Simple and Effective Ways to Master Multiplication Tables (2-9)

Struggling to help students remember their multiplication facts? You’re not alone. Flashcards and timed tests only go so far. This article explores easy and effective strategies to help students quickly learn and retain multiplication tables from 2 to 9.

The Importance of Understanding Multiplication

Before diving into memorization, it's crucial to ensure students understand the meaning of multiplication. What do you want students to learn about multiplication? We want them to know what each number in the equation represents. Building the meaning behind multiplication matters. Word problems help them see what each number in the equation represents. It involves understanding what each number in the equation represents. By using word problems and models, students can visualize what each number in the equation represents.

Using Models to Visualize Multiplication

Help students best learn their multiplication tables by starting with multiplication models. I give students a word problem and then we use a model to solve. Use countable manipulatives such as blocks or counters to turn multiplication into a hands-on concept. For example, to illustrate 3 × 4, have students arrange their manipulatives into three rows, each containing four pieces. This arrangement is an array. Arrays or sets are still helpful. This visual representation helps solidify the concept of multiplication as repeated addition.

One teacher shared her experience of tutoring students who struggled with multiplication: "I tutored two students today. Both struggled with multiplication facts and understanding multiplication this past school year. I bought your meaning of multiplication bundle and it has helped them so much. We started with equal groups then worked forward and ended with area. They now comprehend that multiplication is repeated addition. They now use all of the models for figuring out the product of a multiplication fact they don’t know. Especially those trickier multiplication facts. Even word problems. Thank you for this resource!"

Strategy-Based Instruction: Unlocking Patterns

Our number system is amazing, and there are many patterns we can discover. We can use those patterns as strategies for solving and quickly finding the answer to multiplication facts. When students use these strategies, their brains take a certain pathway to solve. As they get more practice with them, those pathways become stronger and faster. And that’s how to learn times tables quickly and in a meaningful way. It’s not just to pass off a timed test. These strategies bring lasting success.

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Most students won’t discover these strategies for themselves. So as teachers, we need to explicitly teach them. These are perfect for 3rd grade students learning multiplication for the first time.

To teach these lessons, I use display pages as slides to guide me in introducing them. These are very visual and show the strategies with different models. They guide me on what to say and do. Then students are ready for some guided practice. I like to use worksheets for this. I’ll project the worksheet up on the board so we can do a couple problems as a class. After that, I’ll give students one more worksheet. They do this on their own as independent practice. As they work, I sit over at our classroom table. As students finish, they come line up by me and I quickly look over their work, helping them fix any mistakes. Then I like to get students additional practice with the strategy. So I have them do a scoot activity with task cards. I tape task cards around our classroom. These show the strategy with models. Then students take a recording sheet, go around to the different task cards, and write the matching equation. I love how this activity gets students up out of their seats and moving. This is also a great activity to have students work with a partner. That way they can support and help each other. Once they are finished with the scoot activity, I have students work with that same partner to complete a puzzle activity on that strategy. The puzzle has different pieces showing the strategy in a visual way with models. Finally, I’ll have students complete an exit ticket. I like to have a 10 minute math fact center each day. There are 5 centers and students go to just one of these a day. We don’t want to just jump into having students memorize the facts.

Starting with Easy Multiplication Facts

Wondering how to remember multiplication tables easily? Start with easy multiplication facts. Focus on the 0s, 1s, 5s, and 10s tables first to build confidence and provide quick wins. Students catch on these patterns super quickly. I actually like to help them discover these fact patterns. By using world problems and models. I can show solving a multiplication fact of 1 by using a set model, then an array, then an area model. I do this with facts multiplied by 0. Then I teach multiplication facts of 10. And then I relate this to multiplication facts of 9.

Multiplication by 0: Any number multiplied by 0 is always 0.
Multiplication by 1: Any number multiplied by 1 is the number itself.
Multiplication by 10: Any number multiplied by 10 is that number with a 0 added to the end.
Multiplication by 5: Numbers in the 5 times table always end in a 0 or 5.

