Grade 8 Math Curriculum Map Erin Murphy

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1 Topic 1 Variables and Expressions 2 Weeks Summative Topic Test: Students will be able to (SWBAT) use symbols o represent quantities that are unknown or that vary; demonstrate mathematical phrases and real-world relationships using symbols and operations; use equations to represent the relationship between two quantities that have the same value; represent the relationship between quantities using tables, equations and graphs. 1-1 Students will be able to (SWBAT) write algebraic expressions Algebraic expression Variable 1-2 SWBAT simplify expressions involving exponents / to use the order of operations to evaluate expressions. 1-3 SWBAT classify, graph and compare real numbers / to find and estimate square roots Evaluate Order of Operations Simplify Integers Real Numbers 1-4 SWBAT identify and use properties of real numbers Equivalent expressions 1-5 SWBAT find sums and differences of real numbers Additive inverse 1-6 SWBAT find products and quotients of real numbers 1-7 SWBAT use the distributive property to simplify expressions Coefficient Like terms Term 1-8 SWBAT solve equations using tables and mental math 1-9 SWBAT use tables, equations, and graphs to describe relationships N- RN.3, N- Q.1, N- Q.2, N- Q.3, A- APR.1, A- APR.7

2 Topic 2 Solving Two- Step Equations 2 Weeks Summative Topic Test: SWBAT solve one-step, two-step, and multi-step linear equations. As well as equations with variables on both sides; use ratios and rates to compare quantities and make conversions; write and solve a proportional; use proportional reasoning to find missing side lengths in similar figures; use the percent proportion to solve; solve percent increase and decrease problems. 2-1 SWBAT solve one-step equations in one variable Equivalent Equations Inverse Operations 2-2 SWBAT solve two-step equations in one variable 2-3 SWBAT solve multi-step equations in one variable 2-4 SWBAT solve equations with variables on both sides / to identify equations that are identities or have no solution 2-5 SWBAT rewrite and use literal equations and formulas Formula Literal Equation 2-6 SWBAT find ratios and rates / to convert units and rates Conversion Factor Rate Ratio Unit Analysis 2-7 SWBAT solve and apply proportions Cross Products Proportion 2-8 SWBAT find missing lengths in similar figures / to use similar figures when Scale measuring indirectly 2-9 SWBAT solve percent problems using proportions / to solve percent problems using the percent equation 2-10 SWBAT find percent change / to find the relative error in linear and nonlinear measurements Percent Change A- SSE.1, A- SSE.2, A- CED.2, A- CED.3, A- CED.4, A- REI.3

3 Topic 3 Solving Inequalities 3 Weeks Summative Topic Test: SWBAT write a mathematical sentence that uses an inequality symbol to compare the values of two expressions; Represent inequalities with symbols; represent a solution on a number line; solve inequalities (including multi-step and compound inequalities; use properties of inequality to solve inequalities (including multi-step and compound inequalities; solve absolute value equations and inequalities; write an equivalent pair of linear equations or inequalities. 3-1 SWBAT write, graph and identify solutions of inequalities Solution for inequality 3-2 SWBAT use addition or subtraction to solve inequalities Equivalent inequalities 3-3 SWBAT use multiplication or division to solve inequalities 3-4 SWBAT solve multi-step inequalities 3-5 SWBAT write sets and identify subsets / to find the complement of a set Compliment of a set Empty Set Roster Form Set-builder notation Universal Set 3-6 SWBAT solve and graph inequalities containing the word and / to solve and graph inequalities containing the word or Compound inequality Interval Notation 3-7 SWBAT solve equations and inequalities involving absolute value 3-8 SWBAT find the unions and intersections of sets Disjoint Sets Intersection Union A- SSE.1, A- SSE.2, A- CED.2, A- CED.3, A- REI.1, A- REI.3 A- REI.12

4 Topic 4 An Introduction To Functions 1.5 Weeks Summative Topic Test: SWBAT represent functions using tables and equations; use function notation; represent arithmetic sequences using function rules; represent relationships between variables using words, tables, equations, sets or ordered pairs and graphs; 4.1 SWBAT represent mathematical relationships using graphs 4.2 SWBAT identify and represent patterns that describe linear functions Dependent Variable Function Independent Variable Linear Function 4.3 SWBAT identify and represent patterns that describe nonlinear functions Nonlinear Function 4.4 SWBAT graph equations that represent functions Continuous graph Discrete graph 4.5 SWBAT write equations that represent functions 4.6 SWBAT determine whether a relation is a function / to find domain and range and use function notation 4.7 SWBAT identify and extend patterns in sequences / to represent arithmetic sequences using function notations Domain Function notation Range Relation Sequence A- CED.2, A- CED.3, A- REI.10, F- IF.1, F- IF.2, F- IF.3, F- IF.5, F- IF.6, F- IF.9, F- BF.1, F- BF.2, 8F1, 8F2, 8F3, 8F4, 8F5

