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

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Multiplication facts can be difficult to learn, and difficult to teach. Luckily, there are strategies that we can use to help us teach the multiplication facts more effectively so that every student can be successful.

One thing that we can do is use mental math strategies that make the calculations easier to understand. Although memorization is still a goal, we want our students to have effective, efficient strategies to fall back on. Read more about effective strategies for multiplication HERE.

**Another thing that we can do is 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 teach students the majority of the basic facts before things even begin to get challenging! This is very motivating for your students, as they can see their progress and how rapidly they are learning their facts.

Now, before I get started talking about these strategies, I do want to let you know that I have a **free webinar** on this topic. Throughout the approximately 40-minute webinar I’ll discuss strategies for every set of facts, as well as a suggested order of teaching that will make multiplication so much easier for your students. **You can read more about that webinar and get registered HERE.**

Alternatively, 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.**

**Recommended Order**

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

- The 0’s
- The 1’s
- The 2’s
- The 5’s
- The 10’s
- The 11’s
- The 9’s
- The 4’s
- The 3’s
- The 6’s
- The 7’s
- The 8’s
- The 12’s

**So why do we teach in this order?**

To make this more visual, I’ll illustrate it with a multiplication chart. I actually do 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.

Once your students master the 0’s facts, their shaded chart will look like this. We have shaded all of the 0’s facts. Now remember that this includes facts that have 0 as the 2nd factor. The **commutative property of multiplication** states that the order of factors does not change the product, so 0x3 is a 0’s fact, but so is 3×0.

Now it’s on to the 1’s. The 1’s facts are a really easy set of facts to learn, so it won’t take students long 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 1’s, we master the 2’s. These are another easy set of facts, because they are just the addition doubles (read more about that strategy here). Now here is our multiplication chart!

Once we master the 2’s, we move on to the 5’s, and then the 10’s. Again, these are both generally fairly simple sets of facts to learn. Take a look at our chart now! We ALREADY have mastered SO many facts on our multiplication table! This comes back to the commutative property – we know 10×8, so we also know 8×10 – which is also an 8’s fact.

After the 10’s we work on mastering the 11’s. This is yet *another* simple set of facts to learn, because it follows an easy pattern. And now look at our chart! We have now mastered the majority of facts, and we haven’t even really gotten into the difficult facts yet!!! Amazing!

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 9’s, 4’s, and then the 3’s. For the 9’s we have a great trick to use – my favorite one, actually (read more about that one here). For the 4’s we use the doubles’ double strategy (read more here), and for the 3’s we use the doubles plus one more group strategy (read more about that one here).

Take a look at that chart above! This is so motivating for your students to see! We still have to master the 6’s, 7’s, 8’s, and 12’s….but we know most of them already anyways (because of the commutative property)! Once we master the 6, 7, and 8’s facts….we only have one more fact to learn – 12×12!!!!

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!

**I’d love to provide you with more support for teaching multiplication in your classroom.**

Join me for a free webinar outlining strategies for all of the facts, as well as this effective order for teaching the facts. Read more about the webinar and get registered HERE.

Alternatively, see my blog post about effective strategies for teaching multiplication HERE.

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]]>The post The Math Choice Board: Free Sample appeared first on Shelley Gray.

]]>If you’d like to see a sample of the types of activities included in the Math Choice Board, sign up below and you will receive the Getting Started Guide and one set of activities direct to your inbox!

Enjoy!

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]]>The post Growth Mindset and Math Facts: Success for Every Student appeared first on Shelley Gray.

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We hear a lot these days about growth mindset. We see it all around us on anchor charts, posters, and in the hallways. But growth mindset in the classroom has to be about more than simply telling our students that they can do hard things. We have to infuse the growth mindset into everything that we teach if we really want our students to develop and use it.

First of all, let’s discuss a few benefits of growth mindset. We know that students with a growth mindset rather than a fixed mindset are more resilient and more excited to learn new things and take on challenges. We also know that students with a growth mindset truly believe that they can get better at something through learning. Students with a growth mindset see mistakes as an opportunity to learn, rather than as a failure.

