If you’re anything like a majority of the world, you’ve never heard of visual math methods, let alone specific ones you can use as “short cuts” to make things easier. In this case, we are going to dive into the W-method of multiplication, it’s brief history, and how to use it.

History of the W-Method of Multiplication

The W-method of multiplication is a modern educational approach designed primarily to aid students in visualizing and systematically performing multi-digit multiplication with 3-digit by 2-digit numbers. Despite its use in some classrooms as a scaffold for learners, the historical origins of the W-method are not well-documented in classical mathematical literature or among traditional algorithms. That’s OK, though, as it works as a fun math tool to show students a visual method for this specific case of multiplication or to use as a party trick to impress and get the attention of the class.

I, personally, use it as a way to get attention from the class by having the kids write the equation at random (for example, I’ll tell 5 students to pick a random number between 1 – 9), then write them down on the board. I’ll solve this as “mental math” a couple times, impressing the kids, then show them how to do it. This generates excitement among bored middle school students.

But where does this trick come from? And is it reliable to pass down in the classroom? Geek on for a brief history lesson.

Context in Multiplication Algorithms

The traditional multiplication techniques such as the Egyptian doubling method, lattice method, and standard algorithm can be directly traced back to ancient civilizations including the Egyptians, Babylonians, Indians, and later refinements in Europe . The lattice method (arriving in India and evolving in Europe), the Italian method (a modification of lattice), and the grid method (popularized by Leibniz) were all developed over centuries of arithmetic instruction . 

The W-method is not found among ancient or medieval multiplication techniques such as cross multiplication (noted by Pacioli as “crocetta” or “little cross” in the 15th century) or lattice multiplication . Nor does it appear within major published systems such as the Trachtenberg system or Vedic mathematics, both of which offer unique, highly structured rapid calculation algorithms . So, where does it come from?

Modern problems require modern solutions. Mathemeticians and math educators stepped up and created some flashier methods that help student see what’s going on in math. This is where the visual and pattern based method tend to shine.

Emergence of Visual and Pattern-Based Methods

Let’s face it. Learning by rote memorisation of the algorithms is not fun. Pattern- and shape-based multiplication strategies emerged in the 20th and 21st centuries, in response to pedagogical needs for concrete and engaging alternatives to the standard written algorithm. The W-method falls into this category: it is a mnemonic or visual guide rather than a system. These methods are influenced by the educational trend of introducing algorithmic variety to improve number sense and reduce calculation anxiety in young learners .

There is nothing wrong with this! Sometimes we have to be creative as educators to guide the students from an island of confusion and ignorance to the continent of knowledge. Sure, it’s flashy, but flashy keeps interest. And when the learner stays interested, you have a chance to teach them more.

Modern Development and Pedagogical Context of the W-Method of Multiplication

The W-method’s name and instructional approach are products of contemporary education. Teacher training and math resources are beginning to have these methods as a way to help pupils with intermediate-sized multiplication. It is a relatively recent teaching innovation aimed at scaffolding the difficult “multiply first, then add” steps, especially for students transitioning from conceptual (area model) to procedural (standard algorithm) strategies.

And trust me, it works. I have used it with kids with dyslexia, ADHD, and just when their brains want to shut down.

Strengths and Weaknesses of the W-Method of Multiplication

Strengths

• Pattern-Based Consistency: The W-method provides a clear step-by-step pattern for solving 3-by-2 digit multiplication problems. This makes it easier for some learners to remember and replicate without relying on rote memorization.

• Engagement: The structure of the W-method injects a sense of novelty and fun into multiplication practice. Its process-based format can motivate students who find traditional methods tedious.

• Designed for Specific Cases: The W-method is particularly effective for 3-digit by 2-digit problems, offering an alternative to the standard algorithm that can serve as a scaffold for students struggling with complex multiplications

• Reduces Simple Calculation Errors: By breaking problems into smaller steps, it may help reduce calculation mistakes common with mental math or stack-based long multiplication.

Weaknesses

• Limited Scope: The method is tailored for 3-by-2 digit problems, meaning it does not generalize as easily to larger numbers or different-sized factors as the standard algorithm does.

• Potential for Confusion: For students who are already comfortable with the standard or area methods, the introduction of the W-method may add unnecessary complexity and confusion.

• Lack of Emphasis on Mathematical Concepts: Unlike the area model or distributive property methods, the W-method may not reinforce conceptual understanding of place value or the distributive nature of multiplication .

• Not Widely Taught: Because the W-method is less common in standard curricula, students may have difficulty finding resources or assistance compared to more established methods.

Using W-Method of Multiplication in YOUR classroom

I already mentioned how I use it as a display, show-off method to introduce the concept to the students. I also make a game of it where the students work in teams, come up with formula, and challenge their classmates to solve them. Then, of course, you can use the ever popular warm-up activities of flash math worksheets if you need some paper trail to show your school.

How to Use the W-Method of Multiplication

This is the quick and dirty instructions. You can get the fully written out instructions in our store for pay what you want pricing.

Start with some numbers, 3 stacked on top, two on the bottom (3×2).

1. Use a W pattern to re-write the numbers starting at the top left. (top left, bottom left, top middle, bottom right, top right)
2. Multiply the first two digits.
3. Then, look at the first 4 numbers. Multiply the outside numbers together, then the inside numbers together.
4. Add the 10s digit to the number from step 2. Then tack on the ones digit.
5. Repeat steps 3 – 4 with the last 4 digits.
6. Multiply the last two digits together, add the tens digit, then tack on the ones.