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1 | Standard | Benchmark | Student Learning Outcome | Glencoe Algebra | McGraw-Hill Algebra I CCSS | |||||||||||||||||||||

2 | 1 Numbers, Operations, and Computation | 1 Apply understanding of the real numbers | a Draw a Venn diagram to show different sets of numbers | |||||||||||||||||||||||

3 | 6 | b Identify and compare real numbers on the number line | 3-1 Rational numbers | 0-1 Real numbers | ||||||||||||||||||||||

4 | c Simplify expressions involving opposites and absolute value | 2-3 Adding integers | 0-3 Operations with integers | |||||||||||||||||||||||

5 | 2 Use arithmetic properties to operate on and simplify expressions that include radicals and other real numbers | a Apply one property, or a combination of properties, to simplify radical expressions | 8-5 Square roots | 10-1 Square roots | ||||||||||||||||||||||

6 | 3 Perform different operations with operations | a Use the distributive function to combine like terms | 9-1 Polynomials | 1-4 The distributive property | ||||||||||||||||||||||

7 | b Simplify expressions with several variables | 3-4 Equations | 1-1 Variables and expressions | |||||||||||||||||||||||

8 | c Multiply expressions containing variables | 9-3 Multiplying polynomials | 1-4 Distributive property | |||||||||||||||||||||||

9 | d Divide expressions containing variables | |||||||||||||||||||||||||

10 | e Model mathematical operations using algebra tiles | |||||||||||||||||||||||||

11 | 4 Apply an understanding of the algebraic order of operations | a Perform all operations within grouping symbols from the innermost outward. | 1-2 Order of operations | 1-2 Order operations | ||||||||||||||||||||||

12 | b Evaluate all operations with exponents | 1-2 Order of operations | 1-2 Order operations | |||||||||||||||||||||||

13 | c Do all multiplications and/or divisions from left to right | 1-2 Order of operations | 1-2 Order operations | |||||||||||||||||||||||

14 | d Do all additions and/or subtractions from left to right | 1-2 Order of operations | 1-2 Order operations | |||||||||||||||||||||||

15 | 5 Apply the laws of exponents to perform operations on expressions with integral [integer?] exponents | a Apply the law of exponents to make it easier to simplify expressions that include integral [integer?] exponents; in the case of a negative exponent, rewrite the expression using a positive exponent and simplify | 8-1 Powers and exponents, 8-2 Multiplying and dividing powers, 8-3 Negative exponents | 7-1 Multiplication properties of exponents, 7-2 Division properties of exponents | ||||||||||||||||||||||

16 | 6 Simplify polynomials and develop an initial understanding of polynomial functions | a Add and subtract polynomials | 9-2 Adding and subtracting polynomials | 8-1 Adding and subtracting polynomials | ||||||||||||||||||||||

17 | b Use algebra tiles to model the products of binomials | |||||||||||||||||||||||||

18 | c Find products of binomials using distributive property | 9-3 Multiplying polynomials | 8-2 Multiplying poly by mono | |||||||||||||||||||||||

19 | d Find products of binomials using the FOIL method | 9-3 Multiplying polynomials | 8-3 Multiplying polynomials | |||||||||||||||||||||||

20 | e Mentally simplify special product binomials | |||||||||||||||||||||||||

21 | f Define polynomial functions | 9-1 Polynomials | ||||||||||||||||||||||||

22 | g Solve problems involving polynomial functions | 11-3 Solving quadratic equations by graphing, 11-4 Solving quadratic equations by factoring, 11-5 Solving quadratic equations by completing the square, 11-6 The Quadratic Formula | 9-2 Solving quadratic equations by graphing, 8-6, 8-7 Solving quadratic equations by factoring, 9-4 Solving quadratic equations by completing the square, 9-5 The Quadratic Formula | |||||||||||||||||||||||

23 | h Factor a polynomial by using the greatest common factor | 10-2 Factoring using distributive property | ||||||||||||||||||||||||

24 | i Factor a polynomial by using a binomial factor | 10-3, 10-4 Factoring Trinomials | ||||||||||||||||||||||||