However, we face challenges with the growth mindset when it comes to math:

- Parents often project their own attitudes about math onto their children. This happens all too often where children are told, “I was no good at math when I was in school either,” by a parent. This is projecting a fixed mindset onto the child, where he believes that because his mom/dad was not successful with math, he will not be either.
- Lack of success. Think about the students that you teach who hate math. Do they experience success on a regular basis? Do they see themselves as able to do the work? Growth mindset is all about challenging students to do difficult work and being motivated to do so. But we have to make sure that our students can be successful too. Success leads to motivation.

We can get past these challenges! Here are a few tips for infusing growth mindset into your teaching, particularly when it comes to math facts.

- Ensure that your students understand that their brain can grow stronger. Tell them, “Your brain is like a muscle. The more you use it, the stronger that it gets!” As your students succeed in areas where they used to struggle, point it out! Say things like, “All of your hard work really paid off,” “Can you tell that your brain is getting stronger in this area?”, or “Remember how hard the 9’s facts used to feel? Now they are easy for you! Your hard work and great attitude is really working.”
- Praise the effort, not the ability. Praising the ability, for example, “You are really good at math!” will encourage a fixed mindset. Praising the effort, for example, “You worked so hard to understand this, and you did it!” will encourage a growth mindset. Students will be more motivated to take on new challenges when they are praised for their effort.
- Keep your standards high, but still ensure success on a regular basis. Your students need to feel successful and able. You can do this by providing work that is achievable, but still challenging. When you teach multiplication, don’t begin with the hardest facts. Start with the easiest ones. Let your students know what it feels like to be successful. It’s a great feeling! Then you can increase your expectations once you see that they are ready for the challenge.
- EMPOWER your students. This can be done through providing lots of choice, and allowing students to be in control of their learning. Everyone loves the feeling of being in control of themselves, your students included!

**Are you using Math Stations to teach math facts in your classroom?**

If you are using any of my self-paced, student-centered Math Stations for basic facts, this is a great way to infuse growth mindset into your classroom! Growth mindset is built right into the stations (which is why students find them so motivating), but here are a few quick tips that will help you even more:

- When you do the oral test with a student, take a second to talk about the set of facts that she just finished. Did it feel challenging? Did it feel easier as she kept working at it? Did she do anything special to make that particular strategy or set of facts easier to learn?
- When a student is beginning to learn a difficult strategy, talk to him about how exciting it is to take on a new challenge! Remind him how past levels felt hard at first, but then got easier as he worked at it.
- Use effort-based praise. Rather than, “You are really good at the partial products strategy,” you might say, “I can sure tell that you have been working hard to understand the partial products strategy! You’re getting fast! That hard work is paying off. We are going to have to find you some more challenging activities to do pretty soon!”
- Have students use their personal tracker progress charts to see just how far they’ve come and think about where they are headed.

I’ve got some friends who have also written about using growth mindset in other areas of the classroom! Check them out below.

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]]>The post The Math Choice Board appeared first on Shelley Gray.

]]>Would you like to implement an engaging, curriculum-related choice board as a math station in your classroom?

Do you need a way to motivate your students when they first arrive in the classroom, at the beginning of class, or when they finish their work early?

I am so excited to introduce you to the Math Choice Board!

Several years ago, I created __ The Early Finisher Board __– a solution for the fast finishers in your classroom. Over the years, thousands of people have successfully used that resource to motivate and engage their students. However, I have literally received hundreds of requests for something similar that focuses on Math only.

This is where The Math Choice Board comes in! The Math Choice Board is similar to The Early Finisher Board in that it allows students to choose which activities they do, and when they do them. This board consists of seven sections: **Facts****, ****Numbers****, ****Dice & Cards****, ****Patterns & Data****, ****Measurement & Geometry****, and two ****Bonus ****Tasks****.**

Each section contains an engaging, curriculum-related activity to engage your students. The tasks are switched out regularly so that your students always have new tasks to choose from!

