Many of my students in the past have come to me lacking conceptual understanding of basic math concepts that were introduced as early as 2nd and 3rd grade. The most important part of my math instruction is fostering a conceptual understanding and this is really important as fifth grade moves into more abstract math concepts. With that in mind, this is one of the first concept lessons I teach every year to my fifth graders. To see my beginning of the year math charts that I make the first weeks of school, click here.

Having a conceptual understanding of basic multiplication and division is key in 5th grade. In 5th grade, we move into decimal and fraction multiplication which requires the students to understand that multiplication is also taking part of a whole or part of a part. However, if they don’t even have the basic understanding of multiplication, this can be very tricky for them. I keep this lesson pretty simple, but it is one of the interactive notebook entries that some students refer back to all year.

To start, we talk about what multiplication is. Some students can rattle off “repeated addition” or “equal groups” but I want them to be able to give examples and discuss it in their own words. This is one key difference between a rote memorization of a concept and a deeper understanding. After discussing that, we move into defining each number in a multiplication problem. This leads to a discussion that in multiplication of whole numbers (I do make the distinction with the students to plant the seed for decimal and fraction multiplication), you have groups and are looking for the total amount of something. This comes in handy when we move into multiplication and division word problems with larger numbers. I am constantly asking the students: What are you looking for? I want them to understand that if they have equal groups and are looking for the total amount, they are multiplying. Here are some shots of the foldable I used. Much more discussion when into this and unfortunately a lot of that discussion was not captured in this particular student’s notes.

After reviewing the concept of multiplication, we move straight into reviewing the concept of division. We follow the same steps as we did with multiplication. We discuss in depth what division is and what it means. I want the students to see the connection between multiplication and division so we use the phrase, “putting a total into equal groups.” This connects right back with the concept that multiplication is determining the total amount in equal groups. Division, on the other hand, is taking a total amount of something in putting it into groups. This is the language I use with the students. It really clicks with a lot of them that had never really grasped the connection between the two.

After discussing the basic concept of division, we move into the two types of division: number of groups unknown and group size unknown. This is really difficult for some of my students. I have to think it is because they are not exposed to those terms and/or not asked to solve a variety of division problems. With that in mind, the students complete two different models to show both types of division. Moving forward, I will definitely have the students label each model as “Group Size Unknown” or “Number of Groups Unknown.”

I refer back to these foldables throughout my multiplication and division unit. This is actually the first interactive notebook entry of the year, and one of the most important. By the time we move into decimal and fraction multiplication, the students are ready to understand this aspect of multiplication.

Click here or on the image to download the foldables used in this lesson.

Do your students come to you lacking a basic conceptual understanding, or are they pretty strong in multiplication and division concepts?

Sarah M says

Ahh! I love this!! I’ve taught middle and high school math, and you’d be amazed at how many kids come through not understanding what multiplication and division are. It totally limits their ability to understand any of the algebra we do. Thanks so much for teaching this concept.

Jennifer Findley says

Yes, it is very limiting! We seriously refer back to this lesson all year for some of my students. They really need that understanding to move forward in their mathematical thinking. Thanks for stopping by!

Brianna Burch says

I totally understand where you are coming from. The vertical articulation SAYS they should understand this, but they don’t. My grade level sat down with fourth grade this week to discuss with them what EXACT verbiage and ideas they need to put out in their first couple units this year to help prepare the kids for us next year and one of our suggestions was to take it alllllll the way back to place value. If the kids don’t understand that place value has a relationship of x10, they struggle with everything (double digit multiplication included)!! Thanks for these, I’m going to put them to use when I do my review next week!

Brianna

Jennifer Findley says

Yes, place value and just basic number sense is also something many of my students struggle with each year. I always *try* to fix the roadblocks early on before we get into the more abstract math. Thanks for stopping by!

Sally Camden says

As a 4th grade teacher, I’m excited about using these ideas with my students. Hopefully I can lay a good foundation for them as they use these concepts in later years.

Alex says

Hi could u expand on the division of the groups size unknown and number of groups unknown. I have never heard of this before. Thanks

Jennifer Findley says

Hi Alex, here are examples that may clear it up:

Number of Groups Unknown: Jackson has fifty-six pieces of candy. He wants to make treat bags with 4 pieces of candy in each. How many bags will he be able to make? In this problem, we know how many goes in each group, but the number of groups is unknown.

Size of Groups Unknown: Jackson has fifty-six pieces of candy. He wants to divide the candy equally among 4 bags. How much candy will be in each bag? In this problem, we known how many groups, but the size of the groups is unknown.

Hope this helps! Thanks for visiting!

Jennifer