Today in Math, the students and I worked on modelling 2-digit by 2-digit multiplication. There are two ways to do this that we worked on together. The first is using base ten blocks to build an array:
Just like when we draw arrays, we need to model the factors vertically and horizontally. Since we are trying to figure out what 13 x 21 is (or 13 groups of 21) we first create rows of thirteen and then columns of 21. Then we fill in the array. Finally we can add up the amount of ones, tens, and one hundreds that we have to discover the answer. You can see this step by step by clicking on the gallery below:
You can model an array for any 2-digit by 2-digit multiplication question using base ten blocks:
Students can also use rectangles and use area to help them to model arrays of 2-digit by 2-digit. Take the example below:
Start as you would for any array: model the first number (23) for the rows; then model the second number (86) for the columns. Then fill in the rest of the array. Calculate what the value of each rectangle (array) would be. Add them together to find the total amount that has been modelled. You can see this step-by-step by clicking on the gallery below:
Modelling is one way that we encourage students to gain a better understanding of 2-digit by 2-digit multiplication. In fact, when you compare it to other methods of multiplying, you can see clearly that modelling a number can help to give students a better understanding of where we get the numbers when we multiply.