If you find it hard to teach the basic multiplication facts, you are certainly not alone. There are a few main challenges that we encounter when teaching basic multiplication facts. First – time. How do we find the time to do a really good job of teaching the multiplication facts, while also doing a really good job of teaching everything else in our overwhelming curriculum? We know that basic fact knowledge is essential as students move into the older grades, but it can be difficult to achieve. Secondly, differentiation. All of our students learn at different speeds. We can’t expect them all to learn the multiplication facts at the same time, but how do we ensure that each student is working to his full potential? One last big challenge is the balance between strategies and memorization. Students used to be expected to memorize the facts without any mental math instruction at all. For students who are good at memorization, this works. But there are many students who just can’t memorize all of the facts and remember them. The bigger problem when it comes to memorization is lack of understanding. When we encourage students to simply memorize without making the important connections that they need for conceptual understanding, we are missing a big learning opportunity. It is time for us to take a step back and really ask ourselves what we want our students to be able to do. Do we want them to be able to recite the multiplication facts to 10×10? Or do we want to enable them to solve ANY problem that they encounter – even if it is beyond 10×10. The way you answer this question will ultimately drive your teaching. Fortunately, there are simple shifts that we can make in our teaching to make multiplication easier for our students and accessible for all of them. We can teach in a strategic order that really makes practical sense. We can also teach our students strategies for each set of facts that will make multiplication FUN, and less challenging.

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  If you are looking for a resource where all of the work is done for you, you may be interested in The Multiplication Station, a self-paced, student-centered math station where students work through the basic multiplication facts and strategies, mastering each one as they go. Strategies are integrated in a strategic manner, ensuring that students build on their understanding progressively. See the Multiplication Station HERE.

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Strategies are ESSENTIAL. Think of them like tools in a tool box. When our students see a problem, we want them to be able to choose an effective strategy that will help them solve it. I’ve listed some effective strategies for the facts below. I’ve also listed them in my preferred order of teaching. Simply click on each strategy for a more detailed explanation of each one: The 2’s Facts: Use the doubles addition facts (See a full explanation HERE) The 10’s Facts: Shift the digits one place to the left (See a full explanation HERE) The 5’s Facts: Use the related 10’s fact and divide in half (See a full explanation HERE) The 1’s Facts: Anything times 1 is itself. The 0’s Facts: Anything times 0 is 0. Square Facts: Learn the squares like 3×3, 4×4, 5×5 by using arrays where we can “see” the square that is created. These facts will be important for deriving facts later on. The 4’s Facts: The double of the double (See a full explanation HERE) The 3’s Facts: The double plus one more group (See a full explanation HERE) The 9’s Facts: The related 10’s fact subtract one group (See a full explanation HERE) The 6’s Facts: Use a known fact. (See a full explanation HERE) The 7’s Facts: Use a known fact. (See a full explanation HERE) The 8’s Facts: Use a known fact.(See a full explanation HERE)     Let’s talk a little bit about strategies vs. tricks. One thing to remember is that a strategy will enable students to solve ANY problem, while a trick is limited. Take for example, the “just add a 0” trick for multiplying by 10. Is this effective for multiplying whole numbers by 10? Yes, absolutely it is. But there is a problem. Once students get into multiplying decimals, they will have to un-learn this trick. To solve 13.4 can you just add a 0 and make it 13.40? No. In this case it is more effective to teach students to shift the digits one place to the left, encouraging a place value understanding of multiplying by 10. The next time that you are teaching a strategy, be sure to ask yourself, “Is this a strategy or a trick?”   NEXT STEPS: Read more about an effective order for teaching the multiplication facts HERE. This order will motivate your students and enable them to see huge progress early on in their learning.

The post Effective Strategies for Teaching the Basic Multiplication Facts appeared first on Shelley Gray.

You may not explicitly teach the 12 facts to your students, as many curriculums specify that students are fluent with facts to 10×10. However, solving 12’s facts can be used to teach a very important strategy – breaking apart numbers.

We can use the 12’s to teach our students how to break up numbers and multiply them in groups. In this case, we divide the 12 into a 10 and a 2.

For example, for the equation 12×3, we could divide that 12 into a 10 and a 2, and multiply each part by 3. So 10×3=30, and 2×3=6. Now we can add the 30 and the 6 together to make 36.

For the equation 12×5, we could divide that 12 into a 10 and a 2, and multiply each part by 5. So 10×5=50, and 2×5=10. Now we can add the 50 and the 10 together to make 60.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 6×12, they should see the 12 as one of the factors, and know that they can use the 12’s strategy to solve this equation.