25 | j Factor perfect square trinomials | 10-5 Special factors | 8-9 Perfect squares | |||||||||||||||||||||||

26 | k Factor the difference of two squares | 10-5 Special factors | 8-8 Difference of squares | |||||||||||||||||||||||

27 | l Factor quadratic trinomials by using a) guess and check, and b) the grouping process | 10-1 Factors | 8-6 Solving x²+bx+c=0, 8-7 Solving x²+bx+c=0 | |||||||||||||||||||||||

28 | 7 Apply understanding of scientific notation | a Recognize the need for special notation in scientific calculations | 8-4 Scientific notation | 7-4 Scientific notation | ||||||||||||||||||||||

29 | b Perform computations involving scientific notation | 8-4 Scientific notation | 7-4 Scientific notation | |||||||||||||||||||||||

30 | 8 Examine matrices | a Determine the dimensions and addresses of a matrix | ||||||||||||||||||||||||

31 | b Determine whether two matrices are equal | |||||||||||||||||||||||||

32 | c Add, subtract, and multiply matrices | |||||||||||||||||||||||||

33 | d Determine the multiplicative identity of a matrix | |||||||||||||||||||||||||

34 | 2 Geometry, Measurement, Transformation | 1 Explore linear functions | a Determine whether a relation is a function | 6-1 Relations | 1-6 Relations | |||||||||||||||||||||

35 | b Describe the domain and range of a function | 6-4 Functions | 1-7 Functions | |||||||||||||||||||||||

36 | c Calculate the slope of a line by using the rise and run. | 7-1 Slope | 3-3 Rate of change and slope | |||||||||||||||||||||||

37 | d Calculate the slope of a line from the ratio of the differences in the y and x coordinates | 7-1 Slope | 3-3 Rate of change and slope | |||||||||||||||||||||||

38 | e Find the rate of change from a graph | 7-1 Slope | 3-3 Rate of change and slope | |||||||||||||||||||||||

39 | f Graph the direct variation equations | 6-5 Direct variation | 3-4 Direct variation | |||||||||||||||||||||||

40 | g Define and explain the components of the slope-intercept form of a linear equation | 7-3 Slope-Intercept form | 4-2 Slope intercept form | |||||||||||||||||||||||

41 | h Identify slope and y-intercept using the slope-intercept form equations | 7-3 Slope-Intercept form | 4-2 Slope intercept form | |||||||||||||||||||||||

42 | i Define and use the standard form and point-slope form for linear equations. | 7-2 Point-Slope form | 4-3 Point slope form | |||||||||||||||||||||||

43 | j Identify parallel lines and perpendicular lines by comparing their slopes | 7-7 Parallel and perpendicular lines | 4-4 Parallel and perpendicular lines | |||||||||||||||||||||||

44 | k Write equations of lines that are parallel or perpendicular to given lines. | 7-7 Parallel and perpendicular lines | 4-4 Parallel and perpendicular lines | |||||||||||||||||||||||

45 | 2 Apply the Pythagorean theorem to solve problems involving right triangles | a Define the Pythagorean theorem | 8-7 Pythagorean theorem | 10-5 Pythagorean theorem | ||||||||||||||||||||||

46 | b Find the side length of a right triangle given the lengths of its other two sides | 8-7 Pythagorean theorem | 10-5 Pythagorean theorem | |||||||||||||||||||||||

47 | c Apply the Pythagorean theorem to real world problems | 8-7 Pythagorean theorem | 10-5 Pythagorean theorem | |||||||||||||||||||||||

48 | d Perform an angle bisector to any equilateral triangle to find the length of the shorter leg. | 10-5 Pythagorean theorem | ||||||||||||||||||||||||

49 | e Use the Pythagorean theorem to find the missing length of any side of a right triangle | 8-7 Pythagorean theorem | 10-5 Pythagorean theorem | |||||||||||||||||||||||

50 | 3 Develop an understanding of the distance formula | a Use the distance formula, d=√[(x₂−x₁)²+(y₂−y₁)²] to find the distance between two points in a coordinate plane | 10-5 Extend | |||||||||||||||||||||||

