makes them easier to master as a whole for students.

the single key to teaching multiplication and division

While this concept can be applied to other mathematical standards, it’s easy to master as a teacher when teaching operations. All you need to do is follow this order of a student’s learning process: concrete, representational, then abstract. Let’s use division within 100 as an example in this case.

Pastel pencil bag that says math in an elementary classroom next to a calculator.

1. Concrete: When first introducing an operation, it’s important to make it as concrete and realistic as possible. Use literal objects and situations. Let’s say we’re teaching division within 100 to our third graders for the first time. Students need to understand that division is breaking a whole number down into equal groups. One idea is to bring 10 students to the front of the room. Tell them to split into groups of 2. They will realize that they created 5 equal groups of 2. Then you can relate that to the fact that 10 ÷ 2 = 5. You could also do this with objects, such as splitting up a bag of 30 Oreos into equal groups of 6 or 18 student backpacks into 3 equal piles.

2. Representational: Once students have shown mastery of the operation in the concrete phase, it’s time to transition into representational learning. Two common ways you probably already do this is by drawing pictures or by using manipulatives. Thinking back to teaching division, you could have students use counters or mini erasers and split them into equal groups. You could also have them draw a large group of dots and circle them in equal groups.

3. Abstract: Once students are able to represent an operation using drawings or manipulatives, then they are ready to think more abstractly and stick to just writing the equations. This is your reminder to not jump into the abstract stage too quickly. Sure, a student can memorize that 20 ÷ 4 = 5, but it’s useless if they don’t know what it means. When introducing this, make sure to relate the equations themselves to a representation–such as a drawing. Having students show the connection between the representational and abstract way of thinking about the operation is key before transitioning to solely abstract.

Now that you know why teaching operations is the best and how to teach it, I want to show you five easy ways you can make it fun for students!

4 ways to spice up teaching and practicing operations

History by the numbers math history worksheets for third and fourth grade.

1. Use manipulatives related to a current season, holiday, or trend while practicing. During the fall, I loved pulling out candy corn as an easy and cheap manipulative to reinforce multiplication and division concepts. Around the holidays, gumdrops are a go-to. Valentine’s Day? Candy hearts. A quick visit to the dollar store can fill you with ideas! I also stocked up on mini erasers when I would see them and save them for various occasions.

2. Make it cross-curricular! The four operations can be incorporated into just about any other subject. Have students practice writing word problems or stories involving multiplication. Teach students about historical events by having them uncover facts using operations. Think about your current units and if you can find a way to bring multiplication or division into them.

Cafe Mathematics coffee shop restaurant room transformation project-based learning for division for fourth grade.

3. Immerse students into a real world situation. One of my favorite things to do while teaching math was turn my classroom into Cafe Mathematics for a couple days. My fourth grade students used menus and their multiplication and division skills to solve various problems in their restaurant. I did this because my students were obsessed with Starbucks, and this was an easy way to show the importance of learning multiplication and division.

4. Encourage them to look at a situation from different angles. If they see an array of 8 rows x 5 columns, can they also see 8 + 8 + 8 + 8 + 8? Give students a model or a situation and see if they can relate it to multiple equations. My free Emoji Stories download (winter themed) is a great way to try this concept out.

Now you can conquer multiplication and division alongside your students! Be prepared for them to not only understand these operations, but also have fun doing it.

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