Integers & Absolute Value Properties of Addition Add Integers Subtract Integers. Add & Subtract Like Fractions Add & Subtract Unlike Fractions

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1 Unit 1: Rational Numbers & Exponents M07.A-N & M08.A-N, M08.B-E Essential Questions Standards Content Skills Vocabulary What happens when you add, subtract, multiply and divide integers? What happens when you add, subtract, multiply and divide rational numbers? Accelerated Math 7/8 p. 1 M07.A-N to add & subtract rational numbers including real world contexts. M07.A-N Represent addition and subtraction on a horizontal or vertical number line. M07.A-N to add & subtract rational numbers including real world contexts. M07.A-N Represent addition and subtraction on a horizontal or vertical number line. Integers & Absolute Value Properties of Addition Add Integers Subtract Integers Add & Subtract Like Fractions Add & Subtract Unlike Fractions Add & Subtract Decimals Rational Numbers Find the absolute value of any integer Use properties of addition to reorganize expressions for ease of evaluation Add any two, three or more positive and negative integers Subtract any two integers by using add the opposite Add any two or more fractions with like denominators Add any two or more fractions with unlike denominators Subtract any two fractions with like denominators Subtract any two fractions with unlike denominators Add any two or more decimals Subtract any two Integer Negative integer Positive integer Absolute value Additive inverse Opposite Commutative Property of Addition Associative Property of Addition Additive Identity Add the opposite Coordinate Inequality Inductive reasoning Numerator Denominator Fraction Mixed number Improper fraction Decimal Rational number Like fractions Unlike fractions

2 What happens when you add, subtract, multiply and divide integers? What happens when you add, subtract, multiply and divide rational numbers? M07.A-N to add & subtract rational numbers including real world contexts. M07.A-N to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. M07.A-N to add & subtract rational numbers including real world contexts. M07.A-N to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. M08.A-N Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats. Properties of Multiplication Multiply Integers Divide Integers Fractions & Decimals Multiply Rational Numbers Divide Fractions Divide Decimals decimals Sequence a set of rational numbers from least to greatest or greatest to least Use properties of multiplication to reorganize expressions for ease of evaluation Multiply any two integers Divide any two integers Multiply any two fractions Divide any two fractions Multiply any two decimals Divide any two decimals Convert back and forth between fractions, decimals and percents Multiplicative Identity Multiplication Property of Zero Commutative Property of Multiplication Associative Property of Multiplication Reciprocal Terminating decimal Repeating decimal Irrational number Bar notation Multiplicative Inverse M08.A-N Convert a terminating or repeating decimal to a rational Accelerated Math 7/8 p. 2

3 How can you solve problems given in real-world context? Why is it useful to write numbers in different ways? Why is it helpful to write numbers in different ways? Why is it helpful to write numbers in different ways? Accelerated Math 7/8 p. 3 number. M07.A-N to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats. M08.A-N Evaluate the value of irrational numbers without a calculator. M08.A-N Use rational approximations of irrational numbers to compare and order irrational numbers. M08.A-N Locate/identify rational and irrational numbers at their approximate locations on a number line. M08.B-E Apply one or more properties of integer exponents to generate equivalent numerical expressions without a calculator. M08.B-E 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. M08.B-E Estimate very large or very 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 Problem Solving Strategies Powers & Exponents Multiply & Divide Monomials Powers of a Monomial Negative Exponents Square Roots & Cube Roots Scientific Notation Compute with Scientific Notation Decode word problems to solve expressions 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 Convert between scientific and standard notation Add, subtract, multiply or divide using scientific 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 Scientific notation

4 than another. notation How are equations and inequalities used to describe and solve multi-step Accelerated Math 7/8 p. 4 M08.B-E 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. Unit 2: Proportionality & Linear Relationships M07.B- E, M07.A-R & M08.B- E, M08.B-F Essential Questions Standards Content Skills Vocabulary Why are algebraic rules useful? How are equations and inequalities used to describe and solve multi-step problems? M07.B-E to calculate with numbers in any form; convert between forms as appropriate. M07.B-E Solve word problems leading to equations of the form and, where p, q and r are specific rational numbers. M07.B-E Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. M07.B-E Solve word problems leading to inequalities of the form or, where p, q and r are specific The Distributive Property Simplify Algebraic Expressions Add Linear Expressions Subtract Linear Expressions Factor Linear Expressions Solve One-Step Addition & Subtraction Equations Use the Distributive Property to factor or combine like terms Add & subtract linear expressions Factor linear expressions Combine like terms Use the Properties of Equality to solve one step equations Use the Properties Linear expression Monomial Factor Factored form Equation Solution Equivalent equation One-step equation Subtraction Property of Equality Addition Property of