**The Math Choice Board is designed to promote:**

*a method of spiraling the curriculum so that students receive continuous review of previously learned skills**organization and independence**freedom to choose based on personal preferences**differentiation based on interests**success for a wide variety of ability levels within your diverse classroom**student engagement**pride and excitement*

**Ways to Use Your Math Choice Board**

There are many ways to use the Math Choice Board within your classroom. You might choose to use it as:

- a Math Station or center. When students are at the Choice Board center, allow them to pick whichever activities they want from the board. This will create a sense of power and control for your students.
- a Math Warm-Up before math class begins
- a way of engaging your early finishers. Have your students choose tasks from the Math Choice Board when they finish their work, rather than simply reading or working on homework
- morning work upon arriving at school. When your students arrive in the classroom in the morning, have them work on the Math Choice Board. This will enhance predictability, routine, and organization first thing in the morning.

**Set-Up Options for your Math Choice Board**

Over the years I have received a lot of pictures of The Early Finisher Board from teachers all around the world. I love to see how teachers put their own spin on this resource in order to make it fit their unique classroom. I’ve decided to include a few of those pictures here, as the Math Choice Board is similar in layout to The Early Finisher Board. I hope that these pictures can give you inspiration for alternative ways to set up the Math Choice Board. You might use extra wall space, a bulletin board, the side of an unused cabinet, folders, or even a binder as an alternative to the tri-fold board.

**Mixing and Matching with The Early Finisher Board**

The Math Choice Board has been designed so that it can be mixed and matched with The Early Finisher Board. All of the activities will fit into either board. You may choose to include math activities from your Early Finisher Board on the Math Choice Board. Alternatively, choose activities from the Math Choice Board to include on your Early Finisher Board.

You might even create a board that has more than 7 pockets, based on the needs of your classroom! For example, you could use all of the pockets from the Early Finisher Board, and all of the pockets from the Math Choice Board to create an even larger Early Finisher Board in your classroom! The options are endless!

**Helpful Links:**

To get started with a Math Choice Board or Early Finisher Board of your own, follow the links below:

Math Choice Boards (Third and Fourth Grades currently available…more grade levels coming soon!)

Have a great day,

Shelley

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]]>The post Free Poster for the 9’s Multiplication Facts appeared first on Shelley Gray.

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]]>The post Webinar: Addition Strategies for First, Second, Third, and Fourth Grades appeared first on Shelley Gray.

]]>If you struggle to teach basic addition strategies in your classroom, you are certainly not alone. It is HARD to do a really good job of teaching addition while also doing a really good job of teaching everything else in your overwhelming curriculum.

How do you make sure that you are meeting every student where he/she needs to be met?

How do you teach a good mix of mental math strategies, while also encouraging automaticity with familiar number combinations?

How do you teach in an organized, strategic way so that students actually UNDERSTAND what they are learning?

We want to equip our students with all of the tools that they need to be successful with their basic addition facts and strategies. Luckily, there is a strategic way of teaching the addition strategies that will make this much easier for your students.

I’m holding a free webinar for teaching Basic Addition Strategies and Facts, and I would love for you to join me!

FIRST AND SECOND GRADE TEACHERS: REGISTER FOR THE FREE WEBINAR HERE.

THIRD AND FOURTH GRADE TEACHERS: REGISTER FOR THE FREE WEBINAR HERE.

Together, we’ll go through a multitude of addition strategies that will make your teaching more effective and efficient than ever before.

I’d love to help you help your students feel smart, successful, and motivated when it comes to addition.

Join me for my free webinar and we’ll get started!

Register HERE for the Grades 1-2 webinar.

Register HERE for the Grades 3-4 webinar.

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]]>The post Effective Strategies 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 of all – 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 acheive.

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 mental math strategies and memorization. Students used to be expected to memorize the facts, without any mental math instruction at all. For those students who can do this, it’s great! But there are many students who just can’t memorize all of the facts and remember them. We need to teach mental math strategies, while also encouraging memorization. This will lead to automaticity with the multiplication facts, which is our ultimate goal.

Fortunately, there are things that we can do 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.

Now, before I get started talking about these strategies, I do want to let you know that I have a **free webinar** on this topic. Throughout the approximately 40-minute webinar I’ll discuss strategies for every set of facts, as well as a suggested order of teaching that will make multiplication so much easier for your students. **You can read more about that webinar and get registered HERE.**

Alternatively, 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.**

**Strategies are ESSENTIAL.** I like to think of strategies like **tools in a tool box**. When our students see an equation, we want them to be able to choose an effective strategy that will help them solve that particular equation.

