Unit 1: The Number System M08.A-N Essential Questions Standards Content Skills Vocabulary Why is it helpful to write numbers in different ways? M08.A-N.1.1.1 Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats. M08.A-N.1.1.2 Convert a terminating or repeating decimal to a rational number. M08.A-N.1.1.3 Evaluate the value of irrational numbers without a calculator. Rational Numbers Compare Real Numbers Classify numbers as rational or irrational Convert back and forth between fractions and decimals Sequence a set of real numbers from least to greatest or greatest to least Rational number Repeating decimal Terminating decimal Irrational number Real number Why is it helpful to write numbers in different ways? M08.A-N.1.1.4 Use rational approximations of irrational numbers to compare and order irrational numbers. M08.A-N.1.1.5 Locate/identify rational and irrational numbers at their approximate locations on a number line. Math 8 p. 1
Unit 2: Expressions & Equations M08.B-E Essential Questions Standards Content Skills Vocabulary Why is it helpful to write numbers in different ways? Why is it helpful to write numbers in different ways? M08.B-E.1.1.1 Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator. M08.B-E.1.1.2 Use square root and cube root symbols to represent solutions to equations of the form and, where p is a positive rational number. Evaluate square roots of perfect squares and cube roots of perfect cubes without a calculator. Powers & Exponents Multiply & Divide Monomials Powers of a Monomial Negative Exponents Roots Estimate Roots Write expressions using positive exponents and the Laws of Exponents Evaluate expressions with exponents leaving the answers in exponential form Convert negative exponent expressions to expressions with positive exponents Evaluate expressions containing negative exponents Find square roots of perfect squares Find square root estimations of nonperfect squares Find cube roots of perfect cubes Power Base Exponent Monomial Product of Powers Quotient of Powers Power of a Power Power of a Product Square root Perfect square Radical sign Cube root Perfect cube Why is it helpful to write numbers in M08.B-E.1.1.3 Estimate very large or very Scientific Notation Compute with Convert between scientific and Scientific notation Math 8 p. 2
different ways? small quantities by using numbers expressed in the form of a single digit times an integer power of ten and express how many times larger or smaller one number is than another. Scientific Notation standard notation Add, subtract, multiply or divide using scientific notation What is equivalence? M08.B-E.1.1.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities. M08.B-E.3.1.1 Write and identify 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 results. M08.B-E.3.1.2 Solve linear equations that have rational number coefficients, including Solve Equations with Rational Coefficients Solve Two-Step Equations Write Two-Step Equations Solve Equations with Variables on Both Sides Solve Multi-Step Equations Solve equations with fractional coefficients using the multiplicative inverse Solve equations with decimal coefficients Solve two-step equations by reversing the Order of Operations Decode and evaluate word problems into two-step equations Solve equations with variables on both Multiplicative inverse Coefficient Two-step equations Addition Property of Equality Subtraction Property of Equality Multiplication Property of Equality Division Property of Equality Null Set Identity Math 8 p. 3
Why are graphs helpful? Math 8 p. 4 equations whose solutions require expanding expressions using the distributive property and collecting like terms. M08.B-E.2.1.1 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. M08.B-E.2.1.2 Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M08.B-E.2.1.3 Derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at b. Constant Rate of Change Slope Equations in Form Slope-Intercept Form sides by collecting like terms on one side Solve multi-step equations by using the Distributive Property and all of the Equality Properties Identify the number of solutions an equation has Identify the rate of change in a graph or table Calculate the slope of any line using a graph, table or the formula Graph and compare direct variation equations Calculate the constants of variation for direct variation equations Write equations in slope-intercept form from graphs, tables or verbal descriptions Linear relationship Constant rate of change Slope Rise Run Direct variation Constant of variation Constant of proportionality y-intercept Slope-intercept form Why are graphs M08.B-E.3.1.3 Solve Systems of Solve systems of Systems of
helpful? Interpret solutions to a system of two linear equations in two variables as points of intersection of their graphs because points of intersection satisfy both equations simultaneously. M08.B-E.3.1.4 Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. Equations by Graphing Solve Systems of Equations by Substitution Solve Systems of Equations by Elimination linear equations in two variables by graphing Solve systems of linear equations in two variables by substituting one of the two variables in one of the equations Solve systems of linear equations in two variables by eliminating one variable first then solving for the other equations Substitution M08.B-E.3.1.5 Solve real-world and mathematical problems leading to two linear equations in two variables. Unit 3: Functions M08.B-F Essential Questions Standards Content Skills Vocabulary How can we model relationships between quantities? Math 8 p. 5 M08.B-F.1.1.1 Determine whether a relation is a function. M08.B-F.1.1.2 Relations Functions Linear Functions Compare Properties Express relations as (x, y) tables or graphs State the domain Relation Domain Range Function
