08-Math 7a-CC3 Unit 5

This chapter is designed to accomplish two objectives:

• To continue a focus on writing equations from word problems.
• To introduce students to solving systems of equations where both equations are in y = mx + b form.

Section 5.1 introduces students to word problems with linear contexts for students to write equations. (For example: When will two bank accounts growing at different rates have the same balance?) Although this is connected to prior work with word problems (perhaps using the 5-D Process as an aid) that began in Chapter 1, students will now use a multiple-representations approach. While analyzing a word problem, students will graph the situation to find a point of intersection. They will also write rules from graphs and directly from the context, using what they know about growth and starting value from Section 4.1.

In Section 5.2, students solve systems of equations in y = mx + b form by graphing and using an Equation Mat. Using the Equation Mat helps students organize information (e. g., information about two different bank accounts that are growing) and can also help them compare two sets of information (e.g., finding when the bank balances are equal). They are introduced to the Equal Values Method, which is a strategy to symbolically solve equations by setting them equal to each other when both are written in the form y = . . . . This is a simplified version of the Substitution Method.

In Chapter 5, students will be using various tools strategically to make sense of problems and persevere in solving them and model with mathematics, while working with systems of equations.

Even when not mentioned specifically for a lesson, encourage abstract and quantitative reasoning, the construction of viable arguments and critiquing of others’ reasoning, and attention to precision in team discussions. One overarching goal of Chapter 5 is to really make sense of problems (finding the connections between the different representations of systems of equations) and persevere in solving them.

8.EE.7 Solve linear equations in one variable.

b. Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.