Hands up if you’ve ever seen a student completely defeated over learning the multiplication facts. Do your students view multiplication as

boring?

un-interesting?

difficult?

impossible?

What if I told you that you can help your students easily master the times tables using this one game-changing strategy that will make multiplication fun, interesting, and meaningful!

Focusing on the connections and relationships between facts will transform how your students understand multiplication. But so often this is left out of multiplication instruction.

In this article I’m going to tell you exactly what you can do in your classroom to help students begin forming the connections and relationships that are so important for true fact fluency and understanding. 

This will give kids the “a-ha” moments and the ability to solve ANY fact – even if it hasn’t been “memorized.” When students understand that multiplication facts are all related – that they can use one fact to help them solve another – the thought of learning the times tables suddenly becomes much less intimidating.

Here are three simple tips for how you can help your students easily master the times tables by focusing on connections and relationships between multiplication facts.

Tip #1: Incorporate Concepts Like Doubles and Halves

Our students need to understand how facts like 3×5 and 6×5 are connected. Or how facts like 10×2 and 5×2 are connected. This concept of doubles and halves can be made visual with an array. When students can look at an array and actually SEE what the facts mean, it becomes easy to visualize 5×2 as half of 10×2.

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I go more into detail on this concept in this free guide – Three Reasons Your Students Aren’t Mastering The Multiplication Facts (and what you can do about it). Students must understand that multiplication facts aren’t isolated pieces of information they need to memorize in a meaningless way. Facts are related and connected, and we can use this knowledge to master the times tables…without having to memorize! When we understand connections, we can literally solve anything!

Imagine how understanding doubles and halves can help when we get past basic facts? What about solving something like 35×7? We could do this quickly in our heads when we understand that it will be half of 70×7. Or how about 25×12? This understanding of doubles and halves can help us solve this by first thinking of 50×12, then simply halving the product.

Tip #2: Treat Sets of Facts as Related to One Another (Not as Isolated Pieces of Information)

When we help students see that sets of facts are related, suddenly multiplication gets a lot more fun. We don’t HAVE to memorize the facts – all we have to do is understand them!

This activity from The Multiplication Station shows how we can help students make a visual connection between the 10’s and 9’s facts. We don’t have to memorize all the 9’s facts! All we have to do is understand how they are related to the 10’s facts! It is this understanding that will enable students to easily solve a fact like 9×25 without resorting to traditional long multiplication or a calculator.

We can help students master the 9’s times tables simply by helping them understand the connection to the 10’s facts.

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Here’s another example, using the x2, x4, and x8 facts. Here we can see that these facts are all related. Using the first example on this page, let’s take a look at all the connections we see! 2×10 is half of 4×10. 4×10 is the double of 2×10. 4×10 is half of 8×10. The product of 8×10 is four times the product of 2×10. And it goes on and on. These connections are powerful.

I encourage you to have your students work with manipulatives to help visualize these connections. Sometimes we make the mistake of thinking our students are “past” manipulatives when they get to Grade 3 or 4 but this couldn’t be further from the truth. Using objects that students can move and manipulate will help them solidify these connections and truly SEE them.

Tip #3: Use Arrays

As you may have noticed, I love using arrays for multiplication. I believe that arrays are THE most powerful way to visualize multiplication. They are NOT simply for introducing multiplication. Arrays are for exploring relationships and connections between facts.

So many students don’t see arrays in their minds when they think about what multiplication means.

To help students begin visualizing arrays, we can use simple tools like a rekenrek. These pictures show how we can build an array to show 3×5 (or 3 rows of 5), and then simply rotate the rekenrek to show that 5×3 (or 5 rows of 3) has the same product (the commutative property). This is a fantastic way to make multiplication concrete.

In this activity from the Design a Playground Math Project, students are using arrays in a representational way, and then connecting that to abstract thinking when they write the facts. Again, we are reinforcing the commutative property and the relationship between facts like 2×8 and 8×2.

