8th GradeCore Connections 3Chapter 7
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills7.1.1 / None – Circle graphs are not in the standards. / The focus of the lesson is to read and construct a circle graph. / 7-10 (8.EE.8b)
7-11 (8.G.1abc) / This is not a standard and therefore teachers may skip this lesson. / N/A
7.1.2 / 8.SP.A.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. / The focus of this lesson is an introduction to constructing and interpreting scatterplots. It also helps to show students why we use scatterplots.
(7-15 and 7-16) / 7-17 (8.SP.1) / 6.NS.C.8
Graphing and determining distances on coordinate grid.
7.1.3 / 8.SP.A.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.A.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. / The focus of the lesson is to provide more practice constructing scatterplots. The lesson then extends to describing associations and drawing and interpreting the line of best fit.
(7-24, 7-26, and 7-27) / 7-29 (8.SP.1)
7-30 (8.SP.2, 3)
7-33 (8.EE.7b)
7-34 (8.G.4) / 6.NS.C.8
Graphing and determining distances on coordinate grid.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
7.2.1 / 8.EE.B.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.A.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. / The focus of the lesson is to write an equation of a line.
(7-35 and 7-36) / None / Teachers may want to have students describe/show the growth triangle in their posters. / 7.G.A.1
Determine scaled side length, creating a scale drawing.
7.RP.A.2
Recognize and represent proportional relationships.
7.2.2 / 8.EE.B.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. / The focus of this lesson is to introduce the word “slope” and using a slope triangle. It also connects slope to the concept of unit rate.
(7-43 and 7-47) / 7-51 (8.F.5) / 7.G.A.1
Determine scaled side length, creating a scale drawing.
7.RP.A.2
Recognize and represent proportional relationships.
7.2.3 / 8.EE.B.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. / The focus of this lesson is to draw slope triangles and understand similar slope triangles have the same slope.
(7-55 and 7-56) / None / 7-57 is not related to this standard; however it assists in examining graphs.
7-59 discusses the slope of parallel lines. / 7.G.A.1
Determine scaled side length, creating a scale drawing.
7.RP.A.2
Recognize and represent proportional relationships.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
7.2.4 / 8.EE.B.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. / The focus of this lesson is understanding more about slope. There is no new material really covered in the lesson, but it does discuss negative growth.
(7-68 and 7-69) / 7-72 (8.SP.1)
7-75 (8.EE.5) / This lesson serves as a reinforcement lesson. If students have a strong grasp on the concepts, the teacher may choose to skip the lesson. / 7.G.A.1
Determine scaled side length, creating a scale drawing.
7.RP.A.2
Recognize and represent proportional relationships.
7.2.5 / 8.EE.B.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.B.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. / This lesson focuses on proportional relationships and the various representations that can be compared.
(7-77) / 7-83 (8.G.1abc) / Adjusted lesson can be used in place of 7.2.5.
Adjusted lesson includes:
Problem 7-77
Contextual practice problems similar to PARCC #12. / 7.G.A.1
Determine scaled side length, creating a scale drawing.
7.RP.A.2
Recognize and represent proportional relationships.
Lesson / MS-CCRS Taught / Focus for Lesson / MS-CCRS Specific Problem(s) / Optional Supplements and Adjustments / Pre-requisite standards and skills
7.3.1 / 8.SP.A.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. / The focus of the lesson is to provide students practice interpreting the contextual meaning of the line of best fit.
(7-88 and 7-89) / 7-91 (8.SP.2) / None
7.3.2 / 8.SP.A.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.A.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. / The focus of this lesson is for students to interpret the line of best fit.
(7-97 and 7-99) / 7-102 (8.SP.1,2)
7-103(8.SP.1-3)
7-105 (8.EE.6) / None
7.3.3 / 8.SP.A.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? / The focus of this lesson is to give students practice answering questions given two-way tables.
(7-107 and 7-109) / 7-110 (8.SP.3)
7-111 (8.SP.4)
7-112 (8.SP.2)
Closure:
7-119 (8.EE.6)
7-120 (8.EE.7b) / Problem 7-108 focuses on bar graphs and histograms which are not 8th grade standards; therefore, the teacher may choose to skip this problem. / None – This is introduced in the 8th grade.
