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.
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.
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 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. 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
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).
In the past, I kept the Division Family anchor chart (pictured below) hanging in my room as a reference to remind students of the steps. But families can look very different, which is why I switched to the McDonald’s mnemonic device.
- 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 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! Having a Sticky-Note anchor chart does make changing problems easier and more fun. There’s just something about sticky notes that students like.
One last thought on the sticky-note anchor charts, students love being assigned to change the numbers. It’s a job that they love being in charge of.
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 provides an explanation of how to use graph paper as a quick and easy intervention resource with your students. 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 method 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 of the multiplication resources that 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 of the multiplication resources that 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 to turn to for promoting advanced long division learning with your students.
- 2 Digit Multiplication Worksheets and Organizers – Differentiated Resource – Visit Teachers Pay Teachers to see the full set of organizers and worksheets included in this original kit.
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