#8 Domain: Functions Standard: CC.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. Targets: KNOWLEDGE: (1) Recognize that slope is determined by the constant rate of change. (2) Recognize that the y-intercept is the initial value where x=0. (3) Determine the rate of change from two (x,y) values, a verbal description, values in a table, or graph. (4) Determine the initial value from two (x,y) values, a verbal description, values in a table, or graph REASONING: (1) construct a function to model a linear relationship between two quantities (2) relate the rate of change and initial value to real world quantities in linear function in terms of the situation modeled and in terms of its graph or a table of values rate of change linear function input/output table slope Determine the slope of a function using a table or graph Determine the rate of change from a verbal description, table or graph Determine the initial value from a verbal description, table, or graph 1! Intellectual Property of McCracken County Public Schools
#5 Domain: Functions Standard: CC.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. Targets: KNOWLEDGE: (1) students will recognize y=mx+b as linear and recognize that any equation/function to the power of 2 is quadratic REASONING: (1) compare/contrast examples of functions that are not linear linear function parabola quadratic square Slope-intercept form Describe the appearance of a linear function Explain y=mx+b as it relates to m = slope and b = y - intercept and (x,y) being any point on the line, and understand itʼs graph is linear Give an example of an equation (function) that is non-linear Can my students -describe a linear function as a straight line -identify the parts of y = mx+b -give an example of non-linear function as one with a power > 1 2! Intellectual Property of McCracken County Public Schools
#4 Domain: Expressions and Equations CC.8.EE.8: Analyze and solve pairs of simultaneous linear equations Standard: CC.8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Targets: KNOWLEDGE: (1) identify the solutions based on intersections or the lack of the intersection linear equations variables points of intersection systems of equations Given two linear equations, identify the point of intersection of the two graphs Name (describe) the solution (point of intersection) Do my students understand: -the solution (ordered pair or point) for the graph of two linear equations is their point of intersection 3! Intellectual Property of McCracken County Public Schools
#2 Domain: Statistics and Probability Standard: CC.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. Targets: KNOWLEDGE: (1) construct and interpret scatter plots using patterns such as clustering, outliers, positive or negative correlation (2) define and label clustering, outliers, positive and negative correlation REASONING: (1) analyze the characteristics of data: clusters, quartiles, gaps and outliers bivariate measurement clustering gaps outliers linear/non linear association Construct and interpret a scatter-plot Identify patterns, clustering, outliers Explain these patterns: positive and negative correlation no or constraint, gap Can my student accurately: -construct and interpret a scatter plot -identify and explain any patterns 4! Intellectual Property of McCracken County Public Schools
#12 Domain: Statistics and Probability Standard: CC.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. Targets: KNOWLEDGE: (1) interpret slope-intercept form within the best fit line to y=mx+b REASONING: (1) evaluate the slope of a line bivariate measurement linear model slope best fit line (line of fit) scatter plot Find slope-intercept from data given on a scatter plot using best fit line Can my student find the slope-intercept form of a line of best fit from a scatter plot 5! Intellectual Property of McCracken County Public Schools
#3 Domain: Statistics and Probability Standard: CC.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 Targets: KNOWLEDGE: (1) understand straight lines are used to model relationships between data REASONING: (1) analyze the association between two sets of data (categorical data) (2) if a correlation is found, draw a line of fit best fit line quantitative variables scatter plot What kind of lines are used to show a relationship between two sets of data? Students: -should know a straight line often indicates relationship 6! Intellectual Property of McCracken County Public Schools
#1 Domain: Statistics and Probability Standard: CC.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? Targets: KNOWLEDGE: (1) construct a two way table REASONING: (1) interpret the data in a two way table (2) the relative frequencies to describe relationships two way tables Construct a two way table using given data Do you observe patterns or relationships? What are they? (Did your students master the standard and how do you know?) Is my student able to: -construct a two way table accurately? -identify and analyze any patterns or relationships between data 7! Intellectual Property of McCracken County Public Schools
#1 Domain: Functions Standard: CC.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.1 Targets: KNOWLEDGE: (1) students will understand input and output relationships of functions with tables and graphs (2) students will learn that x is the input and y is the output function input/output ordered pairs What is a function? Construct a function table with a given equation, then graph the function (Did your students master the standard and how do you know?) Do my students know: -a function is a relationship where every x (input) has exactly one y (output) -how to create a function table, given an equation -to accurately graph the function 8! Intellectual Property of McCracken County Public Schools
#3 Domain: Functions Standard: CC.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. Targets: KNOWLEDGE: (1) identify functions algebraically, graphically, and numerically involving real world situations REASONING: (1) compare and contrast two functions with different representations (2) draw conclusions based on those different representations linear function algebraic expression rate of change rate of change Given an algebraic equation, table and graph explain how each is or is not a function and why Compare and contrast two function with different representations verbally Do my students: -exhibit understanding that an algebraic equation with a power >1 is not a function -that in a table, all x values must have exactly 1 y value to be a function -that a graph must pass the vertical line test to be a function 9! Intellectual Property of McCracken County Public Schools
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