Doubles and the "Doubles Plus One More Set" Strategy

In second grade, students work to memorize addition double facts. These are facts where you are adding the same number together. 2 groups of 4 is 8. 2 groups of 5 is 10. 2 groups of 6 is 12. These are double facts. And they can help students find multiplication facts of 3 easily. So when a student sees a multiplication fact of 3, like 3×4, they can first think of the double fact. 2×4=8. Then just add one more set of 4. When teaching the Doubles +1 Set, I like to first make it very visual. I want students to see the double fact very clearly and then add the additional set. Our brains love novelty, and they see double facts as novelty. It’s easy for students to commit double facts to memory.

This strategy leverages their existing knowledge of doubles to learn the 3s table.

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Mastering the 4s Table: The Double-Double Strategy

What’s the best way for students to learn multiplication facts of 4? We double 8, 8×2=16. I like to show this strategy in very visual ways with set models and area models. For set models I show the 4 sets split in half. Then for area models, I show the area split in half with 2 different colors. After getting students practice with those, I take away the models and have them just work with numbers. This strategy works for multiplication facts of 6 and 8. To multiply by 4, double the number and then double it again.

The Halving and Doubling Strategy for 6s and 8s

Here’s how it works. You think of the fact in sets. Take half of those and get the answer. Let’s look at an example with 6×7. That is 6 groups (or sets) of 7. Take half of those and you have 3 sets of 7. Well 3×7=21. Let’s look at another example with 8×6. We can think of this as 8 groups (or sets) of 6. Half of that would be 4 groups of 6, or 4×6. 4×6=24, then we just double that. Like the strategies before, I like to introduce this strategy in a very visual way with set models and area models. Then I’ll take away the picture and just have students working with the numbers. I like to list the fact out as the repeated addition equation. This is a strong mental math strategy. When students work with 6×7 using this strategy enough, they will start to just associate it with 21+21=42.

The "Adding One More Set" Strategy for 6s and Beyond

A student might not know 6×6, but they do know 5×6=30. Want to learn how to help students remember multiplication facts? This one is really easy for students to see with set models. I’ll show 5 sets of 6 all grouped together, then I show another set of 6 next to it. Area models are also really good to show this. I show 5 rows of 6 in one color, then one more row of 6 in another color. After students get the hang of this with models, I’ll have them work with just the numbers. If a student knows 5 times a number, they can easily find 6 times that number by adding one more set.

Partial Products: Breaking Down Multiplication

Partial products is another multiplication fact strategy that helps students use known facts to find unknown facts. But this time they aren’t limited to just adding one more set. They are going to break apart the fact into easier facts. Teach partial products as a multiplication strategy. Let’s look at an example of 8×8. A student may know that 5×8=40. But that’s only 5 groups of 8. We need 3 more. So 3×8=24. Then you add the answers, 40+24=64. When first introducing this to students, I break apart the equations for them. This strategy involves breaking down a multiplication problem into smaller, more manageable parts. For example, to solve 7 × 8, a student could break it down into (5 × 8) + (2 × 8).

Division Strategies to Reinforce Multiplication

Division is the inverse operation of multiplication, and understanding the relationship between the two can significantly aid in memorization.

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Fact Families: Connecting Multiplication and Division

Teach fact families as a division fact strategy. Let’s look at an example. This is the best strategy to help students learn division facts. If a student doesn’t know 42÷7, then they can think “what number multiplied by 7 equals 42? 6! What’s the best way to get students practice with fact families? Each triangle has the 3 related numbers in the corners. Students use those 3 numbers to write the related facts. It’s great to post a blank one on your math review wall. Each day as part of our math warm up, fill in 3 related numbers and then students give you the 4 matching equations.

Partial Quotients: Using Known Facts to Divide

Teach partial quotients as a division fact strategy. Let’s look at an example with 49÷7. An easy fact of 7 that I know is 35÷7=5. That’s only 35 and we need to get to 49, so what’s the difference? 14. So we divide 14 by 7 to get 2. Then add our two answers, 5+2=7. You can easily show this strategy in a visual way with arrays and area models. I first help students split the facts apart. Then we start with the easy facts so that students find quick wins.

Engaging Activities and Practice

As students learn and work with these strategies, they will be able to solve a fact in a few seconds or less, or just commit the facts to memory. When you follow these lessons, you are also helping students master important 3rd grade math standards.

Incorporating Games and Centers

Make multiplication practice more engaging with a program that drills the concept as part of a game, or captivating story. In Mathletics, for example, students solve multiplication problems as they travel through the outer space “multiverse”.