Connections have the power to change the game for your students when it comes to multiplication and learning the times tables. If you are having trouble getting started with connection-making, begin with these simple steps.

• Use manipulatives to form an array. Ask, “What can we add to this array to form a new fact?”
• Always help students make connections in the concrete and representational phase, not in the abstract. They need to SEE the connections in order to understand them. We can’t expect just to show students two written equations and have them understand the connections at a conceptual level.

The resources mentioned in this blog post are linked below:

• Free Guide: 3 Reasons Your Students Aren’t Mastering the Multiplication Facts (and what to do about it)
• The Multiplication Station: a Self Paced Station for Multiplication Fact Fluency and Conceptual Understanding
• Design a Playground Multiplication Math Project

The post Help Your Students Easily Master the Times Tables with This One Simple Strategy appeared first on Shelley Gray.

The post 5 Fun Multiplication Games to Practice the Times Tables appeared first on Shelley Gray.

The Best Way to Teach Multiplication Facts: 12 Steps to True Understanding

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Target Number: A Card Game to Practice Math Facts

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So you’re ready to implement mental math addition strategies this year, but aren’t sure where to start! All the different ways to teach addition facts

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The post Math Fact Fluency: Simple Steps to Help Students Become More Fluent appeared first on Shelley Gray.

The post Four Ways to Represent Multiplication appeared first on Shelley Gray.

It is so important that each set of multiplication facts is reinforced in a variety of ways, including problem-solving, finding missing unknowns, skip-counting, making groups, arrays, and picture representations. We want our students to REALLY understand each set of multiplication facts so that mastery becomes accessible.

This is why I recently created these Multiplication Task Card sets. With 24 task cards in each of the 17 sets, the basic multiplication facts are reinforced in a wide variety of ways.

If you are currently using The Multiplication Station in your classroom, these task cards are a fantastic way to support your students! Make the task cards available at the end of each level for students to practice before their oral test, or as extra support for students who still need a bit of help mastering the facts after a level.

I’d love to give you a free set of task cards! Sign up HERE and I’ll send you the Multiplication by Two Task Cards right to your inbox.

Want to tackle all of the basic multiplication facts in your classroom?

GET THE FULL MULTIPLICATION TASK CARDS BUNDLE HERE.

Next Steps:

Ready to get serious about teaching multiplication in a strategic way? Read more about effective strategies for teaching basic multiplication HERE.

The post Free Set of Multiplication Task Cards appeared first on Shelley Gray.

The main mindset shift that we must make is that we are not simply teaching students to memorize the facts, but rather we are teaching students how to think about multiplication. We must take a strategic approach to our teaching that emphasizes conceptual understanding first. Fact fluency will be a bi-product of excellent understanding.

One thing that we can do is teach strategies that make multiplication easier to understand.  Although quick recall is a goal, we want our students to have effective, efficient strategies that will enable them to use what they know for many other multiplication situations. Read more about effective strategies for multiplication HERE.

We can also teach the facts in a strategic order. When I first started teaching multiplication, I taught the facts in regular numerical order – the 1’s, then the 2’s, then the 3’s, etc. This is a mistake!

Instead, we want to teach the easiest facts first, and leave the hard ones til last. Why? Simple! Because when we teach like this, we give students a strong foundation early on, enabling them to derive facts easily. This way of teaching also results in high motivation, as students can see their progress and how rapidly they are learning their facts.

This free guide will explain a suggested order of teaching the basic multiplication facts. This will result in maximum confidence, motivation, and success. Just click on the image below  to begin  downloading.

Looking for even more support? Implement all of these ideas easily using The Multiplication Station.

The post Free Guide: A Suggested Order of Teaching for the Basic Multiplication Facts appeared first on Shelley Gray.

The post Five Reasons Your Students Are Struggling With The Multiplication Facts appeared first on Shelley Gray.

INTRODUCTION

Multiplication facts can be intimidating for both students and teacher. Luckily, there are strategies that we can use to help us teach the multiplication facts more effectively so that every student can be successful.

