Common Core Math: Representing Multiplication Using Repeated Addition

Many families tell me that homework has become more challenging since states began adopting the Common Core standards. That makes sense… Math is now taught and assessed very differently than it was when we were children! As a teacher, I had to re-learn quite a bit of elementary math concepts in order to successfully teach them!

For that reason, I am going to start a “Common Core Math” series – addressing common core math problems that you may see your child bring home. I am going to try my best to address a single problem type in each “Common Core Math” post: explaining the reasoning surrounding this question type and how we can help our children complete and understand homework with this question type. My goal is to reduce stress and frustration in your home. I hope that a deeper understanding of your child’s math work will help make homework time a little more peaceful and productive for your family.

Now onto our first topic… Representing Multiplication Using Repeated Addition

I picked this topic because it is all over my Facebook feed. It has been for a couple of years in different ways. It looks a little something like this… (For this post we are going to focus on problem number 1.)

I don’t want to get into my opinion over teachers’ choices – whether this answer should or should not be marked correct. I am not in other teachers’ classrooms and am not working with their students, toward their individual goals and needs. Even if I was, that’s not the purpose of this post. This post is to help YOU and YOUR CHILD when you see math work like this at home. My goal in writing this post is to help make homework time in your house more peaceful and productive.

When your child's teacher is asking them to represent multiplication using repeated addition, they are working with your child on this Common Core standard: Interpret products of whole numbers, e.g., interpret 5×7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5×7.

In order to truly understand multiplication, we would like for our students to know what the multiplication sign (X) actually means. 

X (in the language of Math) means “equal groups of”.

When we see the math sentence 4x2, we can say that we have “4 equal groups of 2”.

When we see the math sentence 2x4, we can say that we have “2 equal groups of 4”.

Although the commutative property in math shows us that 4x2 and 2x4 will result in the same product (8), the number sentences mean two very different things. As I would do if I were working with students, let’s think about the number sentences in terms of the real world. Let’s draw some pictures representing the problems. Pictures of cookies, of course.

Although we know that (according to the commutative property)  4x2 and 2x4 are going to equal the same product, you can see in the picture above that the meaning of each number sentence is different. 

Why does this difference matter? We want our children to know that math is not a mysterious language involving random numbers existing only on worksheets. We want our children to know that math is everywhere – we are surrounded by examples of addition, multiplication and geometry everywhere we look. We want them to have a deep understanding of math instead of just a rote memorization of facts and rules. Understanding the different meanings of the number sentences 2x4 and 4x2 is one step in many we take to provide our students with a deep knowledge of the language of math. We know that this will help students as they encounter tricky problems and more complex math concepts.

Quick Tips to Try at Home:

-       You can help your child by encouraging them to say the words “groups of” whenever they see the multiplication sign. When you see multiplication problems, you can say “2x4 or 2 groups of 4.” This way your child uses these words, hears them, and associates them directly with multiplication.

-       When working with your child on single-digit multiplication problems, use real-world props. You can take out a handful of pretzels (or any favorite snack). Your child can snack on them during homework time and use them for help! Show your child 2x4 by putting the pretzels into 2 groups of 4. To extend this to repeated addition, tell them this is 4+4. They can then write this down.

-       When working with your child on single-digit multiplication problems, ask them to make drawings. You may say “Can you show me what 2 groups of 4 looks like in pictures?” You may encourage them to use stars (or any favorite simple shape or drawing) and circles. Show them that their picture represents 2x4 or 4+4. Using circles and stars, 2 groups of 4 would look like this:

Next post, we will look extend this thinking and look at multiplication arrays. What other math problems stump you on your child's math homework?