Math Fact Centers: Dedicate a portion of each day to math fact practice through centers.
Scoot Activities: Tape task cards around the classroom for students to solve in a dynamic, active way.
Puzzle Activities: Use puzzles that visually represent multiplication strategies.

Real-World Application Through Word Problems

The shift to words can be tricky, so ease students in by visualising the problem to begin with. Look at a collection of multiplication word problems side by side, and help students discover the underlying formula (schema) that links all of them. If you’re tired of reinventing increasingly complex word problems, consider trialing an EdTech program that comes pre-loaded with them. You can also check out our range of online mathematics learning programs.

A Charlotte Mason Approach to Multiplication Tables

Today we want to answer some questions that we have been given about multiplication tables; learning them in a Charlotte Mason way, when to move on and when to stay until the child has learned them completely; all of those wonderful questions that so many of us ask as we work with our child day to day in that mountainous land of mathematics. As we talk about these questions we have with learning the tables and when to move on, we’ve called in the expert, Richele Baburina.

Introducing Multiplication as Quick Addition

The way that we introduce the ideas of multiplication. And we start by introducing the idea of multiplication as quick addition. So we’re giving our students interesting problems for which they already have the tool of addition to solve. But as they are adding more and more times, say the number 4, we have given the number 4, five times. And then we get to show them that there’s actually a shorter method to do this. And we’ll introduce the symbol for times at that point. So even why we say times is going to be evident to the student. And it’s going to help that idea embed in them. So that’s our basic introduction. Once we do that, we’re going to move to the tables. Also, it is important that students don’t memorize tables or math facts without ever having proven them. So this introduction is going to give them a chance to prove each of those facts. It is important that students don’t memorize tables or math facts without ever having proven them.

Memorization with Visualization

Each multiplication table is taken individually. So we start out with the 2s table. We might write one number 2, and then ask “How many times do you have 2?” “One time,” and then we put a little 1 above it. And 2 taken 1 time is 2, and then the answer goes down below. So we’re basically setting up our little column multiplication problem right there. Then we’ll have another 2 in the center row. Now how many times do you have 2? Two times, so we put a little 2 above that. And what is 2 taken 2 times? Four; and we continue on to either 10 or 12. It’s up to you, what you want to do with your student. Once we’ve done this, the student is going to take time to visualize it. And this is where the picture-study part comes in. He has a written table to visualize, to look at, until he can see that in his mind’s eye. Now the difference is we’re not going to turn it over quite yet. He will have the table to continue to use until he doesn’t need it anymore. We’ll erase a few numbers out of there for him to fill in. And then from there he will say it through again. And then we’re going to give him interesting little problems so he will get to use the multiplication table if he wants to. I might have this out of order. We’ve got it all in order in the books. But then he is going to write the same table out in his math notebook. And the child will work with that until he has achieved a comfort level with it. And you’ll see your students start to not look at the table; or some children, their personalities, they don’t want to look at the table. And so we might give them a little extra time to answer those problems. But they have that table whenever they need to refer to it. So then from there, we have some interesting experimental work in longer multiplication. So that student might be multiplying 21 by 2. And so this adds a little more interest to it. Now we want to keep our questions lively and interesting. So, since each child works at this individually, some children learn their multiplication tables quickly, some take a little bit longer, and some actually take quite a long time. When we progress to the next table or the next concept is going to be individual for each child.

Engaging Multiple Senses

Learning the tables involves a lot of senses. It is a multi-sensory experience, if you will. You’ve got the kinesthetics, because they can work with items to set it up and remind themselves, “Well, if I do have seven 2s, how much is it?” And they can make dots, or they can use objects. And you’re discussing it with them. They are saying it through as they go. They’re also having the visual picture-study effect, where you’re taking some out, putting some in. So they have the hearing, and the speaking, and the hands-on, and the visual. It’s all intertwined there. So you can customize it. You’re giving your student a chance to use all of his senses, but you could allow him to use the strongest one more.