NEXT STEPS

Reinforce the 12’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 12 Times Table So It Really Makes Sense appeared first on Shelley Gray.

You may not explicitly teach the 11’s facts if your curriculum expects you to only teach to 10×10. However, the 11’s facts are a great opportunity to reinforce the conceptual idea of using what you know and then adding a group.

So, for example, for a fact like 11×5, you can first think 10×5=50, and then add another group of 5 to make 55.

Or for a fact like 11×7, you could start with 10×7 to make 70, then add another group of 7 to make 77.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 7×11, they should see the 11 as one of the factors, and know that they can use this “add a group” strategy to solve this equation.

Teaching the 11’s as “the same number twice” is a common trick. For example, 5×11 will be a “5” twice to make 55. 8×11 will be an “8” twice to make 88.

This does work, but it is limiting because it only works up to 11×9.

When we focus on strategy, rather than a limiting trick, we enable our students to solve ANY problem – not only those that fit into a certain span of numbers. For example, if we are faced with the problem 11×14, we know that we can simply multiply 10×14 to make 140 then add another group of 14 to make 154. The “same number twice” trick does not enable us to solve a problem like this.

NEXT STEPS

Reinforce the 11’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 11 Times Table So It Really Makes Sense appeared first on Shelley Gray.

The 10’s multiplication facts are typically an easy set of facts to learn.

When you teach to multiply by 10, be sure that your students understand the “number sense” behind multiplying by 10. Teach that when you multiply by 10, you simply shift the digits one place to the left. A zero is used as a place holder. For example, when you multiply 3×10, you shift the digits one place to the left and get a product of 30.

When you multiply 6×10, you shift the digits one place to the left to get the product of 60.

Here’s a video to illustrate this process:

Why not simply teach to add a 0?

Adding a 0 does work for whole numbers. But later on when they begin working with decimals, they will have to un-learn this trick. Think about a problem like 1.34 x 10. Do we simply add a 0 to make 1.340? NO! Instead, we shift all of the digits one place to the left to make 13.4. Learning this now will ensure that they do not have to un-learn later on.

Students will likely discover, on their own, that when you multiply a number by 10, you just add a 0. Be sure to reinforce that this only works with whole numbers.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an expression like 7×10, they should see the 10 as one of the factors, and know that they can use the 10’s strategy to solve this equation.

NEXT STEPS

Reinforce the 10’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 10 Times Table So It Really Makes Sense appeared first on Shelley Gray.

The 6’s, 7’s, and 8’s are typically some of the most difficult multiplication facts to learn. However, there is good news! If you are teaching your students using a strategic order of facts, they will only have a few facts left to learn for the 6’s, 7’s, and 8’s.

For these facts we can teach students how to use a known fact.

For example, for the equation 6×6, we could use a fact that we know like 5×6, and then just add one more group of 6.

For 7×7, we could use a fact that we know, such as 5×7. We know this is 35. Now we could add 2 more groups of 7 to make 49.

For 8×8, we could use a fact that we know, such as 9×8. We know that this is 72. Now we could SUBTRACT one group of 8 to make 64.

When I work with these facts with my students, I am ALWAYS asking this question: “What do you know,” because my goal is for students to begin asking themselves, “What do I know?” when they see a tricky equation.

Using known facts is a really important skill to learn. Although it may take a bit longer, it’s so important for students to learn that they can work with and manipulate numbers in order to solve an equation.

Ultimately, I prefer that my students memorize those really tough facts like 6×6, 6×7, 7×7, and 7×8. I work with these facts over and over and over again with a goal of students committing them to memory. However, those strategies are really important to fall back on.

NEXT STEPS

Reinforce the 6’s, 7’s, and 8’s multiplication facts with multiplication task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more. Find the 6’s task cards HERE, the 7’s HERE, and the 8’s HERE.

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 6, 7, and 8 Times Tables So They Really Make Sense appeared first on Shelley Gray.

I usually find that students memorize the 5’s multiplication facts fairly easily. There are a couple of ways to help them learn these facts.

First of all, you can teach students to first multiply by 10, and then divide that product in half.

For example, when you have an equation like 5×8, you could first do 10×8 to make 80, and then divide that in half to make 40. The reason that this works is because 5 is half of 10.

As another example, for the equation 5×4, you could first multiply 10×4 to make 40, and then divide that product in half to make 20.

The strategy above is a good one to encourage number-sense understanding of the 5 times table. Arrays are an excellent visual to show the connection between 5 and 10.

In my own experience I have found that skip-counting is a quick and effective strategy for this times table, since students generally memorize the products quickly anyways.

For example, for 5×3, skip-count by 5’s three times: 5, 10, 15.

