Students work in partners on the Think About It problem. After 2-3 minutes of work time, I ask students to share out the expressions they've come up with.
Here is what I'm looking for:
I frame the remainder of the lesson by letting students know that we'll be working to create expressions like 4(9+2). In this lesson, we'll use the Distributive Property to express the sum of two numbers as a multiple of a sum of two whole numbers with no common factor.
To start the Intro to New Material section, I ask students to jot down on their papers the Greatest Common Factor (GCF) of 36 and 8. I'll then ask students to identify the expression that would result if we factor the GCF from the sum, 36 + 8. I'll say, "What expression would we write using the Distributive Property?"
Once students have identified that the correct expression would be 4(9 + 2), I'll ask students to check our work by distributing the 4 back into the terms in the parentheses. I want my students to build the habit of checking their work by getting back to our original expression.
I'll then tell students that we can say say that 4(9 + 2) shows the sum 36 + 8 as a multiple of the sum of two numbers (9 + 2) with no common factor. I ask students to help me fill in the key ideas in the notes:
It may seem strange for students to think about 4(9 + 2) as a product of a number and a whole number, because they see two numbers in (9 + 2), but they should think of (9 + 2) as one quantity. The parentheses around (9 + 2) help them to see that.
I work with students to complete Problems C and D.
For about 15 minutes, my students will work in pairs on the Partner Practice problem set. As students work, I circulate around the room and check in with each group. I am looking for:
After 10 minutes of partner work time, I'll ask students to independently complete the Check for Understanding problem. I circulate around the room to check their responses. An exemplar response might be:
I know that 16 and 60 have a greatest common factor of 4. 4 x 4 = 16 and 4 x 15 = 60. I can express the sum of 16 and 60 as a multiple of 4 and the sum of 4 and 15.
4(4 + 15)
Evidence that students checked their expression by distributing the 4 to the terms inside the parentheses should also be visible.
I'll now ask students to work on the Independent Practice problem set. I'll again encourage students to check their work by distributing. Students should use the fill-in notes from the INM to help them use the vocab to describe the expression.
The steps students should follow to solve these problems:
After independent work time, I bring the class back together to discuss Problem_5. I'll start by having partners turn to one another to talk. One partner shares what Norbert is correct about. The other partner shares what Norbert is confused about. I then Cold Call a student to share how Norbert should express 48 + 18 as a multiple of the sum of two whole numbers with no common factors.
My students will then work independently on the Exit Ticket to close the lesson.