# Teaching Multiplication Shortcuts

Multiplication. Multiplication is a BIG deal in third grade and up. In fact, it’s so vital that teaching multiplication shortcuts can sometimes be your saving grace until the students actually memorize the multiplication facts.

In the past, I have talked about teaching multiplication strategies and tricks to help your students learn their multiplication facts, but today, I’m just going to focus on teaching your students multiplication shortcuts.

## What the Multiplication Shortcuts Are and Why Teach Them

When we begin teaching students their multiplication facts, we definitely begin by helping them understand the concept of why and how we arrived at the answer. Once they understand those strategies of repeated addition, arrays, and equal groups, then we begin to teach them little shortcuts that can help them arrive at the answer a bit faster. For instance, most teachers definitely teach that to find the product of any number times two, we just double the other factor. Therefore, 2 x 7 is 7 doubled, so the answer is 14. This is also typically done with the factors of five (skip counting) and 10 (write the other factor and add a zero). But did you know that there are other shortcuts that can help your students, too?

Of course, of all my years of teaching, I think I have always had the most fun teaching the nines. There are so many multiplication shortcuts to teaching the nines. In fact, some of the ones listed above in that Multiplication Shortcuts Chart (which is yours to download FREE – just click here) may be different from other multiplication shortcuts you have heard or seen – and that’s totally okay!

## How to Teach Multiplication Shortcuts

When I teach the multiplication shortcuts in my class, I pull out my Multiplication Shortcuts Math Workshop Unit and begin by talking about what multiples are. Then, we start discussing patterns we notice on a hundred chart. We list out the multiples for the individual numbers of two to 10 and then discuss our findings. I find this to be very valuable to my students for understanding the shortcuts later.

Then, we begin looking at the patterns and shortcuts for factors with similar rules. In one mini-lesson, we focus on five and 10 together because they are typically relatively easy shortcuts with which students are already familiar. In the next lesson, we focus on the factors two, four, and eight because they are all double, then double-double, and finally double-double-double. (Since students usually know that two is double from 2nd grade, it is really like a review, and they are only learning two shortcuts.)  Our next lesson is the factors of three and six, and then I follow it with the factor of nine to give students an opportunity to soak in the previous lessons but to also feel a bit more at ease. The nines have so many fun shortcuts that it’s easy to create a “mental break” for students. Lastly, we talk about the shortcut for seven by itself. To wrap things up, I like to review how the properties of multiplication (commutative and distributive) also can help us with our facts.

With each individual lesson, after discussing the shortcut, we practice it through engaging partner games and reinforcing practice sheets.

## The Multiplication Shortcut Final Presentations

After we have practiced using the shortcuts, I then have the students show off their knowledge! They have to create a way to present the shortcuts using a Hollywood or movie theme.

Some students presented a long chain hooked together using yarn and index cards.

Here is a closer view:

Some students created a poster with flaps:

Other students created booklets. Overall, the presentations were amazing, and students definitely learned their multiplication shortcuts in a fun and engaging way!

All of these activities, including the lessons, games, and practice sheets can be found in my Multiplication Shortcuts Math Workshop Unit.

Grab the Multiplication Shortcuts Chart to download FREE by clicking here! The “Introducing…” Clapboard is not included in the math workshop unit, but you can also download that free by clicking here.

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### This Post Has 5 Comments

1. I wholeheartedly agree that kids have to go beyond strategies in multiplication and must finally memorize the facts. I wonder how many people feel the same. I feel that this mindset is in the minority and I wish it wasn’t. Do you feel the same way?
I really like your shortcuts. These have been tried and true for years. My only problem with shortcuts is that many times students feel if they have these, why bother to memorize the facts. They make their knowledge of short cuts (sometimes called “tricks”) their end-all in learning the multiplication facts.
What I really love about your post is having the kids do a presentation on what they learned. There is no better way to learn than to teach what you know to others.

1. I totally agree with you! I also find that it’s the minority about memorization. I find nothing wrong with children having to simply memorize and be drilled frequently for basic facts. Sometimes I feel that lack of fluency and accuracy puts us behind a bit in math. I also wholeheartedly agree that students need to be held accountable for what they learn by teaching it back. That’s how I know they really understand it if they can teach it to others! 🙂

2. Your methods are teaching students to decompose the factors into workable portions. Going from the known (ex:the 5’s) to help learn the unknown is a good idea. Can you explain the 7’s for me though? I don’t get that one. Thx!

1. Thank you for your kind words. The sevens can appear a bit tricky at first glance, especially when you just hear/see “multiply by 5, then double.” It’s really two steps and then you combine those two steps to find the answer. It’s probably not the most ideal strategy, but it still works. First (step 1) have students take the factor and multiply it by five. They will take the product and set it aside. Now (step 2) they will take the factor (from the first problem) and double it. Finally (step 3) they will take the product from step 1 and the answer (from doubling) in step 2 and add them to get the answer to the original problem. Here it is with numbers:
Original Problem: 7 x 6
Step 1: 6 x 5 = 30
Step 2: 6 doubled is 12
Step 3: 30 + 12 = 42
Thus the answer to 7 x 6 is 42.
I hope this makes sense. 🙂

3. Rebecca Gerl

I LOVE THIS! This is almost all of the things we are teaching the students in our new Bridges Math series. Would I be able to get an editable format to change 5 and 7 so it’s what I’m teaching my students. OR one that says 5- (Multiply by 10, then split in half) and 7 (Multiply by 5, then add one double). THANK YOU!!