For 5×6, skip-count by 5’s six times: 5, 10, 15, 20, 25, 30.

For both of these strategies, it is very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 4×5, they should see the 5 as one of the factors, and know that they can use the 5’s strategy to solve this equation.

NEXT STEPS

Reinforce the 5’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 5 Times Table So It Really Makes Sense appeared first on Shelley Gray.

The 4’s multiplication facts are typically an easy set of facts to learn. This is because there is a specific strategy for this set of facts that is very effective.

The 4’s facts can be thought of as the doubles’ doubles.

For example, when you have an equation like 4×5, you can double the 5 to make 10, and then double the 10 to make 20.

For 4×6, find the double of 6 (12), and then double the 12 to make 24.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 7×4, they should see the 4 as one of the factors, and know that they can use the 4’s strategy to solve this equation. In this case students can think, “the double of 7 is 14, and the double of 14 is 28.”

NEXT STEPS

Reinforce the 4’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 4 Times Table So It Really Makes Sense appeared first on Shelley Gray.

The 3’s multiplication facts use students’ knowledge of the doubles addition facts. Students can think of a 3’s equation as “the double plus one more group.”

For example, to solve the equation 3×4, think, “the double of 4 plus one more group of 4,” which equals 12.

For 3×9, think, “the double of 9 plus one more group of 9,” to make 27.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 5×3, they can still use this strategy since 3 is one of the factors. In this case, they can think, “the double of 5 plus one more group of 5,” to make 15.

NEXT STEPS

Reinforce the 3’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 3 Times Table So It Really Makes Sense appeared first on Shelley Gray.

Sorry, this mini course is no longer available. However, I have a wealth of information on my website about teaching the basic multiplication facts. Start HERE with effective strategies for basic multiplication.

The post Free Mini Course: Basic Multiplication and Division – Mastery for ALL Students appeared first on Shelley Gray.

The 2’s multiplication facts are some of the easiest ones to learn. This is because they can be taught as the addition doubles, which your students should already know.

For example, when you have an equation like 2×3, you can think of this as the double of 3, which is 6.

An equation like 2×7 can be thought of as the double of 7, or 14.

It’s also very important to reinforce the commutative property.

This means that the order of factors does not change the product. For example, if students are faced with an equation like 8×2, they should see the 2 as one of the factors, and know that they can use the 2’s strategy to solve this equation. In this case students can think, “the double of 8.”

NEXT STEPS

Reinforce the 2’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

OTHER HELPFUL RESOURCES

Multiplication Strategy Posters

Multiplication Equation of the Day: Multiplication Fact Booklets

The Multiplication Station: a Self-Paced Program for Mastering the Basic Multiplication Facts

The post How to Teach the 2 Times Table So It Really Makes Sense appeared first on Shelley Gray.

Multi-digit multiplication is a difficult concept to teach. Long gone are the days where we teach one method, such as long multiplication, and just *hope* that all of our students catch on and can use that method effectively. Today we know the importance of teaching multi-digit multiplication more strategically. This ensures that every student in your classroom can experience success in some way. It also ensures that students’ knowledge is built on strategically, and that they really UNDERSTAND the process of multi-digit multiplication.

Alternatively, if you are looking for a resource where all of the work is done for you, you may be interested in this Multi-Digit Multiplication Station, where students work through a variety of strategies at their own pace, mastering each one as they go. Strategies are integrated in a strategic manner, ensuring that students build on their understanding progressively. See the Multi-Digit Multiplication Station HERE.

So how should you begin teaching multi-digit multiplication?

It’s important to start with strategies that will help students solve multi-digit equations mentally. Rather than jumping right into long multiplication or an effective alternative, begin with the following:

1. The commutative and associative properties. First of all, it’s important for students to remember these properties. The commutative property states that the order of the factors does not change the product. For example, 4×3 and 3×4 both equal 12. The associative property states that the factors can be grouped in different ways. For example, (7×2)x5 gives you the same product as (2×5)x7. These properties help students understand that they can manipulate equations to solve them easier.

2. Using Factors. This is a great way to teach students that numbers can be manipulated in order to make an equation easier to solve. When we teach multi-digit multiplication, our goal is not always to get a correct answer as quickly as possible. Sometimes our goal is to be able to think creatively when it comes to number. This is one of those instances. We could take the equation 4×15, and break the 15 into its factors, 3 and 5. Now we have this equation: 4x3x5. Now we could solve it like this: (4×3)x5 -> 12×5 ->60. This is just to show that there is not only one right way to solve this equation.

