Enduring Understanding:
Our actions affect our world.
Overarching Questions:
How can I analyze data to understand a problem exists?
How can I use patterns to make predictions?
How can I use what I know to find what I don't?
How can I use patterns to make predictions?
How can I use what I know to find what I don't?
Essential Questions:
How can we model data, determine trends and make predictions about our community or world?
How can we analyze how waste impacts our environment?
How can we recognize when a mathematical or real life pattern is linear or nonlinear?
How can different representations of linear patterns present different perspectives of situations?
How can a relationship be analyzed with tables, graphs, and equations?
Why is one variable dependent upon the other in relationships?
What properties of a function make it a linear function?
How can you recognize a linear equation? How can you draw its graph?
How can you use the slope of a line to describe the line?
How can you write an equation of a line?
How can we analyze how waste impacts our environment?
How can we recognize when a mathematical or real life pattern is linear or nonlinear?
How can different representations of linear patterns present different perspectives of situations?
How can a relationship be analyzed with tables, graphs, and equations?
Why is one variable dependent upon the other in relationships?
What properties of a function make it a linear function?
How can you recognize a linear equation? How can you draw its graph?
How can you use the slope of a line to describe the line?
How can you write an equation of a line?
Common Core Standards Addressed:
Grade 8>> Expressions and Equations:
Understand the connections between proportional relationships, lines, and linear equations.
CCSS.MATH.CONTENT.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.
Grade 8>> Functions:
Define, evaluate, and compare functions.
CCSS.MATH.CONTENT.8.F.A.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.
CCSS.MATH.CONTENT.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.
Use functions to model relationships between quantities.
CCSS.MATH.CONTENT.8.F.B.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.
CCSS.MATH.CONTENT.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
8th Grade>> Statistics and Probability
Investigate patterns of association in bivariate data.
CCSS.MATH.CONTENT.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.
CCSS.MATH.CONTENT.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.
Understand the connections between proportional relationships, lines, and linear equations.
CCSS.MATH.CONTENT.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.
Grade 8>> Functions:
Define, evaluate, and compare functions.
CCSS.MATH.CONTENT.8.F.A.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.
CCSS.MATH.CONTENT.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.
Use functions to model relationships between quantities.
CCSS.MATH.CONTENT.8.F.B.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.
CCSS.MATH.CONTENT.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
8th Grade>> Statistics and Probability
Investigate patterns of association in bivariate data.
CCSS.MATH.CONTENT.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.
CCSS.MATH.CONTENT.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.