We have done a lot of work previous to this lesson decomposing large areas and working on strategies to find areas mentally. This lesson is the next step, where I am attempting to help the students understand how to demonstrate (write their thinking) mathematically.
Many times, I like to begin the lesson with the students having all of the information in front of them and working together to explain "why it works". Beginning with questions to figure out during the lesson sets up the student thinking to "make sense" rather than merely solve equations.
Listen to these students debate and create sense of the distributive property problem I put up on the board. I ask them to look at it and discuss why it makes sense, or "works".
Following the class discussions in the warm-up, the students and I review what they gleaned from the discussion and defined the distributive property. This definition is drawn out of the students as they express ways to make the work easier.
At this point, I realize the children don't know what the word "distributive" means, so I begin using it in my language.
I ask a student to distribute papers to the others in class, I tell them I will distribute their homework at the end of class, and that during recess we can distribute the cupcakes for the birthday celebration.
You may want to use this analogy with your students:
We use the distributive property all of the time. Do you think the Keebler elves make packages of cookies? Ok..forget the elf part, let’s focus on the cookies. Do they come out of the oven in packages?
So what’s the next step for the baked cookies, so that you can buy them at the market? Packages! Alright...isn’t that the distributive property.
Hmmm… I have 24 cookies, My package can hold 12. The packaging has two rows, how many cookies in each row? How many packages when we’ve put all 24 into packages?
Where else do we use the distributive property? Think about the supermarket...
Next, students write 7 x 4 as different situation, in their journals, and I model how to solve it using the distributive property. At this point, I felt they were ready to try on their own.
I ask the students to draw a 5 x 8 rectangle in their journals and work with a partner to use the distributive property to find the area. I know they can do it by multiplying 5 by 8, but I want to see if they can split a factor and solve the problem that way. What I find is very interesting.
Listen to these boys explain why they chose their strategy and notice that they are actually working backwards from the solution to the property. I am certain this is from all of our work in decomposing rectangles in order to find the areas mentally. However, this gives me some good information.
This student, in her share, realizes that she wasn't sure how to use the property, but knew what the answer should be.
For the close of the lesson, I choose to do another mini lesson with the students to review splitting a factor. I realize as the students work independently that many are unsure of the best way to do this, or in some cases, why to do it.
We do several examples to practice what splitting a factor actually means. I work to express that it is just like splitting our arrays. For example, we worked on splitting a 7 into 6 + 1, 4 + 3, 5 + 2, and so on.
I then assign several numbers to be "split" for home practice.