If you’re looking for the best strategies for teaching multi-digit multiplication and long division, you’ve found a great place to start. These are the easiest methods for student learning. Best of all, they work with 4th grade students, 5th grade students, at-risk students, strugglers, and special education students – ALL STUDENTS! This visual method really does work for most every student!
Years ago, teaching the multiplication and long division algorithms had a HUGE DREAD FACTOR for me. The traditional 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!
Shape Math™ Multiplication & Long Division Strategies
I knew there had to be a better way. To make a long story short, I couldn’t find a better way. So, I developed a strategy of my own and I call it Shape Math™.
I’ve been teaching this multi-digit multiplication and long division strategy in my classroom for years and years, and I’ve received FANTASTIC feedback from other teachers about their successes using it!
About the Organizers
The Shape Multiplication™ and Shape Division™ methods use shapes and colors to help students remember the sequence of steps.
The shapes and colors guide students through the problems until they become very comfortable with the process. Eventually they’ll no longer need the organizer. It’s a very visual process that works for many students – including strugglers!
The organizers look like this for multiplication:
And here’s the organizer for long division problems:
How I Explicitly Teach these strategies
For difficult types of lessons, I typically make use of the SmartBoard in front of the classroom, followed by small group or individual help.
Whole Group Instruction
I introduce the organizer and invite my students to notice the different shapes and colors. We talk about how the different shapes and colors help us when solving long math problems.
I begin reviewing what students are already familiar with, such as solving a 2-digit x 1-digit problem set up in this style. After a quick review of that, I then go on to explicitly teach how to solve the multi-step multiplication problem using the organizer.
I explicitly explain my thinking out loud for students to hear. I say something like, “I need to multiply the 5 in the ones triangle by the 3 in the circle.” I make sure to point to the shapes and fill in the organizer as I speak.
Students watch the process several times, as I begin asking questions about the sequence of steps.
Circles Go With Circles; Squares Go With Squares
In the photo below you can see that any digit multiplied by the 3 in the red circle results in products written in the red circles below the 3. This is why I keep repeating “Circles go with circles.”
The digits multiplied by the 2 in the blue square results in products written in the blue squares on the organizer. This is why I repeat “Squares go with squares” over and over.
This is an older photo – triangles are no longer used in the organizers
While teaching, I sound like a broken record constantly repeating, “Circles go with circles; squares go with squares.” This works even if you differentiate by eliminating colors and using the black and white shape organizer.
Small Group/Individual Instruction
While I’m at the Smartboard, students are following along with their own organizers at their seats. Students enjoy using organizers placed in clear, plastic sleeves with dry erase markers.
Next, we transition from whole group instruction to students working on the assignment independently.
As students work, I take a quick walk through the classroom noticing which students appear confused. That’s when I typically either pull students into a small group at the back table, or offer individual help.
The Reusable Clear Plastic Sleeves
I love using these terrific dry erase sleeves (Click here for similar dry erase sleeves from Amazon). I absolutely love them and use them almost daily in so many ways for different subjects. (I’ll also add here that this is an affiliate link, so I will receive a small amount of compensation if you make a purchase, but they are honestly WONDERFUL additions to the classroom!)
Shape Math™ Uses Colors & Shapes for Differentiation
Differentiation is easy with the organizers and worksheets included in the Shape Math sets. The versatility really allows you to scaffold just the right level of help for each student’s unique needs.
How to Differentiate Using the Organizers
Ramp up the help for students who need maximum support by using both colors and shapes. As students improve their skills, decrease support by eliminating the colors and introducing the pre-made worksheets.
Eventually, you can eliminate both shapes and colors, and use the graph paper worksheets that are included. When the time is right, students can transition to the basic multiplication or division algorithm without colors, shapes, or graph paper.
The scaffolding options offered in these packs increases student confidence and engagement. Confidence and engagement lead to excitement, pride, and eagerness to learn!
Differentiation is easy with different sized organizers featuring colors and shapesThe multiplication and division sets include a variety of different sized organizers. Pre-designed worksheets allow you to choose the right time to introduce more difficult skills.
Typical Scaffolding
Progression typically involves:
- Eliminating colors on the organizers
- Eliminating shapes, which eliminates the organizers
- Transitioning to graph paper
- Transitioning from graph paper to independence.
In the picture above, I had originally eliminated the colors for this student. I noticed that he was really struggling without the colors, 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.
You decide the right time to eliminate colors on the organizers with the eventual goal of totally eliminating the organizer. Students can then transition to graph paper worksheets before they transition to independence with no organizers or graph paper.
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 as a reference for my students.
2-Digit Multiplication Anchor Chart
Anchor chart using the visual organizer with colors and shapesLong Division Anchor Chart
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 – I can never remember the McDonalds one!
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.
