M08.A-N: The Number System

M08.A-N.1: Demonstrate an understanding of rational and irrational numbers.

M08.A-N.1.1: Apply concepts of rational and irrational numbers.

M08.A-N.1.1.1: Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths).

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

M08.A-N.1.1.2: Convert a terminating or repeating decimal to a rational number (limit repeating decimals to thousandths).

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

M08.A-N.1.1.3: Estimate the value of irrational numbers without a calculator (limit whole number radicand to less than 144).

Circumference and Area of Circles

M08.A-N.1.1.4: Use rational approximations of irrational numbers to compare and order irrational numbers.

Circumference and Area of Circles
Square Roots

M08.A-N.1.1.5: Locate/identify rational and irrational numbers at their approximate locations on a number line.

Circumference and Area of Circles
Rational Numbers, Opposites, and Absolute Values
Square Roots

M08.B-E: Expressions and Equations

M08.B-E.1: Demonstrate an understanding of expressions and equations with radicals and integer exponents.

M08.B-E.1.1: Represent and use expressions and equations to solve problems involving radicals and integer exponents.

M08.B-E.1.1.1: Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator (with final answers expressed in exponential form with positive exponents). Properties will be provided.

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

M08.B-E.1.1.2: 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 perfect squares (up to and including 12²) and cube roots of perfect cubes (up to and including 5³) without a calculator.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

M08.B-E.1.1.3: Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10 and express how many times larger or smaller one number is than another.

Number Systems
Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

M08.B-E.1.1.4: Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in 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 (e.g., interpret 4.7EE9 displayed on a calculator as 4.7 × 10 to the 9th power).

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

M08.B-E.2: Understand the connections between proportional relationships, lines, and linear equations.

M08.B-E.2.1: Analyze and describe linear relationships between two variables, using slope.

M08.B-E.2.1.1: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

Beam to Moon (Ratios and Proportions)
Direct and Inverse Variation

M08.B-E.2.1.2: Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane.

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

M08.B-E.2.1.3: 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

M08.B-E.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

M08.B-E.3.1: Write, solve, graph, and interpret linear equations in one or two variables, using various methods.

M08.B-E.3.1.1: Write and identify 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 by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

M08.B-E.3.1.2: Solve linear equations that have 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 I
Solving Algebraic Equations II
Solving Equations by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

M08.B-E.3.1.3: Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously.

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)

M08.B-E.3.1.4: Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection.

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)

M08.B-E.3.1.5: Solve real-world and mathematical problems leading to two linear equations in two variables.

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)

M08.B-F: Functions

M08.B-F.1: Analyze and interpret functions.

M08.B-F.1.1: Define, evaluate, and compare functions displayed algebraically, graphically, or numerically in tables or by verbal descriptions.

M08.B-F.1.1.1: Determine whether a relation is a function.

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

M08.B-F.1.1.2: Compare properties of two functions, each represented in a different way (i.e., algebraically, graphically, numerically in tables, or by verbal descriptions).

Function Machines 2 (Functions, Tables, and Graphs)
Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

M08.B-F.1.1.3: 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.

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

M08.B-F.2: Use functions to model relationships between quantities.

M08.B-F.2.1: Represent or interpret functional relationships between quantities using tables, graphs, and descriptions.

M08.B-F.2.1.1: 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

M08.B-F.2.1.2: 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 or determine a graph that exhibits the qualitative features of a function that has been described verbally.

Arithmetic Sequences
Function Machines 3 (Functions and Problem Solving)
Graphs of Polynomial Functions
Linear Functions
Slope-Intercept Form of a Line
Translating and Scaling Functions

M08.C-G: Geometry

M08.C-G.1: Demonstrate an understanding of geometric transformations.

M08.C-G.1.1: Apply properties of geometric transformations to verify congruence or similarity.

M08.C-G.1.1.1: Identify and apply properties of rotations, reflections, and translations.

Circles
Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures
Translations

M08.C-G.1.1.2: Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them.

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

M08.C-G.1.1.3: Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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

M08.C-G.1.1.4: Given two similar two-dimensional figures, describe a sequence of transformations that exhibits the similarity between them.

Circles
Dilations
Similar Figures

M08.C-G.2: Understand and apply the Pythagorean theorem.

M08.C-G.2.1: Solve problems involving right triangles by applying the Pythagorean theorem.

M08.C-G.2.1.1: Apply the converse of the Pythagorean theorem to show a triangle is a right triangle.

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

M08.C-G.2.1.2: Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. (Figures provided for problems in three dimensions will be consistent with Eligible Content in grade 8 and below.)

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Surface and Lateral Areas of Pyramids and Cones

M08.C-G.2.1.3: Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Circles
Distance Formula
Pythagorean Theorem

M08.C-G.3: Solve real-world and mathematical problems involving volume.

M08.C-G.3.1: Apply volume formulas of cones, cylinders, and spheres.

M08.C-G.3.1.1: Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical problems. Formulas will be provided.

Prisms and Cylinders
Pyramids and Cones

M08.D-S: Statistics and Probability

M08.D-S.1: Investigate patterns of association in bivariate data.

M08.D-S.1.1: Analyze and interpret bivariate data displayed in multiple representations.

M08.D-S.1.1.1: 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 correlation, linear association, and nonlinear association.

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

M08.D-S.1.1.2: For scatter plots that suggest a linear association, identify a line of best 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

M08.D-S.1.1.3: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.

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

M08.D-S.1.2: Understand that patterns of association can be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

Histograms

M08.D-S.1.2.1: 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 associations between the two variables.

Histograms