Assessment Understanding According to PARCC (Section Quiz and Chapter Assessment)
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery8.SP.A.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. / EOY / 3, 5,
and 7 /
- Tasks might have spreadsheet-like technology features, such as the ability to select data ranges for the two axes and have the scatterplot automatically generated.
Full mastery is expected.
Future
No further lessons in the text.
8.SP.A.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. / EOY / 2, 5,
and 7 /
- Tasks might have technology features such as the ability to adjust the position of a line and rotate it.
- Tasks do not require students to write or identify an equation.
Full mastery is expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
8.SP.A.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. / EOY / 2, 4, 6, and 7 /
- Tasks are word problems based on bivariate measurement data that require students to sue the equation of a linear model.
- The testing interface can provide students with a calculation aid of the specified kind for these tasks.
Full mastery is expected.
Future
No further lessons in the text.
8.SP.A.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? / EOY / 2, 4, 5, and 7 /
- One-third of tasks involve basic comprehension questions about a two-way table, such as “How many students who don’t have chores have a curfew?”
- One-third of the tasks involve computing marginal sums or marginal percentages.
- One-third of tasks involve interpretation or patterns of association.
- Tasks that require finding missing values within the categories are excluded.
- Tasks are limited to two-by-two tables.
- The testing interface can provide students with a calculation aid of the specified kind for these tasks.
Full mastery is expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
8.EE.B.5-1
Graph proportional relationships, interpreting the unit rate as the slope of the graph. / EOY and PBA / 1 and 5 /
- Pool should contain tasks with and without contexts.
- The testing interface can provide students with a calculation aid of the specified kind for these tasks.
Full mastery is expected.
Future
No further lessons in the text.
8.EE.B.5-2
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. / EOY and PBA / 7 /
- Pool should contain tasks with and without contexts.
- The testing interface can provide students with a calculation aid of the specified kind for these tasks.
Full mastery is expected.
Future
No further lessons in the text.
8.EE.B.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. / EOY / 2 and 7 /
- Tasks do not have context.
- Given a non-vertical line in the coordinate plane, tasks might for example require students to choose two pairs of points and record the rise, run, and slope relative to each pair and verify that they are the same.
- The testing interface can provide students with a calculation aid of the specified kind for these tasks.
8.C.1.1 – Base reasoning on the principle that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
- Note especially the portion of 8.EE.6 after the semicolon.
- Note especially the portion of 8.EE.6 after the semicolon.
Full mastery is expected.
Future
No further lessons in the text.
MS-CCRS / EOY or PBA / Math Practice / Clarifications / Calculator or No Calculator / Chapter Mastery
8.F.A.3-1
Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; / EOY / 2 and 7 /
- Tasks have a “thin context” or no context.
- Tasks require students to approach linear equations from a functional perspective, for example by computing outputs from inputs or by identifying equations that do or do not define one variable as a linear function of the other.
- Equations can be presented in forms other than y = mx + b. For example, the equation can be viewed as a function machine with x the input and y the output – or as a function machine with y the input and x the output.
Focus stays on linear functions.
Future
Lessons 8.1.1 and 8.3.1 will provide additional instruction on non-linear.
8.F.A.3-2
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. / EOY / 7 /
- Tasks have a “thin context” or no context.
- Tasks require student to demonstrate understanding of function nonlinearity, for example by recognizing or producing equations that do not define linear functions, or by recognizing or producing pairs of points that belong to the graph of the function yet do not lie on a straight line.
- Tasks do not require students to produce a proof; for that aspect of standard 8.F.3, see Grade 8 PBA.
- Tasks involving symbolic representations are limited to polynomial functions i.e. .
8.C.3.1 – Construct, autonomously, chains of reasoning that will justify or refute propositions or conjectures.
- Note especially the portion of 8.F.3 after the semicolon. Tasks require students to prove that a given function is linear or nonlinear.
Focus stays on linear functions.
Future
College Preparatory MathematicsDesoto County Schools