51 | b Determine whether a triangle is a right triangle | 10-5 Pythagorean theorem | ||||||||||||||||||||||||

52 | c Apply the midpoint formula: ½(x₂+x₁)², ½(y₂+y₁)² | |||||||||||||||||||||||||

53 | 4 Apply different geometric properties | a Define and use the equation of a circle | ||||||||||||||||||||||||

54 | b Use the coordinate plane to investigate the diagonals of a rectangle and the mid-segment of a triangle | |||||||||||||||||||||||||

55 | c Use given information about a focus and directrix to write an equation describing a parabola | |||||||||||||||||||||||||

56 | 5 Analyze different transformations (translation, stretches/compressions, reflections) and describe the size, position, and orientation of the resulting shapes. | a Define reflection, rotation, and translation. | ||||||||||||||||||||||||

57 | b Graph and describe how changes to the rule of a function correspond to translation of its graph (vertical or horizontal translations) | 7-6 Families of linear graphs | ||||||||||||||||||||||||

58 | c Graph and describe how changes to the rule of a function stretch or compress its graph (vertical or horizontal stretch or compress) | |||||||||||||||||||||||||

59 | d Graph and describe how changes to the rule of a function correspond to a reflection of its graph (reflection across the x- and y-axis) | |||||||||||||||||||||||||

60 | e Study real world application of transformed functions | |||||||||||||||||||||||||

61 | f Graph functions that involve more than one transformation (order of vertical transformations) | |||||||||||||||||||||||||

62 | 6 Explore the basic trigonometric functions | a Identify and use the tangent ratio in a right triangle | 10-6 Trigonometric ratios | |||||||||||||||||||||||

63 | b Find the unknown side and angle measures in right triangles using the tangent ratio | 10-6 Trigonometric ratios | ||||||||||||||||||||||||

64 | c Define sine and cosine ratios in a right triangle | 10-6 Trigonometric ratios | ||||||||||||||||||||||||

65 | d Find unknown side and angle measures in right triangles using sine and cosine ratios | 10-6 Trigonometric ratios | ||||||||||||||||||||||||

66 | 3 Patterns and Algebra | 1 Determine if a linear pattern exists in a set of data and represent the data algebraically and graphically | a Use an organized table of the data and/or a graph of the data to justify whether a linear pattern exists or not | 7-4 Scatter plots | 4-5 Scatter plots and lines of fit, 4-6 Regression and median fit lines | |||||||||||||||||||||

67 | 2 Represent mathematical situations as algebraic expressions and equations, and describe algebraic expressions using words | a Compare and contrast algebraic expressions and equations | ||||||||||||||||||||||||

68 | b Translate algebraic expressions and equations into words, or word back into expressions and equations | |||||||||||||||||||||||||

69 | c Translate mathematical sentences into algebraic expressions and equations | |||||||||||||||||||||||||

70 | 3 Solve linear equations or inequalities in one variable using a variety of methods | a Show/explain how to solve for the variable in a linear equation or inequality using a selected strategy (algebraic method, graphing, or graphing technology), and show how to find the solution using a different strategy. | 13-1 Graphing systems of equations, 13-2 Solutions of systems of equations | 2-2, 2-3, 2-4, 2-5 Solving equations, 3-1 Solving linear equations, 3-2 Solving linear equations by graphing, 5-1, 5-2, 5-3, 5-4 Solving inequalities | ||||||||||||||||||||||

71 | 4 Apply different strategies to solve systems of equations and inequalities | a Show/explain how to solve systems of equations using a selected method (graphing, elimination, substitution) and show how to find the solutions using a different strategy. | 13-2 Solutions of systems of equations | 6-1, 6-2, 6-3, 6-4, 6,6 Solving systems of equations and inequalities | ||||||||||||||||||||||

72 | 5 Perform operations on polynomials | a Add (or subtract or multiply) polynomials (or divide polynomials by monomials) by selecting and applying appropriate strategies | 15-1 Simplifying rational expressions, 15-2 Multiplying and dividing rational expressions, 15-3 Dividing polynomials | 8-1 Adding and subtracting polynomials, 8-2 Multiplying a polynomial by a monomial, 8-3 Multiplying polynomials | ||||||||||||||||||||||

