Learn the best way to teach multi-digit multiplication and long division. This differentiated strategy helps 3rd grade, 4th grade, 5th grade, and special education students.
You’ve found a great place to start if you want the best strategies for teaching multi-digit multiplication and long division. I’ve found that 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 works successfully for so many students!
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 got so confused. They forgot the steps. 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. But, to make a long story short, I couldn’t find a better way. So, I developed a strategy of my own, which I call 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’re comfortable with the process. Eventually, they’ll no longer need the organizer. It’s a visual process that works for many students – including struggling students!
The organizers look like this for multiplication:
And here’s the organizer for long division problems:
How I Explicitly Teach these strategies
Be sure to watch this short video for step-by-step help with teaching 2-digit multiplication.
Below is the step-by-step directions video for long division using the standard algorithm.
Whole Group Instruction
I typically use the SmartBoard (interactive whiteboard) in front of the classroom for whole group lessons, followed by small groups and individual help.
To start, I introduce the organizer and invite my students to notice the different shapes and colors. Then, we talk about how the different shapes and colors help us solve long math problems.
As I introduce this strategy, I start by demonstrating basic multiplication (or division) problems. For example, I would start with a 2-digit x 1-digit problem using the organizer. Then, after a quick review, I explicitly teach how to solve the multi-step multiplication problem using the organizer.
I explicitly explain my thinking out loud for students to hear. For example, I say, “I need to multiply the 5 in the one’s pentagon by the 3 in the circle.” I make sure to point to the shapes and numbers, and I fill in the organizer as I speak.
Students watch as I model the process several times. As I’m modeling the procedure, I ask questions about the sequence of steps.
While I’m at the Smartboard, students follow along with their own organizers at their seats. Students enjoy using organizers placed in clear, plastic sleeves with dry-erase markers.
Circles Go With Circles; Squares Go With Squares
The photo below shows that any digit multiplied by the 3 in the red circle results in the product 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 result in products written in the blue squares on the organizer. So I repeat “Squares go with squares” over and over.
While teaching, I sound like a broken record, constantly repeating, “Circles go with circles; squares go with squares.” This technique works even as you begin differentiating, eliminating colors, and moving to the black and white shape organizer.
Next, we transition from whole group instruction to independently working on the assignment.
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 ones from Amazon). I love them and use them almost daily in so many ways for different subjects.
Shape Math™ Uses Colors & Shapes for Differentiation
Differentiation is simple with the organizers and worksheets in the Shape Math sets. The versatility allows you to scaffold to the just-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 colors and shapes. As students improve their skills, decrease reliance by eliminating the colors and introducing the pre-made worksheets.
Eventually, you can eliminate shapes and colors and transition to the included graph paper worksheets. Then, 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 sets increase student confidence and engagement. Confidence and engagement lead to excitement, pride, and eagerness to learn.
The multiplication and division sets include a variety of different-sized organizers. In addition, pre-designed worksheets allow you to choose the right time to introduce more complex skills.
Progression typically involves:
- Eliminating colors on the organizers
- Eliminating shapes
- Eliminating the organizers
- Transitioning to graph paper
- Transitioning from graph paper to independence.
I initially eliminated the colors on the student’s organizer in the above photo. However, I noticed that he was struggling without the colors, so I used markers to add the colors back in for him. There are many ways to assist your students in providing the right level of support.
You decide the right time to eliminate colors on the organizers with the eventual goal of eliminating the organizer. Students can then transition to graph paper worksheets before transitioning 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 I use and display as a reference for my students.
2-Digit Multiplication Anchor Chart
Long Division Anchor Chart
I’ve begun using this mnemonic device featuring good ole’ McDonald’s:
- Does (Divide)
- McDonald’s (Multiply),
- Serve (Subtract),
- Cheese (Check),
- Burgers (Bring down),
- Really? (Repeat and start over).
I used the Division Family pneumonic device in the past, but families can look very different, so I switched to the McDonald’s saying instead.
- Daddy, (Divide)
- Mommy (Multiply),
- Sister (Subtract),
- Brother (Bring Down),
- Rover (Repeat and start over).
Sometimes I have a problem ready to go at the beginning of math class, like morning work.
Once students catch on to the long division routine, I change the Post-It Notes numbers. I do my best to keep it color-coordinated, but life happens. Having a Sticky-Note anchor chart does make changing problems easier and more fun. There’s just something about sticky notes that students like.
I have one final thought on the sticky-note anchor charts. Students love being in charge of changing the numbers. Plus, some students need that additional attention and confidence boost.
I’d love to hear how you use sticky notes in your classroom!
Articles about Multi-Digit Multiplication:
- 3 Ideas for Teaching Multi-Digit Multiplication – Here are 3 FAST ideas for teaching multi-digit multiplication. These interventions are easy and quick for busy teachers.
- 2-Digit Multiplication Worksheets: Differentiated – Here’s a visual method for teaching 2-digit multiplication using differentiated, visual cues to guide students’ learning for success.
- 2-Digit Multiplication Made Easier! – Here’s how to use the double-digit multiplication organizers and worksheets.
Articles about Long Division:
- Differentiated Long Division Worksheets for FREE – Grab these differentiated long division worksheets for FREE and dramatically boost student success and your teaching success!
- Graph Paper Math Intervention – This blog article explains how to use graph paper as a quick and easy intervention resource with your students. In addition, it includes links to free printable graph paper and ideas about how to use it in your classroom.
Differentiated Multiplication Resources:
- 2 Digit Multiplication Worksheets and Organizers Set – This new double-digit multiplication method uses colors and shapes to provide a visual, concrete strategy for teaching 2-digit multiplication.
- 2-Digit Multiplication and 3-Digit Multiplication Worksheets and Organizers – This multi-digit (3-digit x 2-digit) multiplication method uses colors and shapes for a visual, concrete strategy.
- Multiplication 2-Digit x 1-Digit and 3-Digit x 1-Digit Worksheets and Organizers – This set includes 2-digit x 1-digit and 3-digit x 1-digit multiplication with these worksheets and organizers.
- 3-Digit and 4-Digit Multiplication Worksheets and Organizers – This multi-digit (3-digit x 3-digit and 4-digit x 3-digit) multiplication method uses colors and shapes for a visual, concrete strategy.
- All Multiplication Resources – Check out all the multiplication resources I offer in my Teachers Pay Teachers store.
Differentiated Long Division Resources:
- Long Division Differentiated Worksheets and Organizers – Visit Teachers Pay Teachers to see the complete set of organizers and worksheets included in the original kit.
- All Division Resources – Check out ALL the multiplication resources I offer in my Teachers Pay Teachers store.
- 2-Digit Divisors Long Division Differentiated Worksheets and Organizers – When you get ready to move on to 2-digit divisors, this is the perfect resource for promoting advanced long division learning with your students.
- 2 Digit Multiplication Worksheets and Organizers – Differentiated Resource – Visit Teachers Pay Teachers to see the complete set of organizers and worksheets included in this original kit.