Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Input-Output Relationships
Making Tables
Complete a table of values from an equation or situation to solve problems.
Create and use tables of values from an equation or situation to solve problems.
Graphing on the Coordinate Plane
Identify and graph points in the coordinate plane, describing their relationship to axes and quadrants.
Create graphs from a table or situation and use them to solve problems.
Interpreting Graphs
Analyze qualitative graphs.
Interpret information given in a graph.
Create a graph to model a situation.
Tables, Graphs and Equations
Translate tables and graphs into equations.
Generate different representations of the same two variable data.
Recognize that tabular and graphical representations may be partial representations.
Using Technology to Explore Data
Identify the basic features of the Graphing Calculator
Use the Graphing Calculator to perform basic calculations
Use a graphing calculator to investigate graphs of a linear function
Use interactive tables to investigate graphs of a linear function
Introduction to Functions
Identify functions from tables, graphs and equations.
Determine if a real world situation describes a functional relationship.
Linear vs. Nonlinear Functions
Interpret rate of change from a graph or table.
Differentiate functions as either linear or non-linear.
Linear Functions
Constructing Linear Functions
Analyze a table of values to find rate of change and initial value.
Interpret the rate of change and initial value of a linear function in terms of the situation it models, or a table of values.
Rate of Change and Introduction to Slope
Determine the positive slope of a line from a table and a graph.
Compare positive slopes in a real world situation.
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Exploring Slope
Recognize the difference between positive slope, negative slope, no slope and zero slope.
Determine the value of the slope of a line from a table or a graph.
Proportional Relationships
Determine whether a linear function is a direct variation.
Solve problems involving direct variation.
Compare proportional and non-proportional linear functions in the form of a table, graph and equation.
Slope Intercept Form
Analyze a graph to determine slope and y-intercept.
Graph a linear function using the slope and y-intercept.
Write a linear equation in slope-intercept form given the slope and y-intercept.
Standard Form
Analyze a linear graph to determine the intercepts.
Write linear equations in standard form to model real world scenarios.
Determine and interpret the intercepts of a linear function from an equation in standard form.
Graphing in a Variety of Contexts
Construct and analyze graphs given two components of a linear function
Estimate y-intercepts on a graph
Writing Equations for linear relationships
Writing Linear Equations
Write a linear equation in slope-intercept form given the slope and a point other than the y-intercept
Compare and contrast using point-slope form and the slope-intercept form to get an equation to slope-intercept form
Writing Linear Equations Given 2 points
Write a linear equation in slope-intercept form given two points.
Applying Linear Functions
Determine what the slope and y-intercept are and what they represent in real-world functional relationships
Use real world scenarios of linear functions to write an equation in slope-intercept form.
Evaluate inputs and outputs for linear equations in slope-intercept form.
Comparing Slopes and Intercepts
Determine slope and y-intercept of linear functions represented differently.
Compare the slope and intercepts of linear functions, including when they are expressed as equations written in different forms
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Comparing Functions in the Real World
Analyze real world linear relationships in order to make comparisons.
Performance Objective
Patterns in Bivariate Data
Constructing Scatterplots
Create a scatterplot using a table of values.
Analyze a scatterplot.
Classify dependent and independent variables.
Interpreting Clusters and Outliers
Identify clusters and outliers in a scatterplot and table of values.
Analyze the influence outliers and clusters have on the data set.
Explain the meaning of clusters and outliers in context
Exploring Assosiation
Analyze the correlation and association in scatterplots.
Drawing Trend Lines
Use a graphing calculator to graph scatterplots and draw the trend line
Draw a line of best fit in scatterplots and identify its purpose.
Using Equations to Represent Trend Lines
Find and interpret the slope of a trend line
Create the linear equation of the trend line.
Making Predications
Use a calculator to graph a scatterplot and create line of bet fit.
Substitute x and y values into the data to create predictions of a real world scenario.
Analyze data to determine interpolate and extrapolate predictions.
Comparing Data Sets
Analyze data sets using the trend line
Compare and contrast sets of data
Making Two-Way Tables
Create a two-way table that organizes bivariate data.
Determine variables of a scenario in bivariate data.
Label components of the two-way table accordingly.
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Interpreting Two-Way Tables
Compute relative frequencies and identify associations in a two-way table.
Generate conclusions of the data.
Peformance Task
Linear Equations
Simplify Algebraic expressions
Identify and combine like terms in algebraic expressions.
Simplify algebraic expressions.
Write and identify equivalent expressions.
Using the Distributive Property
Use the distributive property to simplify expressions.
Identify and justify distributed expressions.
Combining Like Terms to Solve Equations
Identify and combine like terms to solve one-variable linear equations.
Determine and apply properties of equality when solving an equation.
Solving with the Distributive Property
Solve one-variable linear equations using the distributive property.
Justify the steps taken to solve one-variable linear equations involving the distributive property.
Solving Equations with Rational Numbers
Identify the least common denominator of fractions to combine like terms and solve equations.
Solve one-variable linear equations with rational numbers using properties of equality.