73 | 6 Identify functions as linear or nonlinear and contrast their properties from tables and graphs | a Define functions including input and output concept in a function | 6-4 Functions | 1-7 Functions | ||||||||||||||||||||||

74 | b Explain one-to-one functions | 6-4 Functions | 1-7 Functions | |||||||||||||||||||||||

75 | c Identify linear functions and justify when a relation (presented as ordered pairs, in a table, algebraic expressions, or a a graph) is a function | 1-6 Relations, 1-7 Functions | ||||||||||||||||||||||||

76 | d Identify, create, analyze, and graph linear and nonlinear functions | 7-5 Graphing linear equations, 11-1 Graphing quadratic functions | 3-1 Graphing linear equations, 9-1 Graphing quadratic functions | |||||||||||||||||||||||

77 | 7 Represent data involving linear relationship from tables as graphs and equations, and vice versa | a Draw graphs using data from data tables | 4-5 Scatter plots and lines of fit, 4-6 Regression and median fit lines | |||||||||||||||||||||||

78 | b Draw the graph of a linear equation | 7-5 Graphing linear equations | 3-1 Graphing linear equations | |||||||||||||||||||||||

79 | c Use graphing paper and a calculator to graph linear equations | 7-5 Graphing linear equations | 3-1 Graphing linear equations | |||||||||||||||||||||||

80 | 4 Statistics and probability | 1 Investigate probability | a Find the experimental probability that an event will occur using P(E)=(number of favorable outcomes/total number of outcomes) | 5-6 Probability and odds | 0-11 Simple probability and odds | |||||||||||||||||||||

81 | b Experiment by tossing coins, rolling number cubes, etc. | 5-6 Probability and odds | 0-11 Simple probability and odds | |||||||||||||||||||||||

82 | c List and describe the sample space of an experiment | |||||||||||||||||||||||||

83 | d Find the theoretical probability of a favorable outcome | 5-6 Probability and odds | 0-11 Simple probability and odds | |||||||||||||||||||||||

84 | e Find the union and intersection of sets | |||||||||||||||||||||||||

85 | f Count the elements of a sets | |||||||||||||||||||||||||

86 | g Apply the addition of probabilities principle | 5-6 Probability and odds | 0-11 Simple probability and odds | |||||||||||||||||||||||

87 | h Use a tree diagram to count the number of choices that can be made from sets | |||||||||||||||||||||||||

88 | i Use the fundamental counting principle to count the number of choices that can be made from sets | |||||||||||||||||||||||||

89 | j Find the probability of independent events | 5-7 Compound events | 0-11 Simple probability and odds | |||||||||||||||||||||||

90 | k Design and perform simulations to find experimental probabilities | |||||||||||||||||||||||||

91 | 2 Compare data sets using statistical (measures of central tendency, standard deviation, range, stem-and-leaf plots, and box-and-whisker graphs) | a Select a representation that supports the desired purpose of the study and shows a visual comparison of the data sets (studying the relationship between height and arm span, choose to represent the data in a scatter plot, since scatter plots are designed to determine if correlations between two variables exist. | ||||||||||||||||||||||||

92 | 3 Apply proportional reasoning and percent problems | a Identify the means and extremes of a proportion | ||||||||||||||||||||||||

93 | b Use proportions to solve problems | 5-1 Solving proportions | 0-6 Percent proportion | |||||||||||||||||||||||

94 | c Find equivalent fractions, decimals, and percents | 5-3 Percent proportion | 0-6 Percent proportion | |||||||||||||||||||||||

95 | d Interpret step (stem?)-and-leaf plots, histograms, and box-and-whisker plots | 12-3 Distributions of data, 12-4 comparing sets of data | ||||||||||||||||||||||||

96 | e Represent data with stem-and-leaf plots, histograms, and box-and-whisker plots | 12-3 Distributions of data, 12-4 comparing sets of data | ||||||||||||||||||||||||

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