How can we model relationships between quantities? Compare properties of two functions, each represented in a different way. M08.B-F.1.1.3 Interpret the equation as defining a linear function whose graph is a straight line; give examples of functions that are not linear. M08.B-F.2.1.1 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 relationship or from two (x, y) values, including reading these from a table or 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. M08.B-F.2.1.2 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch or determine a graph that exhibits the qualitative of Functions Linear & Nonlinear Functions Construct Functions Qualitative Graphs and range of a relation or function Graph linear functions from function tables Compare two functions by their rates of change (slopes) and y- intercepts Identify linear and nonlinear functions Analyze graphs, verbal descriptions and tables Construct a function with given qualities in a verbal description, table or graph Sketch and analyze qualitative graphs Function table Independent variable Dependent variable Linear function Continuous data Discrete data Nonlinear function Qualitative graphs Math 8 p. 6
Math 8 p. 7 features of a function that has been described verbally. Unit 4: Geometry M08.C-G Essential Questions Standards Content Skills Vocabulary How can algebraic concepts be applied to geometry? How can we best show or describe the change in position of a figure? M08.C-G.2.1.1 Apply the converse of the Pythagorean Theorem to show a triangle is a right triangle. M08.C-G.2.1.2 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. M08.C-G.2.1.3 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. M08.C-G.1.1.1 Identify and apply properties of rotations, reflections and translations. M08.C-G.1.1.3 Describe the effect of Angles of Triangles The Pythagorean Theorem Use the Pythagorean Theorem Distance on the Coordinate Plane Translations Reflections Rotations Dilations Use the Angle Sum of a Triangle to find unknown angle measures Use interior, remote interior and exterior angles of triangles to find unknown angle measures Use the Pythagorean Theorem and its converse to find missing measurements Use the Pythagorean Theorem in realworld context Use the distance formula or Pythagorean Theorem to find the distance between two points Translate lines or two-dimensional figures on the coordinate plane Reflect a line or two-dimensional Triangle Interior angle Exterior angle Remote interior angles Legs Hypotenuse Pythagorean Theorem Converse Distance formula Transformation Preimage Image Translation Congruent Reflection
How can you determine congruence and similarity? Why are formulas important in math and science? dilations, translations, rotations and reflections on two-dimensional figures using coordinates. M08.C-G.1.1.2 Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. M08.C-G.1.1.4 Given two similar twodimensional figures, describe a sequence of transformations that exhibits the similarity between them. M08.C-G.3.1.1 Apply formulas for the volumes of cones, cylinders and spheres to solve realworld and mathematical problems. Congruence and Transformations Congruence Similarity and Transformations Volume of Cylinders Volume of Cones Volume of Spheres figure across one of the axes Rotate twodimensional figures 90, 180 or 270 Dilate a two dimensional figure by a given scale factor Explain and demonstrate that two figures are congruent through transformations Use corresponding parts to determine congruence and missing measures Explain and demonstrate that two figures are similar through transformations Determine the scale factor of two similar figures Find the volume of cylinders and composite solids that contain cylinders or parts of cylinders Find the volume of cones and composite solids that contain cones Line of reflection Rotation Center of rotation Scale factor Corresponding parts Similar Volume Cylinder Composite solid Cone Sphere Hemisphere Math 8 p. 8
or parts of cones Find the volume of spheres, hemispheres and composite solids that contain spheres or hemispheres Unit 5: Statistics & Probability M08.D-S Essential Questions Standards Content Skills Vocabulary How are patterns used when comparing two quantities? M08.D-S.1.1.1 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 correlation, linear association and nonlinear association. Scatter Plots Construct an x, y scatter plot for a set of bivariate data Identify the types of associations found in scatter plots Bivariate data Scatter plot How are patterns used when comparing two quantities? M08.D-S.1.1.2 For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of the data points to the line. M08.D-S.1.1.3 Use the equation of a linear model to solve Lines of Best Fit Graph a set of bivariate data on an x, y scatter plot and determine the line of best fit for the data Write the equation of a line of best fit from an x, y scatter plot Line of best fit Math 8 p. 9
problems in the context of bivariate measurement data, interpreting the slope and intercept. How are patterns used when comparing two quantities? M08.D-S.1.2.1 Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible associations between the two variables. Two-Way Tables Construct a two-way table for data with two different categories Calculate and interpret relative frequencies from a two-way table Relative frequency Two-way table Math 8 p. 10