Multiplication Facts: 3 Ways to Promote Conceptual Understanding that Lead to Memorization

3rd, 4th, and 5th grade teachers: We've all been there. Students do not know their "multiplication facts".

We all know that memorization is important, but it doesn't come without students having the conceptual understanding of numbers first. Students need many experiences with numbers in order to be fluent with memorization and deep understanding.

Check out this article by the Stanford Graduate School of Education. If you don't have time to read the whole thing, here are some snippets I found interesting:

• "While research shows that knowledge of math facts is important, Boaler said the best way for students to know math facts is by using them regularly and developing understanding of numerical relations. Memorization, speed and test pressure can be damaging, she added."

• One study done had these results: "The conclusion was that the low achievers are often low achievers not because they know less but because they don't use numbers flexibly."

• "When we emphasize memorization and testing in the name of fluency we are harming children, we are risking the future of our ever-quantitative society and we are threatening the discipline of mathematics," she said. "We have the research knowledge we need to change this and to enable all children to be powerful mathematics learners. Now is the time to use it."

Wow. Very powerful words and examples.

I have seen in my own classroom that high-achieving students are not great at memorization. However, with their flexible thinking, they are able to solve problems at the same speed, or faster, than classmates with their multiplication tables memorized.

Here are 3 things I do in my classroom to promote number sense and conceptual understanding in multiplication:

1. Use Math Talks

If you haven't heard of math talks, here is a quick how-to article. You don't need to purchase anything and it is a practice you can start tomorrow.

Here is an example of a math talk I did with my 4th grade students last week:

15 x 32 =

I gave my students a few minutes to think about this problem mentally. They put their thumb up in their lap if they have one strategy and then add their pointer finger, then middle finger for each way they can solve it.

Here are some solutions my class came up with:

• Break apart 15 into 10 + 5. 10 x 32 =320, 5 x 32 = 160. 320 + 160 = 480.

• Break apart 15 into 10 + 5. Break apart 32 into 30 + 2. 10 x 30 = 300, 10 x 2 = 20, 30 x 5 = 150, 5 x 2 = 10. 300 + 20 + 150 + 10 = 480.

• Use doubles and halves. 15 x 32 = 30 x 16. 3 x 16 = 48 so 30 x 16 = 480.

• I added this one that no one thought of: Break apart 32 into 30 + 2. 30 x 15 = 450, 2 x 15 = 30. 450 + 30 = 480.

Really impressive the way my students were able to be flexible with those numbers. Did this happen the first time I gave a problem? No. Did all students get it right? No. Did all students try to use numbers to solve? Yes.

Give it a try with your class. It's not perfect and emphasize to your students that their thinking and process is more important than getting the correct answer. We don't want them to be scared of math, we want students to be confident risk takers!

2. Give Your Students Manipulatives

This may seem simple, but manipulatives really do help students understand numbers. In my class, students love using Snap Cubes and Base 10 Blocks.

Here is a picture of my manipulatives shelf. Students can access them any time they want.

Students can use these to build models to represent problems. For multiplication, we use the blocks to create arrays. When students are comfortable using concrete models, then we move to abstract models, such as grid paper to represent the arrays.

3. Give Students Tools to Promote Flexible Thinking

The tool I use for helping my students use flexible thinking with multiplication is this flipbook.

This is for students who already know and understand x0, x1, x2, x3, x5, and x10. Most of the students who come into my 4th grade classroom know those, but are stuck on the harder times tables.

Each page of flipbook gives flexible thinking strategies for students to use.

This is my own resource and you can click here to download it for $1.00. It is three pages folded together and then stapled.

Do you have other strategies for promoting number sense and conceptual understanding in your classroom? Comment below and let me know!