Why Use The Lattice Method In Math?

As a high school math teacher, I've seen students struggle to multiply binomials since the FOIL method is the one usually taught and is the one frequently expected on standardized tests.  Years ago, I learned the lattice method of multiplication from an elementary teacher and realized it could be used with binomial multiplication in Algebra.  In fact, there was a long term substitute in one of the elementary classes who was trying to teach multiplication and didn't have any luck using the traditional methods. So I popped in and gave a quick 20 minute lesson.  At the end, most of the struggling students were able to multiply two digit numbers.

When it comes to teaching multiplication in elementary school, the debate between the traditional algorithm and the lattice method often arises. While both methods get the job done, the lattice method offers a unique advantage – it lays the groundwork for understanding algebraic multiplication later on.

The traditional algorithm excels in drill-based multiplication problems. However, it can feel abstract to young students who rely on memorized steps without necessarily building conceptual understanding. The lattice method, on the other hand,provides a visual representation of the multiplication process.

Imagine a lattice grid – a diamond - shaped arrangement of squares. Each digit of the numbers being multiplied is placed on the grid according to its value (units digit on the bottom right, tens digit above it, and so on). Then, multiplication happens at each intersection of the grid. For example, the product of the units digit of one number and the tens digit of the other is written diagonally in the corresponding square.

This visual approach offers several benefits. First, it breaks down multiplication into smaller, more manageable steps,making it easier for students to grasp the concept. Second, it reinforces place value – the position of a digit determines its weight in the final product. Each diagonal line in the lattice represents the multiplication of two digits and their corresponding place values.

More importantly, the lattice method provides a stepping stone to algebraic multiplication. In algebra, letters are used as placeholders for unknown values. The lattice method, with its emphasis on multiplying individual digits based on their positions, translates beautifully to multiplying algebraic terms.

Imagine multiplying (x + 2)(x + 3) using the lattice. You'd place the x, 2, and 3 on the grid just like numbers. The process of multiplying each term and placing the products diagonally is identical to multiplying numbers. This visual representation helps students see how the same principles apply to multiplying algebraic expressions.

While the traditional algorithm eventually leads to algebraic multiplication through a series of steps, the lattice method offers a smoother transition. It builds the foundation for understanding how multiplication works with both numbers and variables, preparing students for the complexities of algebra that lie ahead.

In conclusion, the lattice method goes beyond simply teaching multiplication. It fosters a deeper understanding of place value, provides a visual framework for problem-solving, and crucially, bridges the gap between arithmetic and algebra.For these reasons, the lattice method offers a valuable tool for educators looking to equip their young students with a strong foundation for future mathematical success. Let me know what you think, I'd love to hear.  Have a great day.