In third grade, one of the most important math goals is teaching multiplication and division understanding.
Don’t make the mistake of jumping right into solving equations without first building a solid understanding of the concepts of multiplication and division
The goal is not to memorize math facts, but to understand the concept of multiplication and the concept of division. This will help them later down the line with more complex problems.
3rd graders who struggle with multiplication and division often fall back to counting on their fingers.
While this may help them get the correct answer in the short term, it makes things extremely tough when they go to 4th grade and are expected to multiply fractions by whole numbers or solve two-digit by two-digit problems and lack basic conceptual understanding.
Wondering, how to prevent this from happening?
First, let’s explore some common misconceptions students have about multiplication and division. Then you’ll learn what to do to prevent and fix them.
Multiplication Understanding Misconceptions
In multiplication, one factor represents the number of groups and the other number represents the number of items in a group.
Although this seems simple enough, it’s extremely important how we communicate this when talking to our students. If we’re too vague in our language, it’s hard for our students to understand what we’re asking. And the problem just becomes a multiplication fact with no context.
Let’s look at an Example:
Which statement do you think promotes more understanding?
- “5 groups of 2 is the same as 10”
- “5 times 2 equals 10”
The first one!
It’s important that we use precise language because it helps develop understanding and makes learning new concepts clearer for kids.
Now, let’s talk about division.
Division Understanding Misconceptions
There are two different division models: partitive division, and measurement division.
In the partitive division model, we’re trying to find out how many items are in a group.
In the measurement division model, we’re trying to find out how many groups there are.
This can be very confusing for children who struggle with identifying information in a problem (i.e. which number represents the number of groups, which number represents the number of items in a group).
Let’s Look at an Example:
Tina is making charms for a necklace. Each charm needs 3 beads. If Tina only has 21 beads, how many charms can she make using all the beads?
Oftentimes, as soon as kids see 3 and 21, they automatically start multiplying or dividing numbers without truly understanding what is happening in the problem.
They may have no idea if the answer is:
- 7 necklaces
- 7 beads
- 7 charms
To avoid any misconceptions, we can walk our kids through the language and numbers within a problem. This simple process is a quick way to build student understanding.
First, restate the information they know.
In this problem…
- Tina is making charms
- Each charm needs 3 beads
- Tina had 21 beads in all
Next, explain what the numbers represent and what they need to find.
- 21 represents the total number of objects (beads) Tina has
- 3 represents the number of objects (beads) in each group (charm)
- need to find the number of groups (charms) Tina can make with 21 objects (beads)
Because we’re looking for the number of groups, this is a measurement division problem.
Last, solve the problem.
This problem can be solved by either drawing a measurement division model or using the equation 21 ÷ 3 = ? Drawing a model helps when introducing this concept, and helps scaffold instruction for students that need more support.
The solution is 7. So, Tina can make 7 groups (charms).
The most important part of this process is NOT the answer. Instead, it’s how children get to the answer.
We can set our students up for success by teaching them how to determine what a problem is asking them to do! Once they master this, they’ll be able to solve a wide variety of problems by themselves.
PRO TEACHING TIP: Mix real division and multiplication problems into your lessons and work with your students to break down the language in the problem.
So, what else can you do to build your students’ multiplication and division understanding?
How to Teach Multiplication and Division Understanding
- Use precise language when discussing multiplication and division situations to add context for understanding. For Example: 5 groups of 3 apples is equal to 15 apples
- Use a variety of multiplication and division models, representations, and strategies so that students can easily identify groups and numbers of items within a group
- Provide a wide variety of division problems so that students get experience with solving partitive (how many items are in a group?) and measurement problems (how many groups?)
- Connect concrete models and pictorial representations to symbolic representations to eliminate misconceptions
- Ask students to show their work and explain their thinking
Top Teaching Tips
- Use equal groups models, arrays, and area models to help students visualize multiplication and division problem situations
- Use manipulatives like counting chips and square tiles when introducing topics and continue to use for students that still need more concrete examples
- Provide word problems so that students see multiplication and division in context
Make Teaching Multiplication and Division a Breeze with these Done-for-You Lessons
If you want to teach multiplication and division so that your students really get it, then you need the 3rd Grade Understanding Multiplication and Division Simplified Math Curriculum Unit.
You’ll have everything you need to teach including, pre and post-assessments, lesson presentations, student math journals, and more!
Learn more by clicking below.
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Done-for-you math unit including: teaching slides, assessments, warm-ups, a student journal and more.
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