I’ve listed all of the 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 0’s Facts:** Anything times 0 is 0.

**The 1’s Facts:** Anything times 1 is itself.

**The 2’s Facts:** Use the doubles addition facts (See a full explanation HERE)

**The 5’s Facts:** Use skip-counting OR multiply by 10 and divide in half (See a full explanation HERE)

**The 10’s Facts:** Increase the place values by one place OR just add a 0(See a full explanation HERE)

**The 11’s Facts:** The same number twice for facts 0-9; use a known fact for 10, 11, and 12 (See a full explanation HERE)

**The 9’s Facts:** the 10’s subtract one group OR the sum of the digits in the product equals 9 (See a full explanation HERE)

**The 4’s Facts:** The doubles’ doubles OR 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 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)

**The 12’s Facts:** Break the 12 up into a 10 and a 2, and multiply in parts. Lastly, add the parts together. (See a full explanation HERE)

**I’d love to provide you with more support for effective strategies for every single set of basic multiplication facts, as well as a suggested order that will make your teaching more effective and efficient.**

Join me for a free webinar outlining strategies for all of the facts, as well as an effective order for teaching the facts. Read more about the webinar and get registered HERE.

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

]]>The post How to Teach the 12’s Multiplication Facts appeared first on Shelley Gray.

]]>The 12’s multiplication facts are the last set that I teach. This is because I want students to have strategies for all of the other facts first. By the time we reach the 12’s, they really only have one fact left to learn: 12×12.

Even though students have already learned strategies for all of the different facts, I still want them to practice a strategy for the 12’s facts. This strategy is one of my favorites, and can be used in so many different circumstances than just the 12’s multiplication facts.

For the 12’s facts, we want 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.

**I’d love to help you with effective strategies for every single set of basic multiplication facts.**

Join me for a free webinar outlining strategies for all of the facts, as well as an effective order for teaching the facts. Read more about the webinar and get registered HERE.

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]]>The post How to Teach the 11’s Multiplication Facts appeared first on Shelley Gray.

]]>I like to teach the 11’s multiplication facts early on. This is because the 11’s facts from 0-9 are very simple.

For the 11’s facts, simply look at the other number (not the 11) and write that number twice. For example, 11×2 is 22, 11×5 is 55, 11×8 is 88.

When I first teach this trick, I like students to come up with the rule on their own. So I show them a list of all of the facts, and ask, “What do you notice?”

Within a couple of minutes, most students will have realized the rule on their own.

This trick does not work for 11×10, 11×11, or 11×12, so you will need to teach these facts differently.

For 11×10, use the 10’s strategy of adding a 0. So you will add a 0 to the 11 to make 110.

For 11×11 and 11×12, you can use a known fact. For example, for 11×11, think, “10 groups of 11 is 110, and then one more group of 11 makes 121.” For 11×12, think, “10 groups of 11 makes 110, and two more groups of 11 makes 132.”

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 the 11’s strategy to solve this equation.

**I’d love to help you with effective strategies for every single set of basic multiplication facts.**

Join me for a free webinar outlining strategies for all of the facts, as well as an effective order for teaching the facts. Read more about the webinar and get registered HERE.

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]]>The post How to Teach the 10’s Multiplication Facts appeared first on Shelley Gray.

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

Before teaching the usual trick for the 10’s facts, you’ll want to make sure that your students understand the “number sense” behind multiplying by 10. You’ll want to teach them that when you multiply by 10, you simply increase the place values by one place.

For example, when you multiply 3×10, you increase the place values one place to get the product 30.

When you multiply 6×10, you increase the place values one place to get the product 60.

Once students have a good grasp of this rule, you can teach them the “adding zeros” trick.

I like to begin this by showing students a list of all of the facts, and asking them to find the rule. What do you notice about the products?

Students will discover, on their own, that when you multiply a number by 10, you just add a 0. For example, for 10×5, add a 0 to 5 to make 50. For 10×8, add a 0 to 8 to make 80.

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 7×10, they should see the 10 as one of the factors, and know that they can use the 10’s strategy to solve this equation. In this case students can think, “add a 0 to 7 to make 70.”