5 problems? How can you identify and represent proportional relationships? How can you identify and represent proportional relationships? Accelerated Math 7/8 p. 5 rational numbers. M07.B-E Determine the reasonableness of answer(s) or interpret the solution(s) in the context of the problem. M08.B-E 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 Solve linear equations that have rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. M07.A-R Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. M07.A-R Determine whether two quantities are proportionally related. M07.A-R Identify the constant of Solve One-Step Multiplication & Division Equations Solve Two-Step Equations Solve Equations with Variables on Each Side Inequalities Solving Inequalities Solving Multi-Step Equations and Inequalities Ratios Unit Rates Complex Fractions & Unit Rates Convert Rates Proportional and Nonproportional Relationships Graphing Proportional of Equality and Order of Operations to solve two-step equations Decode word problems to solve one- and two-step equations Use the Properties of Inequality to solve one-step inequalities Use the Properties of Inequality and Order of Operations to solve two-step inequalities Decode word problems to set up one- or two-step inequalities Calculate unit rates given a rate Calculate unit rates given coordinates or a graph Convert between units using a unit ratio and dimensional analysis Identify proportional relationships from graphs, tables, equations by using Equality Division Property of Equality Multiplication Property of Equality Two-step equation Subtraction Property of Inequality Addition Property of Inequality Division Property of Inequality Multiplication Property of Inequality One-step inequality Two-step inequality Rate Unit rate Complex fraction Unit ratio Dimensional analysis Proportional Nonproportional Equivalent ratios Coordinate plane Quadrants

6 proportionality in tables, graphs, equations, diagrams and verbal descriptions of proportional relationships. M07.A-R Represent proportional relationships by equations. M07.A-R Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation with special attention to the points (0,0) and (1, r) where r is the unit rate. Relationships Solve Proportions Scale Drawings & Models Similar Figures ratios Identify and calculate the constant of proportionality (unit rate, slope) from graphs, tables or equations Graph proportional and nonproportional relationships Ordered pair x-coordinate y-coordinate x-axis y-axis Origin Scale drawing Scale model Scale Scale factor M07.C-G Solve problems involving scale drawings of geometric figures including finding length and area. M08.B-E 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 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 Derive the equation for a line through the origin and the equation for a line intercepting the vertical axis at b. Accelerated Math 7/8 p. 6

7 How can you use proportional relationships to solve real-world percent problems? How are linear functions used to model proportional relationships? M07.A-R Use proportional relationships to solve multi-step ratio and percent problems. M08.B-F Determine whether a relation is a function. M08.B-F Compare properties of two functions, each represented in a different way. M08.B-F 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 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 Use the Percent Proportion Use the Percent Equation Percent of Change Discount & Markup Simple & Compound Interest Functions Representing Linear Functions Constant Rate of Change and Slope Direct Variation Slope-Intercept Form Solve Systems of Equations by Graphing Solve Systems of Equations by Elimination or Substitution Solve proportions using cross products Solve percent problems using proportions of the form Solve percent increase/percent decrease problems using proportions Solve problems involving simple interest Express relations as (x, y) tables or graphs State the domain 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 Proportion Cross products Percent increase Percent decrease Markup Discount Simple interest Compound interest Constant of Proportionality Slope Accelerated Math 7/8 p. 7

8 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 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally. description, table or graph Sketch and analyze qualitative graphs M08.B-E 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 Solve systems of two linear equations in two variables algebraically and estimate solutions by graphing the equations. Solve simple cases by inspection. M08.B-E Solve real-world and mathematical problems leading to two linear equations in two variables. Unit 3: Geometry M07.C-G & M08.C-G Essential Questions Standards Content Skills Vocabulary How can you determine Accelerated Math 7/8 p. 8 M07.C-G Identify or describe the Angle & Line Relationships Use the scale on a drawing or model to Acute triangle Right triangle

9 congruence and similarity? properties of all types of triangles based on angle and side measures. M07.C-G Use and apply the triangle inequality theorem. M07.C-G Describe the two-dimensional figures that result from slicing three-dimensional figures. M07.C-G Identify and use properties of supplementary, complementary and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. M07.C-G Identify and use properties of angles formed when two parallel lines are cut by a transversal (alternate interior, alternate exterior, vertical and corresponding). M08.C-G Apply the converse of the Pythagorean Theorem to show a triangle is a right triangle. M08.C-G Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in realworld and mathematical problems in two and three dimensions. M08.C-G Apply the Pythagorean Theorem to find the distance between two Triangles Polygons find missing measures Calculate scale factors Classify triangles by side length or angle measure Draw triangles without violating the triangle inequality theorem Draw threedimensional figures Name the faces, edges and vertices of three-dimensional figures Find twodimensional cross sections of threedimensional figures Identify angles by size (right, obtuse, acute, straight) Identify complementary and supplementary angles Use complementary and supplementary angles to find a missing angle measure Use properties of parallel lines and transversals to Obtuse triangle Scalene triangle Isosceles triangle Equilateral triangle Equiangular triangle Congruent segments Triangle inequality theorem Prism Pyramid Bases Polyhedron Edge Face Vertex Diagonal Skew lines Cylinder Cone Cross section Acute angle Obtuse angle Right angle Straight angle Complementary angles Supplementary angles Parallel lines Transversal Vertical angles Alternate interior angles Alternate exterior angles Accelerated Math 7/8 p. 9

