KY.8.NS: The Number System

1.1: Know that there are numbers that are not rational and approximate them by rational numbers.

KY.8.NS.1: Understand informally that every number has a decimal expansion; the rational numbers are those with decimal expansions that terminate in 0s or eventually repeat. Know that other numbers are called irrational.

Circumference and Area of Circles
Percents, Fractions, and Decimals

KY.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.

Circumference and Area of Circles
Square Roots

KY.8.EE: Expressions and Equations

2.1: Work with radicals and integer exponents.

KY.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

KY.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 perfect squares and perfect cubes are rational.

Operations with Radical Expressions
Simplifying Radical Expressions
Square Roots

KY.8.EE.3: Use numbers expressed in the form of a single digit times an integer power of 10 (Scientific Notation) to estimate very large or very small quantities and express how many times larger or smaller one is than the other.

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

KY.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. Interpret scientific notation that has been generated by technology.

Unit Conversions
Unit Conversions 2 - Scientific Notation and Significant Digits

2.2: Understand the connections between proportional relationships, lines and linear equations.

KY.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

KY.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; know 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

2.3: Analyze and solve linear equations and pairs of simultaneous linear equations.

KY.8.EE.7: Solve linear equations in one variable.

KY.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

KY.8.EE.7.b: Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms.

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

KY.8.EE.8: Analyze and solve a system of two linear equations.

KY.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; understand that a system of two linear equations may have one solution, no solution, or infinitely many solutions.

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)

KY.8.EE.8.b: Solve systems of two linear equations in two variables algebraically by using substitution where at least one equation contains at least one variable whose coefficient is 1 and by inspection for simple cases.

Solving Equations by Graphing Each Side
Solving Linear Systems (Slope-Intercept Form)
Solving Linear Systems (Standard Form)

KY.8.EE.8.c: 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)

KY.8.F: Functions

3.1: Define, evaluate and compare functions.

KY.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)
Function Machines 3 (Functions and Problem Solving)
Introduction to Functions
Linear Functions
Points, Lines, and Equations

KY.8.F.2: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Graphs of Polynomial Functions
Linear Functions
Quadratics in Polynomial Form

KY.8.F.3: Understand properties of linear functions.

KY.8.F.3.a: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line.

Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
Standard Form of a Line

KY.8.F.3.b: Identify and give examples of functions that are not linear.

Absolute Value with Linear Functions
Linear Functions

3.2: Use functions to model relationships between quantities.

KY.8.F.4: Construct a function to model a linear relationship between two quantities.

KY.8.F.4.a: 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)
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Function Machines 1 (Functions and Tables)
Translating and Scaling Functions

KY.8.F.4.b: 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.

Cat and Mouse (Modeling with Linear Systems)
Compound Interest
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Function Machines 1 (Functions and Tables)
Translating and Scaling Functions

KY.8.F.5: Use graphs to represent functions.

KY.8.F.5.a: Describe qualitatively the functional relationship between two quantities by analyzing a graph.

Cat and Mouse (Modeling with Linear Systems)
Distance-Time Graphs
Distance-Time and Velocity-Time Graphs
Exponential Functions
Graphs of Polynomial Functions
Introduction to Exponential Functions
Radical Functions
Translating and Scaling Functions

KY.8.F.5.b: 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
Function Machines 3 (Functions and Problem Solving)

KY.8.G: Geometry

4.1: Understand congruence and similarity using physical models, transparencies, or geometry software.

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

KY.8.G.1.1: Lines are congruent to lines.

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

KY.8.G.1.2: Line segments are congruent to line segments of the same length.

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

KY.8.G.1.3: Angles are congruent to angles of the same measure.

Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

KY.8.G.1.4: Parallel lines are congruent to parallel lines.

Reflections
Rotations, Reflections, and Translations

KY.8.G.2: 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

KY.8.G.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

KY.8.G.4: 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

KY.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.

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

4.2: Understand and apply the Pythagorean Theorem.

KY.8.G.6: Explain a proof of the Pythagorean Theorem and its converse.

Pythagorean Theorem
Pythagorean Theorem with a Geoboard

KY.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.

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

KY.8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Circles
Distance Formula

4.3: Solve real-world and mathematical problems involving volume of cylinders, cones and spheres.

KY.8.G.9: Apply the formulas for the volumes and surface areas of cones, cylinders and spheres and use them to solve real-world and mathematical problems.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

KY.8.SP: Statistics and Probability

5.1: Investigate patterns of association in bivariate data.

KY.8.SP.1: Construct and interpret scatter plots for bivariate numerical 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

KY.8.SP.2: Know that lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a 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

KY.8.SP.3: Use the equation of a linear model to solve problems in the context of bivariate numerical data, interpreting the slope and intercept.

Correlation
Solving Using Trend Lines
Trends in Scatter Plots

Correlation last revised: 1/22/2020

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