The main mindset shift that we must make is that we are not simply teaching students to memorize the facts, but rather we are teaching students how to think about multiplication. We must take a strategic approach to our teaching that emphasizes conceptual understanding first. Fact fluency will be a bi-product of excellent understanding.

One thing that we can do is teach strategies that make multiplication easier to understand.  Although quick recall is a goal, we want our students to have effective, efficient strategies that will enable them to use what they know for many other multiplication situations.

Related: 12 Steps to Teaching Multiplication for True Understanding

We can also teach the facts in a strategic order. When I first started teaching multiplication, I taught the facts in regular numerical order – the 1’s, then the 2’s, then the 3’s, etc. This is a mistake!

Instead, we want to teach the easiest facts first, and leave the hard ones til last. Why? Simple! Because when we teach like this, we give students a strong foundation early on, enabling them to derive facts easily. This way of teaching also results in high motivation, as students can see their progress and how rapidly they are learning their facts.

A STRATEGIC ORDER FOR TEACHING THE MULTIPLICATION FACTS

Here is a recommended order for teaching the facts. Later, I will discuss the reason for teaching in this order.

x2

x10

x5

x1

x0

square facts (ex. 3×3, 4×4, 5×5, etc)

x4

x3

x9

x6

x7

x8

WHY DO WE TEACH IN THIS ORDER?

To make this more visual, I’ll illustrate it with a multiplication chart. I encourage you to have your students shade in a multiplication chart as they master the facts. If you are using my Multiplication Station to teach basic facts, this has been included for you.

Since most students already know the x2 facts (addition doubles), we start there. Once your students master this set of facts, their shaded chart will look like this. We have shaded all of the 2’s facts. Now remember that this includes facts that have 2 as the 2nd factor. The commutative property of multiplication states that the order of factors does not change the product, so 2×3 is a 2’s fact, but so is 3×2.

Now it’s on to the 10’s. The 10’s facts are typically another easy set of facts to learn, so it won’t take long for students to master these ones. Once they have mastered them, they can shade in the chart, and it will look like this! It’s really motivating for your students to see how many facts they already know!

After the 10’s, we learn the 5’s using the “half of 10” strategy. Now here is our multiplication chart!

Once we master the 5’s, we move on to the 1’s, and then the 0’s. Now that students understand multiplication, it is easier for them to grasp the somewhat abstract nature of multiplying by 1 and 0. Look at our chart now! We ALREADY have mastered SO many facts on our multiplication table! This is so motivating to see!

After the 0’s we work on the square facts like 4×4, 5×5, 6×6, etc. Knowing these facts well is going to enable us to use them in the future to solve other derived facts. For example, we’ll be able to use what we know about 6×6 to solve 6×7. We have now mastered most of the facts, and we haven’t even really gotten into the more difficult facts yet!

This is where we get into the facts that are going to demand a bit more work. The great news is that we really don’t have that many facts left to master when it comes right down to it. Next, we move on to the 4’s, 3’s, and then the 9’s. For the 4’s we use the doubles’ doubles strategy, and for the 3’s we use the doubles plus one more group strategy. For the 9’s we will use what we know about 10’s and then just subtract one group. (read more about that here.)

We still have to work with the 6’s, 7’s, and 8’s, but we know most of them already anyways (because of the commutative property)! Once your students learn the 7’s, they will see that they have now worked with every single fact on the multiplication chart.

As you can see, this suggested order of teaching the multiplication facts is exciting, motivating, and encourages success for your students! Let’s make multiplication as easy as possible!

If you would like a printable copy of this suggested order of teaching, you can download one free from HERE.

Need further support for teaching multiplication?

If you are looking for a resource where the work is done for you, you may be interested in The Multiplication Station – a self-paced, strategic 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.

Or see all Multiplication resources that will help bring multiplication to life in your classroom, including math projects, escape rooms, games, task cards, and more here!

The post A Suggested Order for Teaching the Basic Multiplication Facts appeared first on Shelley Gray.

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.