MGSE8.NS: The Number System

MGSE8.NS.2: Use rational approximation of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions (e.g., estimate π² to the nearest tenth)

 Circumference and Area of Circles

MGSE8.EE: Expressions and Equations

MGSE8.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

MGSE8.EE.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 lxl ≤ 25) has 2 solutions and x³ = p (where p is a negative or positive rational number and lxl ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000.

 Operations with Radical Expressions
 Simplifying Radical Expressions
 Square Roots

MGSE8.EE.4: Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Understand 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. calculators).

 Unit Conversions
 Unit Conversions 2 - Scientific Notation and Significant Digits

MGSE8.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

MGSE8.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

MGSE8.EE.7a: 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 on the Number Line
 Solving Two-Step Equations

MGSE8.EE.7b: Solve linear equations with 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 on the Number Line
 Solving Two-Step Equations

MGSE8.EE.8a: 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)

MGSE8.EE.8b: Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection.

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

MGSE8.EE.8c: 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)

MGSE8.F: Functions

MGSE8.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

MGSE8.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

MGSE8.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

MGSE8.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

MGSE8.G: Geometry

MGSE8.G.1: Verify experimentally the congruence properties of rotations, reflections, and translations: lines are taken to lines and line segments to line segments of the same length; angles are taken to angles of the same measure; parallel lines are taken to parallel lines.

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

MGSE8.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

MGSE8.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

MGSE8.G.6: Explain a proof of the Pythagorean Theorem and its converse.

 Pythagorean Theorem
 Pythagorean Theorem with a Geoboard

MGSE8.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

MGSE8.G.8: Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

 Distance Formula
 Pythagorean Theorem

MGSE8.G.9: Apply the formulas for the volume of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

 Prisms and Cylinders
 Pyramids and Cones

MGSE8.SP: Statistics and Probability

MGSE8.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

MGSE8.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

MGSE8.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

MGSE8.SP.4: Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.

MGSE8.SP.4.a: Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.

 Histograms

Correlation last revised: 1/19/2017

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.