5 Topic 5 Linear Functions 1.5 Weeks Summative Topic Test: SWBAT use ratios to show a relationship between changing quantities, such as vertical and horizontal change; represent a linear equation and know the forms slope-intercept; point-slope, and standard forms; determine the relationship between two lines by comparing their slopes and y-intercepts; quickly graph absolute value equations by shifting the graph of y = x ;graph two sets of numerical data as ordered pairs, if sets are related, a line on the graph will be used to estimate or predict values. 5-1 SWBAT find rates of change from tables / to find slope Rate of Change Slope 5-2 SWBAT write and graph an equation of a direct variation Direct Variation 5-3 SWBAT write linear equations using slope-intercept form / to graph linear equations in slope-intercept form Linear Equation Slope-intercept form y-intercept 5-4 SWBAT write and graph linear equations using point-linear form Point-slant Form 5-5 SWBAT graph linear equations using intercepts / to write linear equations in standard form Standard Form x-intercept 5-6 SWBAT determine whether lines are parallel, perpendicular, or neither / to write equations of parallel lines and perpendicular lines Parallel Lines Perpendicular Lines 5-7 SWBAT write and equation of a trend line and of a line of best fit / to use a trend line and a line of best fit to make predictions Trend Line 5-8 SWBAT graph an absolute value function / to translate the graph of an absolute value function A- SSE.1, A- SSE.2, A- SSE.3, A- REI.3, A- APR.1, A- APR.7

6 Topic 6 Systems of Equations and Inequalities 1.5 Weeks Summative Topic Test: SWBAT use systems of linear equations to model problems using graphing, substitution, or eliminating a variable; Represent the solutions of a system of linear inequality by the region where the graphs of the individual inequalities overlap; solve problems by modeling systems of linear equations; represent solution to a linear inequality in two variables in the coordinate plane as the set of all points on one side of a boundary line; represent the solutions of a system of linear inequalities by the region where the graphs of the individual inequalities overlap. 6-1 SWBAT solve systems of equations by graphing / to analyze special systems Consistent Dependent Inconsistent Independent Solution of a system of linear equations 6-2 SWBAT solve systems of equations using substitution Substitution method 6-3 SWBAT solve systems by adding or subtracting to eliminate a variable Elimination method 6-4 SWBAT choose the best method for solving a system of linear equations 6-5 SWBAT graph linear inequalities in two variables / to use linear inequalities Linear Inequalities when modeling real-world situations 6-6 SWBAT solve systems of linear inequalities by graphing / to model real-world situations using systems of linear inequalities A- CED.2, A- CED.3, A- CED.4, A- REI.1, A- REI.3, A- REI.5, A- REI.6, A- REI.10, A- REI.12, 8EE.8 Solution of an inequality Solution of a system of linear inequalities

7 Topic 7 Exponents and Exponential Functions 2 Weeks Summative Topic Test: SWBAT extend the idea of exponents to include zero and negative exponents; use Scientific Notation as a shorthand way to write numbers using powers of 10;use properties of exponents to simplify products or quotients of powers with the same base or powers raised to a power or products raised to a power; develop important families of functions through transformations of the simplest form of the function. Performance Assessment: SWBAT 7-1 SWBAT simplify expressions involving zero and negative exponents 7-2 SWBAT write numbers in scientific and standard notation / compare and order numbers using scientific notation Scientific Notation 7-3 SWBAT multiply powers to the same base 7-4 SWBAT raise a power to a power / to raise a product to a power 7-5 SWBAT divide powers with the same base / raise a quotient to a power 7-6 SWBAT evaluate and graph exponential functions Exponential function 7-7 SWBAT model exponential growth and decay Compound Interest Decay Factor Exponential decay Exponential Growth Growth Factor NS.1, NS.2, EE.1, EE.2, EE.3, EE.4

8 Topic 8 Polynomials and Factoring 1.5 Weeks Summative Topic Test: SWBAT use monomials to form larger polynomial expressions; add and subtract polynomials; find the product of two binomials by using models, algebra and tables; factor trinomials in equivalent forms which are the product of two binomials; Use the property of real numbers to multiply a monomial by a polynomial or simplify the product of binomials; use the properties of real numbers factor trinomials. Performance Assessment: SWBAT 8-1 SWBAT classify, add, and subtract polynomials Binomial Degree of a monomial Degree of a polynomial Monomial Polynomial Standard form of a polynomial Trinomial 8-2 SWBAT multiply a monomial by a polynomial / factor a monomial from a polynomial 8-3 SWBAT multiply two binomials or a binomial by a trinomial 8-4 SWBAT find the square of a binomial and find the product of a sum and difference 8-5 SWBAT factor trinomials of the form x 2 + bx +c 8-6 SWBAT factor trinomials of the form ax 2 + bx + c 8-7 SWBAT factor perfect-square trinomials and the differences of two squares Difference of two squares Perfect-square trinomial 8-8 SWBAT factor higher-degree polynomials by grouping Factoring by grouping A- SSE.1, A- SSE.2, A- SSE.3, A- APR.1, A- APR.7

