This is an activity that I created based upon a teaching method that I employ to assist my students in understanding how to apply the distributive property. Frequently when I teach my students how to use the distributive property with just multiplication techniques the students often obtain an incorrect expression. Example: 2(3x + 4) is equivalent to 6x + 8 but often my students will give 6x + 4 because they will incorrectly only multiply 2(3x).
This year while discussing how to view the expression 2(3x + 4) I had my students remember back to when they learned how to multiply numbers such as 2(3). I asked them to draw two groups with three items in each group and then tell me how many items were in the group. They correctly drew the picture and told me that there were six total items. I then changed the problem back to 2(3x + 4) and asked them to draw two groups with 3x + 4 in each group and to be able to tell me how many items were in the groups. They drew their pictures and then told me there were a total of 6x + 8 items altogether.
Now prior to this time we had spent some time on combining like terms so the students understood which terms they could combine. And as well, after having my students draw the models of these types of problems they still needed to connect to a shortcut to be able to accurately evaluate expressions like 20(15x + 18) which are too time consuming to model.
After the lesson I created these worksheets to allow my students to have something to work on that we had talked about and to try and connect with them the various equivalent expressions that could be written.
There are a total of 5 student worksheets included in this activity, as well as a page with example problems, and an answer key for a total of 11 pages.