Lesson 5 1 1 Teacher Notes Standard Preparation

Lesson 5. 1. 1 – Teacher Notes Standard: Preparation for 8. EE. C. 8 b Solving and graphing systems of equations. • Full mastery can be expected by the end of this chapter. Lesson Focus: This lesson serves as a foundation for getting students prepared for solving systems of equations. (5 -2 and 5 -3) • I can determine if there is one solution, many solutions, or no solution to the system of equations. Calculator: No Literacy/Teaching Strategy: Pairs Check or Hot Potato (5 -3)

Bell Work

So far in this course, you have used your Equation Mat and/or symbols to find solutions for all types of linear equations with one variable. Today you will learn how to apply these skills to solving linear equations with two variables. As you work today, keep these questions in mind: What is a solution to an equation? What does it look like? What is the growth pattern? What is the y-intercept?

5 -2. CHANGING FORMS You can find the growth rate and starting value for y = 4 x + 5 quickly, because the equation is in y = mx + b form. But what if the equation is in a different form? A. The line − 6 x + 2 y = 10 is written in standard form. Can you tell what the growth of the line is? Its y-intercept? Predict these values.

5 -2. CHANGING FORMS CONTINUED Explore this situation below using 5 -2 b tiles (CPM). B. The equation − 6 x + 2 y = 10 is shown on the Equation Mat at right. Set up this equation on your Equation Mat using tiles. Using only “legal” moves, rearrange the tiles to get y by itself on the left side of the mat. Record each of your moves algebraically.

5 -2. CHANGING FORMS CONTINUED C. Now use your result from part (b) to find the growth pattern and y-intercept of the line − 6 x + 2 y = 10. Did your result match your prediction in part (a)?

5 -3. Your teacher will assign you one of the linear equations listed on the next slides. For your equation: • Use Algebra tiles with Equation Mat e. Tool (CPM) to set up the equation on your Equation Mat.

5 -3. Continued • Using only “legal” moves, rearrange your tiles to create an equation that starts with “y = …” Be sure to record all of your moves algebraically and be prepared to share your steps with the class. • What is the pattern of growth for your line? What is the y-intercept? How can you tell?

Extra Practice Solve each equation for the specified variable. 1. y in 5 x + 3 y = 15 2. x in 5 x + 3 y = 15 3. w in 2 l + 2 w = P

3. m in 4 n = 3 m -1 4. a in 2 a + b = c 5. a in b – 2 a = c