I walked into the 8th grade classroom before school this morning, and this is what I saw.
I said to Mr. Brian, “Wow, this is what my 4th graders are doing!” Of course, they’re not using variables, but they are doing this with whole numbers.
Students often ask why they need to know how to draw the array when they already know how to do the multiplication. This is why! To some students, the distributive property does not seem complicated when using whole numbers, but when we have expressions and variables in algebra, the parts get more confusing. If they become comfortable with modeling the situations now, they will be able to model more easily and make sense of algebraic representations in the future. What was really exciting to see was that I drew the second picture on the board without the areas filled in and asked them what each section’s area would be. They were able to tell me each section. They realized that the top left section would be x times y, the top right would be y times a, and so on. It’s great to see them becoming comfortable with and internalizing the models.
Here is some student work that shows the open array used for multiplying 2 digits by 2 digits, along with the partial products algorithm. The partial products algorithm really the same as using the open array and distributive property, but always breaking up the numbers into place values.
Just a reminder: There will be a multiplication test on Monday. All topics are listed on School Loop and students will receive a review sheet on Friday.
Enjoy the rest of your week!