10 How can you determine congruence and similarity? Accelerated Math 7/8 p. 10 points in a coordinate system. M08.C-G Identify and apply properties of rotations, reflections and translations. M08.C-G Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. M08.C-G Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. M08.C-G Given two similar twodimensional figures, describe a sequence of transformations that exhibits the similarity between them. Translations and Reflections on the Coordinate Plane Rotations on the Coordinate Plane Congruence and Transformations Dilations on the Coordinate Plane Similarity and Transformations identify angles Use properties of parallel lines and transversals to calculate missing angle measures Translate lines or two-dimensional figures on the coordinate plane Reflect a line or two-dimensional 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 Corresponding angles Interior angle Exterior angle Remote interior angles Legs Hypotenuse Pythagorean Theorem Converse Distance formula Transformation Preimage Image Translation Congruent Reflection Line of reflection Rotation Center of rotation Scale factor Corresponding parts Similar

11 How are twodimensional figures used to solve problems involving three-dimensional figures? M07.C-G Find the area and circumference of a circle. Solve problems involving area and circumference of a circle(s). M07.C-G Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. M08.C-G Apply formulas for the volumes of cones, cylinders and spheres to solve real-world and mathematical problems. Circles and Circumference Area of Circles Three-Dimensional Figures Volume of Prisms Volume of Cylinders Volume of Pyramids, Cones and Spheres Surface Area of Prisms Surface Area of Cylinders Surface Area of Pyramids and Cones Explain and demonstrate that two figures are similar through transformations Determine the scale factor of two similar figures Calculate the circumference of a circle Calculate the radius or diameter of a circle Calculate the area of a circle or semicircle Calculate the radius or diameter of circle or semicircle Calculate the area of composite figures by breaking them into known polygons Calculate the volume of triangular or rectangular prisms Calculate the volume of triangular, rectangular or square pyramids Calculate the surface area of triangular or rectangular prisms Calculate the surface area of triangular, rectangular or square Circle Center Circumference Diameter Radius Pi ( ) Semicircle Composite figure Volume Lateral face Surface area Lateral surface area Slant height Regular pyramid Cylinder Composite solid Cone Sphere Hemisphere Accelerated Math 7/8 p. 11

12 pyramids 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 or parts of cones Find the volume of spheres, hemispheres and composite solids that contain spheres or hemispheres Unit 4: Statistics & Probability M07.D-S & M08.D-S Essential Questions Standards Content Skills Vocabulary How are statistics used to draw inferences about and compare populations? Accelerated Math 7/8 p. 12 M07.D-S Determine whether a sample is a random sample given a real-world situation. M07.D-S Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. M07.D-S Compare two numerical data distributions using measures of center and variability. Measures of Center Measures of Variability Mean Absolute Deviation Compare Populations Using Sampling to Predict Scatter Plots Lines of Best Fit Identify different types of random samples Identify sources of bias Use a sample to predict outcomes for a larger population Identify misleading data displays Compare Statistics Survey Population Sample Unbiased sample Biased sample Simple random sample Systematic random sample Convenience sample Voluntary response

13 How are statistics used to draw inferences about and compare populations? M08.D-S 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. M08.D-S 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 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. M07.D-S Predict or determine whether some outcomes are certain, more likely, less likely, equally likely or impossible. M07.D-S Determine the probability of a chance event given relative frequency. Predict the approximate relative frequency given the probability. Probability of Simple Events Theoretical & Experimental Probability Probability of Compound Events Two-Way Tables populations using box plots and dot plots Use appropriate displays based on the type of data (pie graphs, histograms, line graphs, box plots, dot plots, stem-and-leaf plots) Construct an x, y scatter plot for a set of bivariate data Identify the types of associations found in scatter plots 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 Calculate the probability of a simple event occurring Calculate the complement of a simple probability Construct a two-way table for data with two different categories sample Double box plot Double dot plot Bivariate data Scatter plot Line of best fit Probability Outcome Simple event Complementary events Uniform probability model Theoretical probability Experimental probability Accelerated Math 7/8 p. 13

14 M07.D-S Find the probability of a simple event, including the probability of the event not occurring. M07.D-S Find probabilities of independent events using organized lists, tables, tree diagrams and simulation. M08.D-S Construct and interpret a twoway 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. Calculate and interpret relative frequencies from a two-way table Calculate the theoretical or experimental probability of an event Identify a sample space Identify possible outcomes using tree diagrams or organized lists Calculate the probability of compound events Sample space Tree diagram Compound event Relative frequency Two-way table Accelerated Math 7/8 p. 14

of triangles, exterior, 112 interior, 112 real-life application, 113 similar, 128 vertical constructions,

of triangles, exterior, 112 interior, 112 real-life application, 113 similar, 128 vertical constructions, This student-friendly index will help you find vocabulary, key ideas, and concepts. It is easily accessible and designed to be a reference for you whether you are looking for a definition, real-life application,