3. Multiplying by 10, 100, and 1000, as well as multiples of 10, 100, and 1000. Although I’ve grouped these two concepts together for the purposes of this blog post, this should be taught slowly and carefully, piece by piece. When you teach this concept, it’s important to focus on the place value rules before teaching tricks like the “adding zeros” trick. For example, when students are faced with the equation 45×100, they need to understand that the place values increase by 2 places, to make the product 4500. Similarly, when multiplying an equation like 3×1000, the place values increase by 3 places to make 3000. After students have mastered this concept, we can teach them that when there are 2 zeros in the factors, we add 2 zeros to the product. Keep in mind that these tricks should only be taught AFTER students possess an excellent understanding of the math behind the concept.

4. Breaking Up Numbers. This is one of the most useful mental math strategies out there. It involves breaking up one of the factors, multiplying in groups, and then adding those groups together. Here’s an example: In this example we break up the 12 into a 10 and a 2, and then multiply it in parts. So 12×30 becomes (10×30) + (2×30). This is much easier to solve!

We can also use this strategy to multiply bigger numbers, like 103×9. We can break the 103 up into a 100 and a 3, and then multiply in parts, like this: (100×9) + (3×9).

5.   The Box/Window Method. I love the box/window method because it utilizes the expanded form of each factor, making this a great strategy to reinforce number sense concepts. To use this strategy, we draw a box (the number of columns and rows depend on the number of digits in the factors), and then write the expanded forms of the factors along the top and the side. Then we multiply each part, and add the parts together when we are finished. If you’d like a more detailed tutorial for this strategy, please see THIS blog post, which also includes a video tutorial.

6. Partial Products. This is one of the most important strategies to teach as an alternative to long multiplication. In partial products, the equation is set up like in traditional long multiplication, but the way we multiply is different. For example, for the equation 35×3, we first multiply 3×5 to make 15. Then we multiply 3×30 to make 90. Notice that we multiplied by THIRTY, not three. This is because that 3 represents 30. This gives us 90. Now we add the 15 and 90 together to make 105. If you’d like a more detailed tutorial for this strategy, please see THIS blog post, which also includes a video tutorial.

The strategies that I’ve outlined above are the MOST important ones for teaching multi-digit multiplication. All of these strategies place an emphasis on number sense understanding and ensure that students really understand what the numbers in each equation mean. But what about strategies like traditional long multiplication?

This is a controversial topic. Some teachers believe that our teaching should be ONLY number sense focused, so that we don’t teach strategies that don’t focus on number sense understanding. These teachers tend to use strategies like partial products all year long as a very effective alternative to traditional long multiplication. Other teachers believe that we should teach the way that multiplication was taught years ago. It worked then, so why wouldn’t it work now?! These teachers tend to focus more on strategies like traditional long multiplication, and less on more current methods like box/window or partial products.

I’m not here to tell you which way is better This depends on you and your students. However, I will tell you my personal belief. Personally I tend to not go to either extreme. I am a huge believer in strategies that promote number sense understanding. However I also believe that there is a place for traditional methods for SOME of your students. You will have to be the judge here. If you have students who are struggling with multi-digit multiplication, you’ll probably choose to let them focus on partial products and box/window and leave it at that. Why add more confusion? They can be very successful with those strategies. HOWEVER, you might have some students who have an excellent number sense understanding of what you have taught so far, and are ready for more of a challenge! These students might thrive with other, less number-sense focused methods, since they already have a strong grasp of math concepts. For these students, I am going to talk about a couple of other strategies.

These next strategies are less number-sense focused, but they can be a fun way to multiply for those students who are ready for a challenge.

1. Lattice Multiplication. This is a really fun method that involves drawing a grid and using that grid to organize the numbers. Some teachers find that carrying is easier for students using this method, because the numbers are arranged in diagonal rows, so it’s easier to see where they need to be added. This strategy takes awhile to explain, so please view THIS blog post, which also includes a video tutorial of the strategy.

1. Halving and Doubling. This is a really neat strategy when multiplying by numbers like 5, 10, 25, 50, etc. All you do is divide one factor in half, and double the other one in order to change the equation, making it easier to solve. For example, if we have an equation like 25×14, we could double the 25 to make 50, and divide the 14 in half to make 7. Now we have 50×7, which is MUCH easier to solve! We can calculate this mentally, very quickly, and get our product of 350. For this strategy, students must understand that it only works well with certain numbers, and they’ll need plenty of practice with knowing which equations it works well with.
2. Traditional Long Multiplication. This brings us to traditional long multiplication. I’m not going to explain how to do this, because I think most of us already know, but this can be taught to students who are ready for an additional challenge.

The post Effective Strategies to Teach Multi-Digit Multiplication appeared first on Shelley Gray.