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A New Strategy for Multiplication and Long Division

Years ago, teaching multiplication and long division had a HUGE DREAD FACTOR for me. That’s completely true. The methods I was using just weren’t working. My students forgot the steps. They got confused, they couldn’t line up their numbers, and – they couldn’t even read their own writing!

New Multiplication and Long Division Strategy for Students

I knew there had to be a better way. To make a long story short, I couldn’t find the better way. So, I developed a strategy of my own. I call it Shape Math™.

My Shape Math™ Multiplication & Long Division Strategies:

Multiplication and long division strategy using colors and shapes

There’s no magical, easy fix for teaching students how to solve 2-Digit x 2-Digit Multiplication and Long Division problems. If I had that magic, I’d be a BILLIONAIRE!

math remediation and special education students benefit from visual techniques!

I’m not a billionaire or a millionaire, but I DO have a unique strategy for teaching 2-Digit Multiplication and Long Division that I haven’t seen anywhere else. I’ve been using it in my classroom for years and years, and I’ve received some FANTASTIC feedback from other teachers about their successes!

 

The Shape Multiplication™ and Shape Division™ methods use shapes and colors to help students remembers the sequence of steps. Students are guided through the problems until they become comfortable enough with the process to stop using the organizer. It’s a very visual process that works for many students – especially the strugglers!

 

The organizers look like this for multiplication:

Differentiated Multiplication Organizer for Student Learning

And this for division:

Differentiated Division Strategy

How I Explicitly Teach these strategies:

As I’m working on my SmartBoard up front I explicitly teach how to solve problems using the organizer. Students watch the process several times, then I begin asking them questions about the sequence of steps. You can see below that any digit multiplied by the 3 in the red circle are written in the red circles below the 3. The digits multiplied by the 2 in the blue square are written in the blue squares on the organizers. I constantly repeat, “Circles go with circles, squares go with squares.” This works even if you decide to eliminate the color portion of the scaffolding and use only the shapes in black and white.
Two digit multiplication strategy - new strategy helps students remember the sequence of steps!
While I’m at the Smartboard, students are following along with their own organizers using dry erase markers. I love using these terrific dry erase sleeves (you can get them from many different places – just Google “dry erase sleeves“). I absolutely love them and use them almost daily for so many different things. (I’ll also add here that I have no affiliate links, so I’m not getting paid for stating that I like them!)
Two digit multiplication strategy - visual approach helps students remember the steps

Shape Math™ Uses Colors & Shapes for Differentiation:

These organizers and worksheets are an easy way to visually differentiate for my students – the versatility really allows you to scaffold just the right level of help! It’s easy to ramp up the help for students who need it – use both the colors and the shapes. Or eliminate the colors or eliminate the shapes. Eliminate them both, and begin using the graph paper worksheets that are included. When the time is right, students can transition to just the typical multiplication or division algorithm.
 
 
The multiplication pack includes organizers of different sizes, and you can choose the right time to introduce regrouping. You can also choose the right time to eliminate the colors or the whole organizer, and move students right into graph paper worksheets as students transition to independence!
 
 
In the picture below, I had originally eliminated the colors for this student. He was really struggling, so I used markers to add the colors back in for him. There are many ways to assist your students to provide the right level of help.
A new approach to two digit multiplication
I love how the worksheets are custom made for the problems. If you look at problem #6 below, you will notice that the number of circles and squares perfectly match the products, which is very helpful to new learners.
shapes and colors help students solve 2-digit x 2-digit multiplication problems
I also appreciate how these organizers make it easy to correct student errors. (Below) For example, on problem #5 the student kept multiplying the 3 in the square times the 6 in the triangle before multiplying the 3 by the 0 in the triangle. I simply highlighted the ones place (0 in the triangle) and the square in which the product will be placed, so that the student would remember the correct sequence.
 
You will also notice that on problem #6, the 1 in the circle was crossed out to remind the student that the 1 (in the circle) was finished and no longer needed.
Highlighting helps struggling students and visual learners!

Anchor Charts in the Classroom:

I LOVE anchor charts – they’re easy to make, and FABULOUS reference tools! Below is the multiplication anchor chart that I use and display for shape multiplication.
Anchor chart showing Shape Multiplication for 2-digit problems
I keep this division anchor chart (pictured below) hanging in my room as a reference to remind students of the steps – the mnemonic device that I use is the Division Family: Daddy, (Divide) Mommy (Multiply), Sister (Subtract), Brother (Bring Down), Rover (Repeat and start over). I think it’s easy for students to remember.
Another poster that I use is pictured below. Once students catch on to the routine of long division, I change out the Post-It Notes numbers. I do my best to keep it color coordinated, but, well, life happens! Sometimes I have a problem ready to go at the beginning of math class, like morning work.
Long division anchor chart is a great reference tool for students

Fun Ways to Practice Multiplication & Division

Xtramath.org

If you aren’t already using Xtramath.org, you need to head to that website ASAP! Xtramath is a math fluency program that helps students master addition, subtraction, multiplication, and division facts. Really, it’s FREE and it’s helpful for students. You can even sign up to receive free weekly reports sent directly to your email! My students typically spend the first five minutes of class warming up on Xtramath.org. (By the way, I’m not getting paid to promote xtramath.org, just in case you were wondering!☺)

Xtramath.org is a free program for students!

For more about how I use Xtramath.org in my classroom, head to this blog post:  Xtramath.org in Caffeine Queen Teacher’s Classroom.

Games & Task Cards

Task cards can be used in so many different ways. They’re great for stations/rotations, games, scavenger hunts, entry and exit tickets, SCOOT, – you get the idea! I like to use them along with games. That’s such an easy way to really add fun to learning in a “sneaky” way. Students think they’re just playing a game, but they have to earn their turn by solving a math problem. In my classroom, all of the students involved in playing the game must solve the problem, then they compare answers (or check it with the answer key) to make sure that players really earn their turns. Any game can be used.

Games motivate students to solve math problems

Candy Land with flashcards

Any game can be converted to a learning game just by adding task cards. Students all work at solving the task card problem, then they check each other’s work before someone earns a turn. Most of my students are independent as they work through the games. The only issue I have, is that they often are unable to finish the game because it takes them longer during their turns (as they solve task cards). If you have the space, you could allow students to leave games set up so they can return to them at a later time.

Dominoes help teach math facts!

Ordinary dominoes become teaching tools!

 

Task Cards turn ordinary games into learning opportunities!

Task Cards turn ordinary games into learning opportunities!

Centers, Stations, & Rotations

multiplication Fact Practice - Beat the Clock Game

Multiplication Fact Practice – Beat the Clock Game

Multiplication and Long Division Resources:

Here is the Money-Saving Shape Multiplication™ and Shape Long Division™ BUNDLE! Check it out – I think you’ll like what you see! You can also purchase JUST the Multiplication and JUST the Division packets. Click on the picture to visit my store!
New differentiated instructional strategy for teaching 2-digit multiplication and long division
Shapes and colors provide scaffolding for students to learn 2-digit multiplication
Shapes and colors provide scaffolding for students to learn long division
Beginning the process of the traditional multiplication algorithm
2-Digit and 3-Digit Shape Multiplication!
long division problems on task cards

Beginner Long Division Task Cards

I really do believe in these strategies! I think they can help your students, and I think that you will find them helpful and easy to use! If you have any questions, please ask!

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