I start today with the lesson I learned from my student who didn't want to use the pizza approach to solving expressions.
I show the students that an expression is only representing 1/2 of an equation. My focus is to develop their understanding of why it is important to solve one part, then move downward to continue to simplify an expression.
I write 2x + (13 - 2 x 4) = 15 / 5 + 3
This model show the students the importance of organization while simplifying expressions. I make two PEMDAS pizzas on the board when I have simplified each side.
I cross out the terms that I solve to keep myself organized. One student adds to this idea and says that it looks like cheese and the circled answer makes a pepperoni. The students have fun with this analogy.
Students have an extended amount of time to practice simplifying expressions. I have the students work with partners and check in frequently. I know that the next few lessons are adding to the complexity of these expressions, so I want students to have a strong foundation.
As I circulate the room to check for understanding, I notice that for the most part, students are organized, and careful when checking which operation to solve first. Because of this, I decide that I want to extend their understanding and ask them to simplify a more complex expression than the now you try it examples. However, I'm not asking students to do this on their own, because I wanted them to feel successful and I want to hear, and make explicit, their thinking.
I ask two students who need extension/enrichment (they have completed more problems than any other pair and have most problems correct) to create two expression each. I give them parameters:
I use their problems to ask pairs of students to consider evaluating an expression when there is more than one operation within the parenthesis. These problems incorporate decimals as well, so it extends understanding because it includes applications from lessons prior to this.
Today, the group share is longer because the students have worked on simplifying many expressions. I ask students to share any challenges, mathematical arguments, or discoveries.
As students share, I capture their comments on chart paper. These charts are references we can use later.