 # Visual Multiplication

## Curriculum Goal

#### Junior: Number Sense

• Represent and solve problems involving the multiplication of two-digit whole numbers by two-digit whole numbers using the area model and using algorithms, and make connections between the two methods.

## Context

• Teacher-led, whole-class introduction followed by an exploratory pair-based activity that strengthens students’ understanding of multiplication.

## Materials

• Instructions for visual multiplication (Appendix A)
• Large chart paper
• Markers
• Paper and pencil crayons for each student
• Multi-coloured sticks/straws (or something similar)

## Lesson

• Give students one minute to draw or write down anything they know about multiplication on large chart paper.
• Suggested questions:
• What is multiplication?
• What do you know about multiplication?
• How do you solve multiplication problems?
• Do you use any “tricks” to solve multiplication problems?
• Have students share ideas with the class and highlight central ideas in multiplication, such as arrays and repeated addition.
• Background information on this multiplication strategy is available at the end of this lesson plan.
• Introduce visual multiplication using coloured lines to show place value (Appendix A).
• Ensure you explain each step with visuals to the students. Demonstrate how you would do a one-digit by one-digit question, as well as a two-digit by two-digit question.
• Explain that the sticks represent the digits of each number and that the intersections of the sticks are counted in a particular way to get your product. Please refer to examples one and two in the resource from The University of Georgia for additional guidance (see More Information below).
• Challenge students to answer a few questions together as a group. Begin with one-digit by one-digit questions then move to two-digit by two-digit questions. Once proficient, have them pair up and challenge each other.
• When students have had an opportunity to practice this method, discuss as a group whether they would use this method of multiplication.
• Challenge students to think about when this method is helpful and when it might not be (e.g., When is this method more laborious than algorithms you know?).
• Ask students to explain how this method works.
• Ask students whether there is a limit to this way of multiplication?

## Look Fors

• Are students able to draw out the multiplication questions using the visual multiplication method?
• Are they able to group the intersections together? Do the students understand what the intersection of sticks represents?

## Extension

Visual Multiplication Further Explained
In this video from tecmath, they break down each step required to multiply two-digits by two-digits using this method. They also breakdown how to multiply three-digit by two-digit numbers.