Equivalent Equations
Re-write equations in an equivalent form.
Modeling with Variables on Both Sides
Use algebra tiles to model one-variable equations with variables on both sides.
Use algebra tiles to solve one-variable equations with variables on both sides with and without using zero pairs.
Solving with Variables on Both Sides
Determine and apply the steps needed to isolate a variable in a linear equation with variables on both sides.
Solve equations with variables on both sides.
Solving Multistep Equations with Variables on Both Sides
Build a process for solving multistep linear equations with variables on both sides.
Solve multistep linear equations with variables on both sides.
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Modeling Real World Multistep Equations
Write multistep linear equations for mathematical problems.
Write multistep linear equations from real world scenarios.
Solving Real World Multistep Equations
Use real world scenarios to solve multistep linear equations.
Analyzing Solutions
Solve equations that have one solution, infinitely many solutions and no solution.
Identify equations that have one solution, infinitely many solutions and no solution.
Write equations that have infinitely many solutions and no solution.
Representing Linear Systems Graphically
Exploring Systems of Linear Equations
Determine if a given coordinate point is a solution to a system of linear equations.
Identify the unique solution of a system of two linear equations from a graph.
Determining the Number of Solutions
Identify that a system has infinitely many solutions when the lines are equivalent.
Identify that a system has no solution when the lines are parallel.
Determine the number of solutions by inspection.
Using Graphs to Solve Systems
Re-write linear equations to slope-intercept form.
Graph linear systems on the coordinate plane.
Determine the solution of a linear system from the graph.
Estimating Solutions of Systems
Estimate solutions of linear systems
Writing and Solving Systems
Create systems of equations from mathematical problems
Solve systems of two linear equations
Exploring Systems in the Real World
Write the algebraic model that represents a real world scenario.
Solve a system of two linear equations represented by a real world scenario.
Interpret solutions in the original context.
Using Technology to Solve Systems
Use a graphing utility to explore and solve systems of two linear equations
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Page 5 of 11
Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Algebraic Approaches to Linear Systems
Solving Systems by Guess and Check
Use guess and check techniques to solve systems of two linear equations.
Finding the Number of Solutions
Identify the number of solutions by comparing the slope and y-intercept of the two equations.
Using Substitution to Solve Systems 1
Use substitution to solve a linear system.
Using Substitution to Solve Systems 2
Solve equations for one variable to use substitution to solve linear systems.
Determine which equation to solve for the variable.
Write equations of a linear system from a real world scenario.
Using Addition to Solve Systems
Use linear combination method to solve linear systems.
Multiplying 1 Equation to Solve Systems
Multiply one equation to create an equivalent equation to solve a system.
Solve a system using the linear combination method after multiplying one equation.
Write equations of a linear system in standard form from a real world scenario.
Multiplying 2 Equations to Solve Systems
Multiplying 2 equations to solve systems
Use linear combination method to solve systems of linear equations after multiplying both equations.
Write equations of a linear system in standard form from a real world scenario.
Solving Systems with Fractions
Multiply equations with leading fractional coefficients.
Use linear combination method to solve systems of linear equations after multiplying one or both equations.
Write equations of a linear system in standard form from a real world scenario.
Problem Solving with Systems
Write a system of linear equations to represent a real world scenario.
Solve a system of linear equations.
Transformations
Congruence
Determine congruence of figures by measuring corresponding sides and angles.
Identify and write corresponding parts of congruent figures.
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Overview of Transformations
Identify transformation and the types of transformation.
Recognize pre-image and post-image of transformations and label/name the post-image.
Translations
Identify and describe a translation on the coordinate plane.
Translate figures on the coordinate plane given as an ordered pair and verbal expression.
Describe a translation using coordinates.
Reflections
Identify and describe a reflection on the coordinate plane.
Reflect figures on the coordinate plane given the line of reflection.
Describe a reflected figure using the line of reflection and coordinates.
Rotations
Identify and describe a rotation on the coordinate plane.
Identify angles and direction of rotation.
Rotations in the Coordinate Plane
Rotate figures on the coordinate plane given the degree and direction.
Describe a rotation of a figure using coordinates.
Congruence and Transformations
Identify transformations for which the transformed image is congruent to the pre-image.
Describe a sequence of transformations that exhibits that a given pre-image is congruent to a transformed figure.
Dilations
Identify and describe a dilation on a coordinate plane.
Identify the scale factor, given the pre-image and the dilated-image.
Describe a dilation by its coordinates using the scale factor.
Dilations in the Coordinate Plane
Use the scale factor to graph dilations on the coordinate plane.
Describe the dilation of a figure on the coordinate plane by the scale factor.
Similarity and Transformations
Determine similarity of figures by measuring corresponding side lengths and angle measure.
Recognize similar figures.
Identify the transformation in which the post-image is similar to the pre-image.
Describe a sequence of transformations that result in a similar figure.
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Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Congruence and Similarity
Angle Relationships
Identify vertical, adjacent, complementary and supplementary angles.
