Developing Multiplication Strategies

by Treve Brinkman, Professional Learning Specialist
June 02nd, 2017

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Once students have mastered addition and subtraction, they get to move on to bigger equations: multiplication. Many adults recall days spent memorizing tables and writing out their work, but you can take an approach that doesn’t require merely committing numbers to memory. Help your students really understand what multiplication is and how it works by developing some strategies. Here are tips and tricks for making the subject more palpable in your classroom:

Show the addition in multiplication

Your students already understand addition, and the concept is a huge part of multiplication. Use this fact to your advantage by revealing the latter through the former. Just be sure that any connections you make lead back to multiplication and help students understand the new concept. For instance, you might set up a problem like this:

8 + 8 + 8 + 8 = 32

This is the basis of a multiplication problem. Once students see the above equation, simplify it to:

16 + 16 = 32

Here ends the addition. You can now show how multiplication works.

(2 x 8) + (2 x 8) = 32

As you can see, you replaced the two instances of 8 + 8 with a multiplication problem that has the same outcome. To further simplify addition into multiplication, show this problem:

4 x 8 = 32

This process of whittling the long addition problem into a shorter, equivalent multiplication equation shows students exactly how the concept works. They’ll see you’re adding eight four times – reword that another way and you have four times eight, four groups of eight, or 4 x 8 = 32.

Feel free to utilize different numbers when creating an example problem.

Help students learn multiplication with a few simple strategies.

Understanding landmark numbers

While addition can help students understand multiplication, sometimes it confuses them. For instance, this could happen when students multiply using landmark numbers, which are easy-to-compute numerals, such as 10 and 1.

If you have the problem 9 x 25, students may round 9 to 10 to give them a landmark. The new equation would be 10 x 25. After getting 250, though, students would have to subtract a correct amount to account for the initial rounding up. As you know, they’d have to subtract 1 x 25, or 25 to get 225. However, many students only subtract 1, as they are still reasoning in a mindset of addition and subtraction.

Use landmark numbers in class, but be sure to go over common mistakes students make to help them reason in terms of multiplication.

Doubling and halving

For a more visual approach to teaching multiplication, you can double and halve arrays that portray problems. For instance, 1 x 16 would be a row of 16 boxes. To show a different version of the same problem, rearrange the boxes. You can have 2 rows of 8 boxes each or 4 rows of 4 boxes.

Give your students different problems to solve, and discuss as a class why the strategy works. Centering a math talk on this concept will help students start to reason in terms of multiplication.

For more strategies and ideas when teaching multiplication, check out our book “Number Talks.” It will help you discover tips and tricks to use in class and teach you to construct a math talk based on those concepts. We also offer an array of free resources for you to use on our website.

 

Treve Brinkman is devoted to building the capacity of both teachers and students in order to create classrooms where growth mindset, communication, and deep mathematical understanding are central. In the role of the Professional Learning Specialist, Treve supports districts’ professional learning for leaders and teachers through the facilitation of both whole group learning as well as individual coaching sessions.

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