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Struggling to figure out how to teach multiplication fluency? You’re not alone! Teaching multi digit multiplication needs to be about so much more than the standard algorithm if we want our students to really understand what is happening when we multiply, and apply that learning to everyday problems.
If you missed our post on strategies to build multiplication fact fluency, be sure to read that first. The ideas below really build on those!
Should students memorize multiplication facts? Sure, it helps. But that’s not nearly as important as having a solid understanding and a bank of effective strategies to quickly and efficiently perform mental math multiplication.
If you’d like a complete collection of already done-for-you resources to teach multiplication and all other operations, you might be interested in our Complete Operations Units for grades 4-8. They come with 3-part math lessons for every expectation in the B2 strand, math centres, practice worksheets, review games, vocabulary, assessments and more. If you’d rather shop on TPT, you can check the units out here.
How to Teach Multiplication Fluency Strategies
Throw all the algorithms and tricks out the window! Well not quite, but I would encourage you to save them until later. We want our students to truly understand what is happening when we multiply.
The lattice method, traditional algorithms and other ‘tricks’ are not rooted in number sense. Working from right to left, one digit at a time with no regard for place value is a recipe for disaster in any student who does not have a solid foundational understanding of numbers.
Students need to be able to think flexibly about numbers (decomposing and composing) to develop multiplication fluency strategies that are efficient and make sense.
OK, off my soapbox… So what should we do?
Begin by letting students explore multiplication conceptually. Use an inquiry math lesson approach where students work in pairs to problem solve, experiment and build their own strategies to answer a question. Following this you can discuss the student-generated strategies and add in some direct teaching of specific strategies.
Use manipulatives, models and drawings to build a visual, concrete understanding of what it means to multiply.
Make it clear to students…
- Different strategies work better with different numbers and for different students. There is no one right way.
- The most effective strategy is the one that produces the most accurate results with the least amount of effort. That means it will be different for every student and NOT necessarily the traditional algorithm.
Mental Math Strategies for Teaching Multi Digit Multiplication
The following 3 strategies are great for making the multiplication of some numbers quick and easy to do mentally. This is always more efficient than getting out a pen and paper or even a calculator so we want our students to look for these first!
1. Commutative Property
The commutative property teaches us that numbers can be multiplied in any order for the same result. For example, 4×8 is the same as 8×4.
While this is just something to ‘know’, take a little time to have students really get this by using manipulatives and simple arrays to show it. Knowing this has the potential to make every other strategy more helpful.
2. Halve and Double
This is a strategy we can use for basic math facts but it can work just as well with bigger numbers. For example, 20 x 34 is much easier when turned into 10 x 68.
3. Multiplying by 10, 100 and 1000
It is important to teach this concept by focusing on place value first. Tricks like “adding zeros” are great for a quick result but will cause problems down the road with decimals if students don’t understand what is really happening.
Students need to understand that when we multiply by 100, the value of each digit is increasing by two places. So the ones become the hundreds and so on. THEN, we can show them the shortcut that when there are two zeros (like in 100), we can add two zeros to the product.
For example, when solving 23 x 1000 the ‘2’ moves three places from the tens to the ten thousands place and the ‘3’ moves from the ones to the thousands place making the product 23,000.
Multi-Digit Multiplication Strategies
Let’s explore strategies for teaching multi-digit multiplication. They are loosely organized in the recommended teaching order as they become increasingly more complex and abstract.
However, please do not use this as a teaching list and have all students work to master all strategies. Some students may need to remain at a more concrete strategy while others work better with a more abstract method.
Where should I begin teaching multi-digit multiplication?
4. Equal Groups
This is where we need to start with multiplication strategies for fluency. Have students use concrete materials first, then move onto drawings and models to visualise multiplication in action. Students should understand that 3×4 is 3 groups of 4 and that the same is true for multi-digit numbers too.
5. Repeated Addition
It shouldn’t take long for students to decide it’s time-consuming to model equal groups with larger numbers and want to find more efficient strategies.
This is where repeated addition comes in. Help students recognize that we are adding the equal groups together.
6. Number Lines
Move repeated addition from those equal groups to a number line to help students think more flexibly and visualize it in another way. This also ties the idea of repeated addition to skip counting which may be helpful for some students or some numbers.
What are more advanced strategies for multi-digit multiplication?
Distributive Property is the idea that numbers can be broken apart and built up in various ways. It could also be thought of as a number being the sum of its parts. For example, 24 can also be looked at as 2 x 12, or 20 + 4, or 10 + 10 + 4…
The following strategies all require an understanding of distributive property as we move toward more advanced multiplication strategies.
7. Arrays
Arrays are the perfect building block from using hands-on, visual strategies. When we use arrays we are naturally moving from a grid of physical objects or drawings to an area model that represents those objects.
8. Box Method
The next logical progression is the Window/Box Method. This takes the idea of the array or area model and removes the visual need for the spaces to be a relative size to their value. Students still have the visual cue of breaking down the numbers according to place value.
9. Breaking Up Numbers
This is one of the most helpful mental math strategies that strong math thinkers use all the time. Similar to the Array or Box Method (without the drawing), we can decompose one or more of the factors into easier chunks to multiply. We then simply need to add the groups back together.
For example, in 17 x 23 we can break the 17 into 10 + 7. We can also choose to break the 23 into 20 + 3 if that is easier.
While decomposing according to place value is better, students could also use smaller chunks if it makes the numbers ‘friendlier’ for them. For example, 7 could be decomposed to 5 + 2.
10. Add a Group
When a factor is close to a ‘friendly number’, this strategy can be incredibly useful. When trying to solve 6 x 27, I could solve 5 x 27 (one group less), then add a group of 27 to my answer.
11. Subtract a Group
Subtracting a group is the opposite of the previous strategy. If an easier and/or known multiplication fact is one more than the given question, students can solve then subtract one group from the answer.
12. Partial Product Multiplication
Now we’re getting close to what you were most likely taught in school (whether it made sense to you or not). In partial products, it looks like traditional long multiplication but we continue to focus on place value and multiplying in parts.
When solving the equation 76 x 9, we first solve 9 x 6 which equals 54. Then we multiply 9 x 70 to make 630. Notice we did not multiply 9 x 7 (and then hope students remember to put 63 in the correct column). The 7 is in the tens place so it represents 70. Finally, we add up the parts to find the product.
13. Long Multiplication
There is a time and place for this technique for sure. I just don’t believe it’s the ultimate goal for every student or every multiplication question!
The reality is, it is only effective if…
- students have a solid grasp on the place value and number sense behind multiplication,
- the mental multiplication strategies above don’t work for the numbers involved – because they ARE quicker when possible.
I also make it clear to my students that the traditional algorithm they think they ‘need’ to learn (and their parents are probably showing them at home) isn’t actually any less math. It’s just the math is happening in our heads and we’re simply putting less on paper.
I’m not going to explain this one to you, I’m pretty sure you know it!
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