Since our children might be more kinesthetic learners, they might want to build each individual table using manipulatives or our everyday objects. Pennies are very good for this. A student who maybe just doesn’t like working with objects might be using just hash-marks in his math notebook, just so that he can see kind of the sense there. But the time where they get to visualize and study that math table, they are looking and discovering, on their own, these amazing patterns, which is going to help them. I don’t want to give away every pattern, but if you allow your student time to look for those patterns, it’s amazing what they’re going to find. It’s not just, “Look at this and get a static mental snapshot of it and then see if you can recite it.” You want their minds engaged, looking at it like a puzzle almost. “What can I find here? What can I discover for myself?” Yes, and this might take place, those discoveries, as they’re writing the tables out. They might see those patterns on their own.

Individualized Progression

Some students will pick this up very quickly, some will not take it as quickly, and some will take quite a while to actually get all of those math facts cemented in their minds. So the question is, does my child have to have memorized the 2s table in complete total before we start going to the 3s table? How long do we wait? When do we know when to move?

Maybe for the traditional student, you see he is working comfortably. He no longer needs to use that table. He is ready to move on, and you can see that quite obviously. Second, remember, we are still working with the discipline of good habits. So when we said that there is no royal road, we know that it can be difficult to learn. It is a challenge to learn these tables, especially maybe the 7s and the 8s tables. So we also want to make sure that it isn’t that our student just doesn’t want to put in the hard work. We need to be there watching for that. And then, third, if you feel confident that you have done all of these steps, and it’s growing so wearisome for him, you don’t want to erode his confidence. And so Charlotte tells us, then we can move on to a different concept or a different table. Some children who have a hard time grasping, or just getting into their minds’ eyes that multiplication table, sometimes they might grasp other concepts much more quickly. So we have time to review those tables and to continue to work with those math facts. If we look at our students and say, “It’s time to move on,” and you go to the next concept, we have time of mental math to solidify those facts. We also have a time when we can use our number sentence cards, which is a great resource that Simply Charlotte Mason has. And there are maybe six different problems on each one. I think we have 500 cards for the multiplication facts. And so we can use those as a way to help solidify those facts.

Continuous Review

Even when you move on to another concept, you’re not abandoning the table. You can still have touches along the way.

We could use those math tables as review. And so you’ve moved on to another concept. Now I know my student has a harder time keeping this table in his mind. So we’re going to use that table work for our time of review. So we have bookmarks in our books that you can use to mark which tables that you want to be sure that you keep reviewing. And so that’s another way. Plus, as you move on in concepts, you’re going to be solidifying those facts. So say you’ve moved to finding the area of a rectangle, your student is going to be multiplying the length of those sides. So we are going to continue to use our math facts. Those are another opportunity to review those as well.

Additional Tips and Resources

The Commutative Property: The commutative property of multiplication is the ability to reverse a sum and still get the same result. If students understand the commutative property, they’ll be able to handle multiplication tasks much more flexibly. You might have to drop a few hints, but they’ll soon realise all they need to do is rotate the paper ninety degrees. That’s a good chunk of the 12 × 12 multiplication table that can be calculated with little effort. For example 4 x 9 is easier to work out than 9 x 4. Switching the multiplication sum around makes it easier to answer.
Drill and Practice: Use drill and practice strategies to commit the other multiplication tables to memory. These could be set up as engaging, game show style competitions - but remember to make them inclusive for learners who might need extra support.
Timestables.com: At Timestables.com you can easily practice all of your tables. The arithmetic problems are clear and simple so you can immediately get started on practicing your tables. Select one of the multiplication table you wish to practice from the list below and show what you can do on the speed test or printout great worksheets.
5-Step Plan: Learn the times tables with the 5-step plan. We developed an innovative five step plan to help pupils learn the times tables in an effective and efficient way. This method has been tested at several schools and is recommended by teachers. Step 1a: View, read aloud and repeat. To get familiar with the table. Step 1b: Fill in your times tables answers in sequence and check if you got them all right. Step 2: Drag the correct answers to the questions. Step 3: Fill in your answers for the mixed questions and check if you got them all right. Step 4: Multiple choice questions will help you to improve by looking at the questions in a different way. Step 5: Proof your knowledge and get the diploma. When you finished the 5 steps you can play the memory game or exercise with the worksheet. Other way to train more are with the tempo test, the 1 minute test or to play the times tables games. We advise to exercise daily for 15 minutes for maximum result.

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