Multiplying with the Area Model

Before we use the area model, we need to learn how to 'break' numbers apart. This is called Expanded Form. Instead of looking at the number $24$ as just two digits, we see it as its actual value: $20 + 4$. By breaking numbers into tens and ones, we make them much easier to multiply in our heads. For example, multiplying by $20$ is just multiplying by $2$ and adding a zero! This process of breaking down numbers is the first step to becoming a mental math wizard.

An Area Model is like a map for your multiplication. For a 2-digit by 2-digit problem, we draw a large square and divide it into four smaller boxes (a $2 \times 2$ grid). We write the expanded form of one number across the top and the other number down the side. Each box represents a 'room' where two numbers meet to be multiplied. The result inside each box is called a Partial Product because it is only 'part' of our final answer.

Now for the fun part! You multiply the numbers that meet in each box. Once all four boxes are filled with partial products, you simply add them all together. This is much safer than the 'old way' of multiplication because you can see every step clearly. If you can add $200 + 40 + 60 + 12$, you can solve $20 \times 13$! Always remember to align your place values (ones, tens, hundreds) when adding the final sum.