NS: The Number System

(Framing Text): Know that there are numbers that are not rational, and approximate them by rational numbers.

NS.M.8.1: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually and convert a decimal expansion which repeats eventually into a rational number.

 Part-to-part and Part-to-whole Ratios
 Percents, Fractions, and Decimals

NS.M.8.2: Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram and estimate the value of expressions such as π². (e.g., By truncating the decimal expansion of √2, show that √2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations.)

 Circumference and Area of Circles

EE: Expressions and Equations

(Framing Text): Work with radicals and integer exponents.

EE.M.8.3: Know and apply the properties of integer exponents to generate equivalent numerical expressions. (e.g., 3² × 3–⁵ = 3–³ = 1/3³ = 1/27.)

 Dividing Exponential Expressions
 Exponents and Power Rules
 Multiplying Exponential Expressions
 Simplifying Algebraic Expressions II

EE.M.8.4: Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

 Operations with Radical Expressions
 Simplifying Radical Expressions
 Square Roots

EE.M.8.5: Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. (e.g., Estimate the population of the United States as 3 × 10⁸ and the population of the world as 7 × 10⁹, and determine that the world population is more than 20 times larger.)

 Unit Conversions
 Unit Conversions 2 - Scientific Notation and Significant Digits

EE.M.8.6: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. (e.g., Use millimeters per year for seafloor spreading.) Interpret scientific notation that has been generated by technology.

 Unit Conversions
 Unit Conversions 2 - Scientific Notation and Significant Digits

(Framing Text): Understand the connections between proportional relationships, lines, and linear equations.

EE.M.8.7: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. (e.g., Compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.)

 Direct and Inverse Variation

EE.M.8.8: 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.

 Linear Inequalities in Two Variables
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

(Framing Text): Analyze and solve linear equations and pairs of simultaneous linear equations.

EE.M.8.9: Solve linear equations in one variable.

EE.M.8.9.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).

 Modeling One-Step Equations
 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Two-Step Equations

EE.M.8.9.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms.

 Modeling and Solving Two-Step Equations
 Solving Algebraic Equations II
 Solving Equations on the Number Line
 Solving Two-Step Equations

EE.M.8.10: Analyze and solve pairs of simultaneous linear equations.

EE.M.8.10.a: 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.

 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

EE.M.8.10.b: Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. (e.g., 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.)

 Cat and Mouse (Modeling with Linear Systems)
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

EE.M.8.10.c: Solve real-world and mathematical problems leading to two linear equations in two variables. (e.g., Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.)

 Cat and Mouse (Modeling with Linear Systems)
 Solving Equations by Graphing Each Side
 Solving Linear Systems (Matrices and Special Solutions)
 Solving Linear Systems (Slope-Intercept Form)
 Solving Linear Systems (Standard Form)

F: Functions

(Framing Text): Define, evaluate, and compare functions.

F.M.8.11: 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.

 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Introduction to Functions
 Points, Lines, and Equations

F.M.8.12: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., 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.)

 Graphs of Polynomial Functions
 Linear Functions
 Quadratics in Polynomial Form

F.M.8.13: 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. (e.g., 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.)

 Absolute Value with Linear Functions
 Linear Functions
 Point-Slope Form of a Line
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Standard Form of a Line

(Framing Text): Use functions to model relationships between quantities.

F.M.8.14: 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.

 Arithmetic Sequences
 Cat and Mouse (Modeling with Linear Systems)
 Compound Interest
 Function Machines 1 (Functions and Tables)
 Function Machines 2 (Functions, Tables, and Graphs)
 Function Machines 3 (Functions and Problem Solving)
 Linear Functions
 Points, Lines, and Equations
 Slope-Intercept Form of a Line
 Translating and Scaling Functions

F.M.8.15: 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.

 Distance-Time Graphs
 Distance-Time and Velocity-Time Graphs
 Linear Functions

G: Geometry

(Framing Text): Understand congruence and similarity using physical models, transparencies, or geometry software.

G.M.8.16: Verify experimentally the properties of rotations, reflections and translations:

G.M.8.16.a: Lines are taken to lines, and line segments to line segments of the same length.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

G.M.8.16.b: Angles are taken to angles of the same measure.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

G.M.8.16.c: Parallel lines are taken to parallel lines.

 Reflections
 Rotations, Reflections, and Translations
 Similar Figures
 Translations

G.M.8.17: Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

 Reflections
 Rock Art (Transformations)
 Rotations, Reflections, and Translations
 Translations

G.M.8.18: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.

 Dilations
 Rock Art (Transformations)
 Rotations, Reflections, and Translations
 Translations

G.M.8.19: Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations and dilations; given two similar two dimensional figures, describe a sequence that exhibits the similarity between them.

 Dilations
 Similar Figures

G.M.8.20: Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. (e.g., Arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.)

 Isosceles and Equilateral Triangles
 Polygon Angle Sum
 Similar Figures
 Similarity in Right Triangles
 Triangle Angle Sum

(Framing Text): Understand and apply the Pythagorean Theorem.

G.M.8.21: Explain a proof of the Pythagorean Theorem and its converse.

 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

G.M.8.22: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

G.M.8.23: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

 Distance Formula
 Pythagorean Theorem

(Framing Text): Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

G.M.8.24: Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems.

 Prisms and Cylinders
 Pyramids and Cones

SP: Statistics and Probability

(Framing Text): Investigate patterns of association in bivariate data.

SP.M.8.25: 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.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

SP.M.8.26: 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.

 Correlation
 Least-Squares Best Fit Lines
 Solving Using Trend Lines
 Trends in Scatter Plots

SP.M.8.27: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. (e.g., 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.)

 Correlation

SP.M.8.28: 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. (e.g., 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?)

 Histograms

Correlation last revised: 4/4/2018

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