8.NR: Numerical Reasoning – rational and irrational numbers, decimal expansion, integer exponents, square and cube roots, scientific notation

8.NR.1: Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.

8.NR.1.1: Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.

Ordering and Approximating Square Roots
Percents, Fractions, and Decimals

8.NR.1.2: Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

Circumference and Area of Circles
Square Roots

8.NR.2: Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.

8.NR.2.1: Apply the properties of integer exponents to generate equivalent numerical expressions.

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

8.NR.2.2: Use square root and cube root symbols to represent solutions to equations. Recognize that x² = p (where p is a positive rational number and |x| is less than or equal to 25) has two solutions and x³ = p (where p is a negative or positive rational number and |x| is less than or equal to 10) has one solution. Evaluate square roots of perfect squares less than or equal to 625 and cube roots of perfect cubes greater than or equal to –1000 and less than or equal to 1000.

Square Roots

8.NR.2.3: Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.

Number Systems
Unit Conversions 2 - Scientific Notation and Significant Digits

8.NR.2.4: Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).

Unit Conversions 2 - Scientific Notation and Significant Digits

8.PAR: Patterning & Algebraic Reasoning – expressions, linear equations, and inequalities

8.PAR.3: Create and interpret expressions within relevant situations. Create, interpret, and solve linear equations and linear inequalities in one variable to model and explain real phenomena.

8.PAR.3.1: Interpret expressions and parts of an expression, in context, by utilizing formulas or expressions with multiple terms and/or factors.

Compound Interest

8.PAR.3.2: Describe and solve linear equations in one variable with one solution (x = a), infinitely many solutions (a = a), or no solutions (a = b). 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).

Solving Equations by Graphing Each Side

8.PAR.3.3: Create and solve linear equations and inequalities in one variable within a relevant application.

Exploring Linear Inequalities in One Variable
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

8.PAR.3.4: Using algebraic properties and the properties of real numbers, justify the steps of a one-solution equation or inequality.

Modeling One-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Solving Two-Step Equations

8.PAR.3.6: Use algebraic reasoning to fluently manipulate linear and literal equations expressed in various forms to solve relevant, mathematical problems.

Solving Formulas for any Variable

8.PAR.4: Show and explain the connections between proportional and non-proportional relationships, lines, and linear equations; create and interpret graphical mathematical models and use the graphical, mathematical model to explain real phenomena represented in the graph.

8.PAR.4.1: Use the equation y = mx (proportional) for a line through the origin to derive the equation y = mx + b (non-proportional) for a line intersecting the vertical axis at b.

Slope-Intercept Form of a Line

8.PAR.4.2: Show and explain that the graph of an equation representing an applicable situation in two variables is the set of all its solutions plotted in the coordinate plane.

Slope-Intercept Form of a Line
Standard Form of a Line

8.FGR: Functional & Graphical Reasoning – relate domain to linear functions, rate of change, linear vs. nonlinear relationships, graphing linear functions, systems of linear equations, parallel and perpendicular lines

8.FGR.5: Describe the properties of functions to define, evaluate, and compare relationships, and use functions and graphs of functions to model and explain real phenomena.

8.FGR.5.1: Show and explain that a function is a rule that assigns to each input exactly one output.

Introduction to Functions
Linear Functions

8.FGR.5.2: Within realistic situations, identify and describe examples of functions that are linear or nonlinear. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

Direct and Inverse Variation
Distance-Time Graphs
Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs
Distance-Time and Velocity-Time Graphs - Metric

8.FGR.5.3: Relate the domain of a linear function to its graph and where applicable to the quantitative relationship it describes.

Absolute Value Equations and Inequalities
Points, Lines, and Equations

8.FGR.5.5: Write and explain the equations y = mx + b (slope-intercept form), Ax + By = C (standard form), and (y – y sub 1) = m(x – x sub 1) (point-slope form) as defining a linear function whose graph is a straight line to reveal and explain different properties of the function.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

8.FGR.5.6: Write a linear function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Point-Slope Form of a Line
Standard Form of a Line

8.FGR.5.7: 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.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Distance-Time Graphs
Distance-Time Graphs - Metric
Distance-Time and Velocity-Time Graphs
Distance-Time and Velocity-Time Graphs - Metric

8.FGR.5.8: Explain the meaning of 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.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric

8.FGR.5.9: Graph and analyze linear functions expressed in various algebraic forms and show key characteristics of the graph to describe applicable situations.

Point-Slope Form of a Line
Slope-Intercept Form of a Line
Standard Form of a Line

8.FGR.6: Solve practical, linear problems involving situations using bivariate quantitative data.

8.FGR.6.1: Show that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, visually fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line of best fit.

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

8.FGR.6.2: Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercepts.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

8.FGR.6.3: Explain the meaning of the predicted slope (rate of change) and the predicted intercept (constant term) of a linear model in the context of the data.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

8.FGR.6.4: Use appropriate graphical displays from data distributions involving lines of best fit to draw informal inferences and answer the statistical investigative question posed in an unbiased statistical study.

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

8.FGR.7: Justify and use various strategies to solve systems of linear equations to model and explain realistic phenomena.

8.FGR.7.1: Interpret and solve relevant mathematical problems leading to two linear equations in two variables.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric

8.FGR.7.2: Show and explain that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because the points of intersection satisfy both equations simultaneously.

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

8.FGR.7.3: Approximate solutions of two linear equations in two variables by graphing the equations and solving simple cases by inspection.

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

8.FGR.7.4: Analyze and solve systems of two linear equations in two variables algebraically to find exact solutions.

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

8.FGR.7.5: Create and compare the equations of two lines that are either parallel to each other, perpendicular to each other, or neither parallel nor perpendicular.

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

8.GSR: Geometric & Spatial Reasoning – Pythagorean theorem and volume of triangles, rectangles, cones, cylinders, and spheres

8.GSR.8: Solve geometric problems involving the Pythagorean Theorem and the volume of geometric figures to explain real phenomena.

8.GSR.8.1: Explain a proof of the Pythagorean Theorem and its converse using visual models.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

8.GSR.8.2: Apply the Pythagorean Theorem to determine unknown side lengths in right triangles within authentic, mathematical problems in two and three dimensions.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

8.GSR.8.3: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system in practical, mathematical problems.

Distance Formula

8.GSR.8.4: Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve in relevant problems.

Measuring Volume
Prisms and Cylinders
Pyramids and Cones