UNIT 4  WEEK 12
Manipulating Algebraic Expressions
SummaryIn week 12, we revisit the idea of isolating a variable. This is traditionally a topic covered in grade 8 but usually requires a full review because of the complexity of the concept. Students will encounter questions that require a mastery of solving algebraic expressions and opposite operations. We guide students through a number of activities that will reinforce these ideas. Finally, we will explore how and when we can skip these concepts and graph an equation without having it in standard form.

Week 12  Lesson 1 
Topic of the Day/Driving Question:
Good Questions:
In class activity: A considerable amount of time today is dedicated to understanding that as we begin to manipulate algebraic expressions, it is crucial we do not change the equation. What this means is, we must follow the rules of opposite operations. The original equation that we are given and the solved equation into standard form need to be equivalent. An illustration we can use to demonstrate what we mean is to choose a student in the class and present them with the following information (as a class discussion): “Suppose you run a business and I, as your customer owe you $1,000. Write the corresponding equation for this on the board and show that if we do not follow proper operations, the equation can easily say that the student owes me $1,000. Reinforce that the student just went from earning $1,000 to owing that same amount. Ask students to get into pairs and discuss what they think opposite operations are an examples of them. Create an online space in the LMS where students can input their ideas. Remind students that this is safe place where they can share their ideas and we will have a class discussion on this afterwards. Homework: Students are required to share at least one idea on what they think an opposite operation is, they are encouraged to use the resources that are available to them (Khan Academy, YouTube etc) and they should be sure to cite any references they use. 
Week 12  Lesson 2 
Topic of the Day/Driving Question:
Good Questions:
In class activity: Sometimes we are presented with very complicated expressions that would require a lot of manipulation to get into standard form. We are going to explore how to graph an algebraic expression with two variables without having to do an extensive solving process. What is the minimum number of points we need in order to draw a line? Lead students through a discussion and come to the consensus that we only require two points in order to plot out a line. What two points should we choose? If we have an x and a y, then we know the line must cross over both the x and y axis. How about we choose these points? In order to find the y intercept (vertical axis) we can make x equal to zero and then solve for y. Similarly, in order to solve for the x intercept (horizontal axis) we can make y equal to zero. This gives us our two points we need to plot our line. We can now use interpolation or extrapolation to determine any information we need. We could also use the graph to come up with our standard equation. Homework: Students will require extra questions in order to reinforce the concepts we have learned. 