**I’d love to help you with effective strategies for every single set of basic multiplication facts.**

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]]>The post How to Teach the 9’s Multiplication Facts appeared first on Shelley Gray.

]]>Ohhhhhh, the 9’s facts. My favorite set of facts. People often are surprised when I tell them that the 9’s are a really simple set of facts to learn. This is because there is one trick in particular that makes them easy, not to mention really fun.

But before I teach you that trick, I’m going to teach you a couple of 9’s tricks that I DON’T like.

There are several tricks out there for the 9’s facts. The first one that I’ll show you uses your fingers.

So, if you want to multiply 9×4, you put down your fourth finger.

Then you are left with 3 fingers on one side, and 6 fingers on the other. So the product is 36.

If you want to multiply 9×8, you put down your eighth finger.

Then you are left with 7 fingers on one side, and 2 fingers on the other. So the product is 72.

So I’ll admit that this is kind of a neat trick. However, I just don’t like my students to rely on their fingers. I feel like we are always trying to get our students AWAY from finger counting as a strategy, so I’d rather not have them rely on this one.

Here’s another strategy that I don’t like:

For this one, we list the numbers from 0-9, and then list the numbers from 9-0 beside that.

Now you’ll see that this shows all of the products of the 9’s facts from 0-10. For example, the second row down shows the product of 9 and 2:

The sixth row down shows the product of 9 and 6:

So again, this is a neat trick, but in my mind it’s not practical. When my students are faced with a 9’s equation, the last thing that I want them to do is take 3 minutes to list out all of the numbers, and then count the rows down to figure out the product.

**This next strategy is a true mental math strategy. This is one that you’ll want to introduce your students.**

We know that the 10’s multiplication facts are an easy set to learn – just add a 0. So for the 9’s facts, we can use a 10’s fact, and then just subtract one group.

For example, for 9×3, first do 10×3 to make 30, and then subtract one group of 3 to make 27.

For 9×7, first do 10×7 to make 70, and then subtract one group of 7 to make 63.

Now, FINALLY, I’d love to show you the trick that I always use with my students. I love this one because it is FUN, motivating, and SO fast once you get the hang of it. I always start out by telling my students that it will seem confusing at first. I tell them that they probably won’t get it the first time. But by the second or third time I show it to them, they’ll be starting to catch on, and by about the 5th time I show them, a little light bulb will go off and they will get it! I find that this little “disclaimer” helps take care of any frustration they might have when they don’t understand it the first time around.

I begin by listing all of the 9’s facts from 0-10. I ask students what they notice about the products. In particular, I want them to add the digits in each product.

9×1=9

9×2=18

9×3=27

9×4=36

9×5=45

9×6=54

9×7=63

9×8=72

9×9=81

9×10=90

**So what do you notice? In every product, the digits can be added together to make 9. Students have to remember this.**

Here’s how to perform the strategy:

**Step One:** Look at the equation. Point to the number that is NOT the 9. For example, in the equation 9×4=___, point to the 4.

**Step Two:** Subtract 1 from the number that you are pointing to. In this example, you would think “4-1=3.” The difference (in this case, 3) will be the first number of your product. So now our equation looks like this: 9×4=3__.

**Step 3:** When you add the numbers in the product together, they will make 9. So now we need to think, “What can I add to 3 to make 9?” In this case the answer is 6. Add this 6 as the second digit in your product: 9×4=36.

Let’s try another one: 9×8.

**Step One:** Look at the equation. Point to the number that is NOT the 9. For example, in the equation 9×8=___, point to the 8.

**Step Two:** Subtract 1 from the number that you are pointing to. In this example, you would think “8-1=7.” The difference (in this case, 7) will be the first number of your product. So now our equation looks like this: 9×8=7__.

**Step 3:** When you add the numbers in the product together, they will make 9. So now we need to think, “What can I add to 7 to make 9?” In this case the answer is 2. Add this 2 as the second digit in your product: 9×8=72.

**As you can see, this works with any basic multiplication fact involving a 9. Notice that in every case, the sum of the numbers in the product add up to 9!**

As I mentioned before, you’ll need to show this to your students several times in order for it to really make sense, but once they understand, it is SO effective!

**I’d love to help you with effective strategies for every single set of basic multiplication facts.**

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