8.MP: Mathematical Practices

(Framing Text): Students become mathematically proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes.

8.MP.1: Make sense of problems and persevere in solving them.

Biconditional Statements
Conditional Statements
Estimating Population Size
Pattern Flip (Patterns)

8.MP.1.a: Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Improper Fractions and Mixed Numbers
Linear Inequalities in Two Variables
Modeling One-Step Equations
Multiplying with Decimals
Pattern Flip (Patterns)
Polling: City
Solving Equations on the Number Line
Using Algebraic Expressions

8.MP.2: Reason abstractly and quantitatively.

Conditional Statements
Estimating Population Size

8.MP.3: Construct viable arguments and critique the reasoning of others.

Biconditional Statements

8.MP.3.a: Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

Biconditional Statements
Conditional Statements

8.MP.4: Model with mathematics.

Estimating Sums and Differences

8.MP.5: Use appropriate tools strategically.

Elapsed Time

8.MP.5.a: Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

Segment and Angle Bisectors

8.MP.6: Attend to precision.

Biconditional Statements
Fraction, Decimal, Percent (Area and Grid Models)
Using Algebraic Expressions

8.MP.6.a: Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

Arithmetic Sequences
Finding Patterns
Fraction, Decimal, Percent (Area and Grid Models)
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

8.MP.7: Look for and make use of structure.

Pattern Flip (Patterns)

8.MP.7.a: Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

Arithmetic Sequences
Finding Patterns
Function Machines 2 (Functions, Tables, and Graphs)
Geometric Sequences
Pattern Flip (Patterns)

8.MP.8: Look for and express regularity in repeated reasoning.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Finding Patterns
Geometric Sequences
Pattern Finder
Pattern Flip (Patterns)

8.MP.8.a: Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

8.NS: Number System

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

8.NS.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

8.NS.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 (e.g., π²).

Circumference and Area of Circles
Ordering and Approximating Square Roots

8.NS.3: Understand how to perform operations and simplify radicals with emphasis on square roots.

Operations with Radical Expressions
Simplifying Radical Expressions

8.EE: Expressions and Equations

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

8.EE.1: Know and apply the properties of integer exponents to generate equivalent numerical expressions.

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

8.EE.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 small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

8.EE.3: 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.

Unit Conversions 2 - Scientific Notation and Significant Digits

8.EE.4: 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 relationships.

8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.

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

8.EE.6: 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 inequalities and pairs of simultaneous linear equations.

8.EE.7: Solve linear equations and inequalities in one variable.

8.EE.7.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 by Graphing Each Side
Solving Equations on the Number Line
Solving Two-Step Equations

8.EE.7.b: Solve single-variable linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms.

Absolute Value Equations and Inequalities
Compound Inequalities
Exploring Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Modeling One-Step Equations
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 Linear Inequalities in One Variable
Solving Two-Step Equations

8.EE.7.c: Solve single-variable absolute value equations.

Absolute Value Equations and Inequalities

8.EE.8: Analyze and solve pairs of simultaneous linear equations.

8.EE.8.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)

8.EE.8.b: Solve systems of two linear equations in two variables graphically, approximating when solutions are not integers 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)

8.EE.8.c: Solve real-world and mathematical problems leading to two linear equations in two variables graphically.

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)

8.F: Functions

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

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.

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

8.F.2: Compare properties of two functions, each represented in a different way (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

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.

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.

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.

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

8.F.5: 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

8.G: Geometry

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

8.G.1: Verify experimentally the properties of rotations, reflections, and translations:

8.G.1.a: Lines are taken to lines, and line segments to line segments of the same length.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.1.b: Angles are taken to angles of the same measure.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.1.c: Parallel lines are taken to parallel lines.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

8.G.3: Observe that orientation of the plane is preserved in rotations and translations, but not with reflections. Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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

8.G.5: 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.

Investigating Angle Theorems
Similar Figures
Triangle Angle Sum

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

8.G.6: Explore and explain proofs of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

8.G.7: 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

8.G.8: 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.

8.G.9: 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

8.SP: Statistics and Probability

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

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.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

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.

Correlation
Solving Using Trend Lines

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.

Solving Using Trend Lines