04-Math 7a-CC3 Ch1

This chapter is designed to accomplish several objectives:

• To introduce students to several of the mathematical concepts on which this course is based.
• To establish class norms that will continue throughout the course, such as having students reflect in Learning Logs and use focus questions to drive learning.
• To provide an opportunity for the teacher to assess students’ entry skills and to provide students an opportunity to review basic prerequisite material.
• To establish good teamwork.

Several different mathematical topics are introduced in Chapter 1, including interpreting graphs, collecting data, using a trend line to make predictions, plotting points and linear equations, finding and generalizing patterns, and using problem-solving strategies.

These lessons are only meant as an introduction to the course! By no means should you expect students to have proficiency or mastery of these concepts by the end of this chapter. Instead, stress each day that students will need to apply their previous learning to solve new problems and that as they continue in this course, they will build better understanding of these new ideas. These lessons will also allow you to informally assess your students’ prior knowledge. This may be helpful for guiding the level of scaffolding in future lessons when these topics are revisited.

Section 1.1 includes four engaging activities that set the stage for student work through the course, as shown in the list below. While these problems are not intended to bring closure to any major concept, they are intended to launch major ideas, such as working with variables and the study of probability.

The overarching goal of this text is to stress Practice 1: Make sense of problems and persevere in solving them. Even when not specifically mentioned, your goal in facilitating these lessons is to encourage understanding through your introductions, questioning and closure activities.

In this chapter it is suggested that you do not yet introduce the practices explicitly, but rather encourage students to begin engaging in these practices through your directions and your questions. In the lesson notes for Chapter 1, six of the practices are identified:

Practice 1: Make sense of problems and persevere in solving them.

Practice 2: Reason abstractly and quantitatively.

Practice 3: Construct viable arguments and critique the reasoning of others.

Practice 4: Model with mathematics.

Practice 7: Look for and make use of structure.

Practice 8: Look for and express regularity in repeated reasoning.

After focusing on one practice per day initially, you might begin to encourage the use of more than one if it is appropriate. More practices will be introduced in Chapter 2. It is suggested, if you plan to make these practices explicit in your classroom that you begin Chapter 3 with a formal introduction to all eight of the mathematical practices.

8SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.

8EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two movingobjects has greater speed.

8EE.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.