Assessment Anchors

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

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

Rational Numbers, Opposites, and Absolute Values

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.

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.2.1: 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.

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.3.1: 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 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 II

Solving Equations by Graphing Each Side

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.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.

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).

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.2.1: 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.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.

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.2.1: 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.

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.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.

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.

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.

Correlation last revised: 1/22/2020