9 Topic 9 Quadratic Functions and Equations 1.5 Weeks Summative Topic Test: SVBAT use the family of quadratic functions to model certain situations where the rate of change is not constant; graph by a symmetric curve with the highest or lowest point corresponding to a maximum or minimum value; Solve quadratic equations using graphing, finding the square root, using the Zero-Product Property or using the Quadratic formula; Solve systems of linear and quadratic equations graphically and algebraically; use linear, quadratic, or exponential functions to model various sets of data. Performance Assessment: SWBAT 9-1 SWBAT graph quadratic functions of the form y = ax 2 and y = ax 2 + c Axis of symmetry Maximum Minimum Parabola Quadratic Function Vertex 9-2 SWBAT graph quadratic functions of the form y = ax 2 + bx + c Quadratic Equation 9-3 SWBAT solve quadratic equations by graphing and using square roots Root of an Equation 9-4 SWBAT solve quadratic equations by factoring 9-5 SWBAT solve quadratic equations by completing the square Completing the Square 9-6 SWBAT solve quadratic equations using the quadratic formula / find the number of solutions of a quadratic equation 9-7 SWBAT choose a linear, quadratic, or exponential model for data 9-8 SWBAT solve systems of linear and quadratic equations A- SSE.1, A- SSE.2, A- SSE.3, A- REI.2, F- IF.1, F- IF.2, F- IF.3, F- IF.5, F- IF.6, F- IF.9, F- BF.1, F- BF.2 Discriminant Quadratic Formula

10 Topic 10 Radical Expressions and Equations 3 Weeks Summative Topic Test: SWBAT perform operations with radical expressions, which can be simplified using the multiplication and division properties of square roots; graph square root functions by plotting points or using translations of the parent square root function. Use sine, cosine, and tangent ratios to find the measurements of sides or angles of right triangles; use squaring both sides and testing solutions to solve some radical equations, Performance Assessment: SWBAT 10-1 SWBAT solve problems using the Pythagorean Theorem / identify right triangles Conditional Hypotenuse Pythagorean Theorem 10-2 SWBAT simplify radicals involving products and quotients Radical Expression 10-3 SWBAT simplify sums and differences of radical expressions / simplify products and quotients of radical expressions Conjugates Extraneous solution Like Radicals 10-4 SWBAT solve equations containing radicals / identify extraneous solutions 10-5 SWBAT graph square root functions / translate graphs of square root functions Square Root Function 10-6 SWBAT find and use trigonometric ratios Trigonometric ratios 8NS.2, 8G.6, 8G.7, 8G.8

11 Topic 11 Rational Expressions and Functions 2.5 Weeks Summative Topic Test: SWBAT simplify a rational expression; use addition, subtraction, multiplication and division on rational expressions and polynomials using the same properties used to multiply and divide numerical fractions; identify inverse variation; graph a rational function; solve a rational equation by first multiplying each side of the equation b the LCD; solve an equation using Cross Products Property. Performance Assessment: SWBAT 11-1 SWBAT simplify rational expressions Excluded Value Rational Expression 11-2 SWBAT multiply and divide rational expressions / simplify complex fractions 11-3 SWBAT divide polynomials 11-4 SWBAT add and subtract rational expressions 11-5 SWBAT solve rational equations and proportions Rational Equation 11-6 SWBAT write and graph equations for inverse variations / compare direct and inverse variations Constant variation for an inverse variation Inverse Variation 11-7 SWBAT graph rational functions Asymptote Rational Function A- SSE.1, A- SSE.2, A- SSE.3, A- REI.3, A- APR.1, A- APR.7

12 Topic 12 Data Analysis and Probability 2 Weeks Summative Topic Test: SWBAT used different measures to interpret and compare sets of data; accurately represent the situation when collecting data; Organize data in matrices or in intervals; separate data into subsets; use counting methods to find the number of possible ways to choose objects with and without regard to order; Utilize the probability of a compound event from expressions of the probabilities of simpler events SWBAT organize data in a matrix / add and subtract matrices and multiply a Matrix matrix by a scalar 12-2 SWBAT make and interpret frequency tables and histograms 12-3 SWBAT find mean, median, mode, and range Measure of Central Tendency Outlier 12-4 SWBAT make and interpret box-and-whisker plots / find quartiles and percentiles Quartile 12-5 SWBAT classify data and analyze samples and surveys 12-6 SWBAT find permutations and combinations Combination Permutation 12-7 SWBAT find theoretical and experimental probability Event Outcome Probability Sample Space 12-8 SWBAT find probabilities of mutually exclusive and overlapping events / find probabilities of independent and dependent events S- ID.1, S- ID.3, S- ID.7, S- ID.9, S- IC.2, S- IC.6, N- VM.6, N- VM.7, N- VM.8, N- VM.9, 8SP.1, 8SP.2, 8SP.3, 8SP.4

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