06-Math 7a-CC3 Ch3

Chapter 3 has two main learning objectives:

• Students will learn how to graph lines and parabolas from a table and will learn how to find a rule from a table.
• Students will continue to develop their equation-solving strategies and will begin to understand that a solution is the value (or values) of the variable that makes the rule (equation) true. Students will also continue to develop their understanding what it means for an equation to have no solution or a solution of “all numbers.”

Section 3.1 is designed to provide students with the skills needed to make the connections between the different representations of linear data (pattern, graph, table, and rule) in Chapter 4. It is highly recommended that you not only acquaint yourself with Chapter 4 at this time, but that you also complete the activity in Lesson 4.1.1 yourself before starting this chapter with your students. Doing so will help you understand what your students will need to know by the end of this chapter.

In Section 3.2, students will continue their study of solving linear equations that they began in Chapter 2. This time, a major focus will be on recording the solving process, so that students can begin to solve without the use of algebra tiles. Students will examine equations that have no solution as well as equations with multiple solutions. Finally, students will learn what a solution represents and then will learn how to check their solution.

The main focus of Chapter 3 is for students to make sense of problems (linear equations) and persevere in solving them. They use the appropriate tools they have (tables, graphs, equations, Equation Mats) strategically to solve these problems.

It is up to you how explicit you want the Mathematical Practices to be in your classroom. If you choose to discuss the Mathematical Practices in class with your students, now is a good time to stop and do so directly. This can be done as a quick whole group discussion, reflecting on the practices that they have already begun developing through the last two chapters. You might stop and have them do an entry in their Learning Logs related to their use of these Practices over the past weeks. You also might create a class poster and hang it in a prominent place in your room to keep the eight Mathematical Practices front and center in students’ minds.

Please remember, students are not expected to memorize the Mathematical Practices. Instead, developing these practices throughout the course will help students gain a more complete view of the mathematics that they are learning. Engaging in mathematics through the practices can also help students recognize the connections between the thinking skills that they learn in this class and those that they use in other areas of their lives.

8.F.1 .Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression,determine which function has the greater rate of change.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s² giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1),(2,4) and (3,9), which are not on a straight line.

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

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

a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

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