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Chapter Overview
Chapter Overview
This chapter builds on the single-variable data displays from previous coursework and the coordinate graphing skills students began developing in Chapter 3. In Section 7.1, students will build circle graphs to represent categorical data. Students then analyze two-variable data with scatterplots and look for patterns. Different types of associations are introduced, and students learn how to place a trend line and use it to make predictions.
Section 7.2 extends the concept of slope as growth rates and steepness begun in Chapter 4. Students will use situations involving triathlons, assembly lines and simple interest to solve rate of change problems. They will identify that steeper lines on the same graph indicate faster rates. Positive and negative slope will be explored through slope triangles on graphical representations, and later in equations.
After learning how to find slope and build linear equations using multiple strategies, students will apply this knowledge in a variety of contexts in Section 7.3. Students will create and analyze trend lines for data (with the help of graphing technology), further investigate associations and look at relationships between categorical variables.
Standards for Mathematical Practice
Standards for Mathematical Practice
Students will create several mathematical models in this chapter. They will look for and make use of the structure of linear equations to make sense of problems and persevere in solving them. As students investigate linear situations, they will construct viable arguments and critique the reasoning of their team members. As you monitor student progress, be sure that students are attending to precision as they analyze units and describe associations.
CA Content Standards
CA Content Standards
8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.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.
8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?
8.EE.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 moving objects has greater speed.
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
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.
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