Determine congruence in vertical angle relationships.
Find missing angle measures using angle relationships.
Transversals
Identify and draw transversals crossing two non-parallel lines.
Determine angle relationships created by a transversal line crossing two non-parallel lines.
Find angle measures and recognize congruent angles.
Parallel Lines Cut by a Transversal
Identify and draw transversals crossing parallel lines
Identify interior angles, exterior angles, alternate interior angles and alternate exterior angles when a transversal crosses parallel lines.
Find missing measurements using angles relationships in a diagram of a transversal crossing parallel lines.
Sum of Interior Angles of a Triangle
Investigate and confirm that the sum of interior angles of a triangle as 180 degrees by rearranging the angles to create a straight line.
Informally prove that the sum of the interior angles of the triangle is 180 degrees when a triangle is created by transversals crossing parallel lines using
angle relationships, corresponding angles, and congruence.
Informally prove, using alternate interior angles that the sum of the interior angles of a triangle is 180 degrees.
Exterior Angles of a Triangle
Identify, draw and find degree measure of exterior angles of a triangle by extending a side.
Determine the sum of exterior angles when drawing exterior angles clockwise and counterclockwise.
Identify and apply Exterior Angle Theorem of triangles.
Solving for Unknown Angles in Triangles
Use algebra to find a missing angle measure of an interior angle of a triangle.
Find missing angle measures of interior and exterior angles of triangles when involving transversals and parallel lines.
Similar Triangles
Identify proportionality of side lengths to determine triangle similarity.
Write similarity statements of similar triangles.
Analyze and apply Third Angle Theorem and Angle-Angle Criterion in similar triangles.
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Page 8 of 11
Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Similar Triangles and Slope
Interpret similar triangles created by intersecting transversal and parallel lines.
Find missing measurements of similar triangles from a real world scenario.
Determine similar triangles on the coordinate plane finding the slope and writing linear equations of the triangle sides.
Performance Objective
Working with Exponents
Powers and Exponents
Express a power of a positive integer base in expanded form.
Express expanded form in exponential form.
Evaluate powers using fractional and negative bases.
Zero and Negative Exponents
Determine patterns of exponent values from a table.
Evaluate powers of zero and negative exponents.
Simplify expressions of zero and negative exponents.
Powers with the Same Base
Evaluate powers of the same base through multiplication and division.
Simplify expressions of powers with the same base.
Raising a Power to a Power
Simplify and evaluate expressions of raising a power to a power of integer exponents.
Evaluating Expressions with Exponents
Simplify expressions using the rules of exponents.
Evaluate expressions using substitution of the variables.
Introduction to Scientific Notation
Convert very small or very large numbers between scientific notation and standard notation.
Estimate using scientific notation from real world scenarios when ordering, multiplying and dividing.
Operations with Scientific Notation
Evaluate products and quotients of scientific notation values.
Recognize scientific notation answers generated by technology and identify the symbols associated with the value.
Identify proper units of measurement for quantities written in scientific notation.
Pythagorean Theorem and Irrational Numbers
Exploring Pythagorean Theorem
Identify the hypotenuse in right triangles presented with different orientations.
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Page 9 of 11
Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Finding Hypotenuse in Right Triangles
Given lengths of any two legs of a right triangle, find the length of the hypotenuse.
Estimating and Comparing Square Roots
Write a list numbers up to 144 for which their square roots are integers.
Unknown Leg Lengths in Right Triangles
Given the length of one leg and the hypotenuse of a right triangle, find the length of the other leg.
Given the length of the hypotenuse of an isosceles right triangle, find the length of the legs.
Converse to the Pythagorean Theorem
Determine right triangles by using the Pythagorean Theorem.
Finding Distance in the Coordinate Plane
Plot vertices of a triangle on a coordinate plane.
Given a coordinate pair, construct a right triangle on a coordinate grid with the right angle at the origin.
Calculate the distance from any given coordinate pair and the origin.
Pythagorean Theorem in Three Dimensions
Given the size of a cube and the length of its diagonal, find the other dimension of the right triangle that forms the diagonal.
Exploring Real Numbes
Differentiate between rational and irrational numbers.
Express repeating decimals with bar notation.
Performance task
Volume
Introduction to Volume of a Cylinder
Calculate the volume of a cylinder given the formula.
Applications with Volume of a Cylinder
Solve real-life problems using volume of cylinders.
Find the area of the base of a cylinder given its volume and height.
Introduction to Volume of a Cone
Calculate the volume of a cylinder given the formula.
Applications with Volume of a Cone
Solve real-life problems using volume of a cone.
Find the area of the base of a cone given its volume and height.
Introduction to Volume of a Sphere
Calculate the volume of a sphere given the formula.
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Page 10 of 11
Common Core Math 8
Unit
Lesson
Scope and Sequence
Lesson Objectives
Applications with Volume of a Sphere
Solve real-life problems using volume of a sphere.
Find the area of the radius of a sphere given its volume.
Volume with Composite Figures
Calculate the volume of a composite figures given their formulas.
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