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 realworld 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. 11 Students will be able to (SWBAT) write algebraic expressions Algebraic expression Variable 12 SWBAT simplify expressions involving exponents / to use the order of operations to evaluate expressions. 13 SWBAT classify, graph and compare real numbers / to find and estimate square roots Evaluate Order of Operations Simplify Integers Real Numbers 14 SWBAT identify and use properties of real numbers Equivalent expressions 15 SWBAT find sums and differences of real numbers Additive inverse 16 SWBAT find products and quotients of real numbers 17 SWBAT use the distributive property to simplify expressions Coefficient Like terms Term 18 SWBAT solve equations using tables and mental math 19 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 onestep, twostep, and multistep 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. 21 SWBAT solve onestep equations in one variable Equivalent Equations Inverse Operations 22 SWBAT solve twostep equations in one variable 23 SWBAT solve multistep equations in one variable 24 SWBAT solve equations with variables on both sides / to identify equations that are identities or have no solution 25 SWBAT rewrite and use literal equations and formulas Formula Literal Equation 26 SWBAT find ratios and rates / to convert units and rates Conversion Factor Rate Ratio Unit Analysis 27 SWBAT solve and apply proportions Cross Products Proportion 28 SWBAT find missing lengths in similar figures / to use similar figures when Scale measuring indirectly 29 SWBAT solve percent problems using proportions / to solve percent problems using the percent equation 210 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 multistep and compound inequalities; use properties of inequality to solve inequalities (including multistep and compound inequalities; solve absolute value equations and inequalities; write an equivalent pair of linear equations or inequalities. 31 SWBAT write, graph and identify solutions of inequalities Solution for inequality 32 SWBAT use addition or subtraction to solve inequalities Equivalent inequalities 33 SWBAT use multiplication or division to solve inequalities 34 SWBAT solve multistep inequalities 35 SWBAT write sets and identify subsets / to find the complement of a set Compliment of a set Empty Set Roster Form Setbuilder notation Universal Set 36 SWBAT solve and graph inequalities containing the word and / to solve and graph inequalities containing the word or Compound inequality Interval Notation 37 SWBAT solve equations and inequalities involving absolute value 38 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 slopeintercept; pointslope, and standard forms; determine the relationship between two lines by comparing their slopes and yintercepts; 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. 51 SWBAT find rates of change from tables / to find slope Rate of Change Slope 52 SWBAT write and graph an equation of a direct variation Direct Variation 53 SWBAT write linear equations using slopeintercept form / to graph linear equations in slopeintercept form Linear Equation Slopeintercept form yintercept 54 SWBAT write and graph linear equations using pointlinear form Pointslant Form 55 SWBAT graph linear equations using intercepts / to write linear equations in standard form Standard Form xintercept 56 SWBAT determine whether lines are parallel, perpendicular, or neither / to write equations of parallel lines and perpendicular lines Parallel Lines Perpendicular Lines 57 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 58 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. 61 SWBAT solve systems of equations by graphing / to analyze special systems Consistent Dependent Inconsistent Independent Solution of a system of linear equations 62 SWBAT solve systems of equations using substitution Substitution method 63 SWBAT solve systems by adding or subtracting to eliminate a variable Elimination method 64 SWBAT choose the best method for solving a system of linear equations 65 SWBAT graph linear inequalities in two variables / to use linear inequalities Linear Inequalities when modeling realworld situations 66 SWBAT solve systems of linear inequalities by graphing / to model realworld 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 71 SWBAT simplify expressions involving zero and negative exponents 72 SWBAT write numbers in scientific and standard notation / compare and order numbers using scientific notation Scientific Notation 73 SWBAT multiply powers to the same base 74 SWBAT raise a power to a power / to raise a product to a power 75 SWBAT divide powers with the same base / raise a quotient to a power 76 SWBAT evaluate and graph exponential functions Exponential function 77 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 81 SWBAT classify, add, and subtract polynomials Binomial Degree of a monomial Degree of a polynomial Monomial Polynomial Standard form of a polynomial Trinomial 82 SWBAT multiply a monomial by a polynomial / factor a monomial from a polynomial 83 SWBAT multiply two binomials or a binomial by a trinomial 84 SWBAT find the square of a binomial and find the product of a sum and difference 85 SWBAT factor trinomials of the form x 2 + bx +c 86 SWBAT factor trinomials of the form ax 2 + bx + c 87 SWBAT factor perfectsquare trinomials and the differences of two squares Difference of two squares Perfectsquare trinomial 88 SWBAT factor higherdegree 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 ZeroProduct 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 91 SWBAT graph quadratic functions of the form y = ax 2 and y = ax 2 + c Axis of symmetry Maximum Minimum Parabola Quadratic Function Vertex 92 SWBAT graph quadratic functions of the form y = ax 2 + bx + c Quadratic Equation 93 SWBAT solve quadratic equations by graphing and using square roots Root of an Equation 94 SWBAT solve quadratic equations by factoring 95 SWBAT solve quadratic equations by completing the square Completing the Square 96 SWBAT solve quadratic equations using the quadratic formula / find the number of solutions of a quadratic equation 97 SWBAT choose a linear, quadratic, or exponential model for data 98 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 101 SWBAT solve problems using the Pythagorean Theorem / identify right triangles Conditional Hypotenuse Pythagorean Theorem 102 SWBAT simplify radicals involving products and quotients Radical Expression 103 SWBAT simplify sums and differences of radical expressions / simplify products and quotients of radical expressions Conjugates Extraneous solution Like Radicals 104 SWBAT solve equations containing radicals / identify extraneous solutions 105 SWBAT graph square root functions / translate graphs of square root functions Square Root Function 106 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 111 SWBAT simplify rational expressions Excluded Value Rational Expression 112 SWBAT multiply and divide rational expressions / simplify complex fractions 113 SWBAT divide polynomials 114 SWBAT add and subtract rational expressions 115 SWBAT solve rational equations and proportions Rational Equation 116 SWBAT write and graph equations for inverse variations / compare direct and inverse variations Constant variation for an inverse variation Inverse Variation 117 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 122 SWBAT make and interpret frequency tables and histograms 123 SWBAT find mean, median, mode, and range Measure of Central Tendency Outlier 124 SWBAT make and interpret boxandwhisker plots / find quartiles and percentiles Quartile 125 SWBAT classify data and analyze samples and surveys 126 SWBAT find permutations and combinations Combination Permutation 127 SWBAT find theoretical and experimental probability Event Outcome Probability Sample Space 128 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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