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

PINTEREST BOARDS

I love Pinterest as a visual way to easily organize ideas. On my Multiplication and Division Pinterest board, you’ll find a wealth of ideas from a variety of sources around the web! Be sure to follow my boards, as I am constantly pinning fresh new teaching ideas!

BLOG POSTS

Over the years I’ve written a lot of different blog posts about multiplication tips and strategies. Click on any one below to visit!

Effective Strategies for Teaching the Basic Multiplication Facts

Free Guide: A Suggested Order for Teaching the Basic Multiplication Facts

8 Ways to Use Multiplication Flashcards in your Classroom (with Free Printables)

5 Reasons That Your Students Aren’t Mastering the Basic Multiplication Facts (and what you can do about it)

Free Poster for the 9’s Multiplication Trick

How to Teach the 12’s Multiplication Facts

How to Teach the 11’s Multiplication Facts

How to Teach the 10’s Multiplication Facts

How to Teach the 9’s Multiplication Facts

How to Teach the 6’s, 7’s, and 8’s Multiplication Facts

How to Teach the 5’s Multiplication Facts

How to Teach the 4’s Multiplication Facts

How To Teach the 3’s Multiplication Facts

RESOURCES

I love helping teachers teach multiplication! An effective approach can be such a game-changer for your classroom!

The Multiplication Station

Of any of my multiplication resources, The Multiplication Station has touched the most students – tens of thousands of students around the world. It utilizes all of the most effective ways to teach multiplication, and incorporates those into one, self-contained station that students work on independently, at their own pace. I won’t spend too much time talking about all of the benefits that you will see when you start using this resource, but I encourage you to read through the comments from the thousands of teachers who have used this resource HERE.

Other Multiplication Resources

See my entire selection of multiplication teaching resources here

Multiplication Equation of the Day: Basic Multiplication Facts Booklet

Task Cards for Basic Multiplication: The Big Bundle

Fact Family Array Task Cards: Multiplication and Division with Arrays

Multiplication Arrays Task Cards

Basic Multiplication Problem Solving Task Cards

Multiplication or Division? Problem Solving Task Cards

Multiplication Facts and Strategies Mini-Book

Get Up and Move: Basic Multiplication Gallery Walk

Get Up and Move: Introductory Multiplication Gallery Walk

Multiplication Strategy Posters for 0-12 Times Tables

Basic Multiplication Facts Flashcards: Flashcards for Basic Multiplication Facts

Springtime Multiplication Math Stations (also great for home math bags)

The Math Choice Board (includes a variety of math topics and tasks)

FREE: Quick Tasks for Multiplication Flash Cards

FREE: The 9’s Trick for Multiplication Poster

The post Teaching Basic Multiplication | A Round Up of Ideas, Tips, and Resources 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.

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.

Do you dread teaching long multiplication and division every year? Are you frustrated by the fact that very few of your students actually GET it?  What if you could teach your students strategies that would BOOST their conceptual understanding, as well as make multi-digit multiplication and division FUN to learn? Is that possible? Absolutely. Through a practical, strategic approach, we have the power to make a big impact on the success that our students experience with these operations.

Who is this mini course for?

• 4th-6th grade teachers teaching multi-digit multiplication and division
• 3rd grade teachers who have some students far above grade level and who need an extra challenge
• math intervention teachers
• parents who are interested in helping their child with multi-digit multiplication and division

Content

• “Old Math” vs “New Math” – MYTH BUSTED!
• The essential strategies that need to be taught BEFORE traditional methods for long multiplication and division
• A variety of approaches and which students should be using each one
• Q&A session
• Free resources for all attendees

See the full mini course schedule and get registered HERE.

Or read more about effective strategies for multi-digit multiplication HERE.

Can’t wait to connect with you,

Shelley

The post FREE MINI COURSE: Teaching Multi-Digit Multiplication and Division for REAL Understanding appeared first on Shelley Gray.