Pohnpei Mathematics Standards Textbooks cross-walk
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StandardBenchmarkStudent Learning OutcomeGlencoe Algebra
McGraw-Hill Algebra I CCSS
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1 Numbers, Operations, and Computation
1 Apply understanding of the real numbers
a Draw a Venn diagram to show different sets of numbers
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6b Identify and compare real numbers on the number line3-1 Rational numbers0-1 Real numbers
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c Simplify expressions involving opposites and absolute value
2-3 Adding integers0-3 Operations with integers
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2 Use arithmetic properties to operate on and simplify expressions that include radicals and other real numbersa Apply one property, or a combination of properties, to simplify radical expressions8-5 Square roots10-1 Square roots
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3 Perform different operations with operations
a Use the distributive function to combine like terms9-1 Polynomials1-4 The distributive property
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b Simplify expressions with several variables3-4 Equations
1-1 Variables and expressions
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c Multiply expressions containing variables
9-3 Multiplying polynomials
1-4 Distributive property
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d Divide expressions containing variables
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e Model mathematical operations using algebra tiles
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4 Apply an understanding of the algebraic order of operationsa Perform all operations within grouping symbols from the innermost outward.1-2 Order of operations1-2 Order operations
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b Evaluate all operations with exponents1-2 Order of operations1-2 Order operations
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c Do all multiplications and/or divisions from left to right1-2 Order of operations1-2 Order operations
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d Do all additions and/or subtractions from left to right1-2 Order of operations1-2 Order operations
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5 Apply the laws of exponents to perform operations on expressions with integral [integer?] exponentsa 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 simplify8-1 Powers and exponents, 8-2 Multiplying and dividing powers, 8-3 Negative exponents7-1 Multiplication properties of exponents, 7-2 Division properties of exponents
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6 Simplify polynomials and develop an initial understanding of polynomial functionsa Add and subtract polynomials9-2 Adding and subtracting polynomials8-1 Adding and subtracting polynomials
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b Use algebra tiles to model the products of binomials
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c Find products of binomials using distributive property
9-3 Multiplying polynomials
8-2 Multiplying poly by mono
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d Find products of binomials using the FOIL method
9-3 Multiplying polynomials
8-3 Multiplying polynomials
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e Mentally simplify special product binomials
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f Define polynomial functions9-1 Polynomials
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g Solve problems involving polynomial functions11-3 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 Formula9-2 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
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h Factor a polynomial by using the greatest common factor
10-2 Factoring using distributive property
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i Factor a polynomial by using a binomial factor10-3, 10-4 Factoring Trinomials
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j Factor perfect square trinomials10-5 Special factors8-9 Perfect squares
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k Factor the difference of two squares10-5 Special factors8-8 Difference of squares
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l Factor quadratic trinomials by using a) guess and check, and b) the grouping process10-1 Factors8-6 Solving x²+bx+c=0, 8-7 Solving x²+bx+c=0
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7 Apply understanding of scientific notation
a Recognize the need for special notation in scientific calculations8-4 Scientific notation7-4 Scientific notation
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b Perform computations involving scientific notation8-4 Scientific notation7-4 Scientific notation
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8 Examine matricesa Determine the dimensions and addresses of a matrix
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b Determine whether two matrices are equal
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c Add, subtract, and multiply matrices
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d Determine the multiplicative identity of a matrix
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2 Geometry, Measurement, Transformation
1 Explore linear functionsa Determine whether a relation is a function6-1 Relations1-6 Relations
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b Describe the domain and range of a function6-4 Functions1-7 Functions
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c Calculate the slope of a line by using the rise and run.7-1 Slope
3-3 Rate of change and slope
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d Calculate the slope of a line from the ratio of the differences in the y and x coordinates7-1 Slope
3-3 Rate of change and slope
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e Find the rate of change from a graph7-1 Slope
3-3 Rate of change and slope
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f Graph the direct variation equations6-5 Direct variation3-4 Direct variation
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g Define and explain the components of the slope-intercept form of a linear equation7-3 Slope-Intercept form4-2 Slope intercept form
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h Identify slope and y-intercept using the slope-intercept form equations7-3 Slope-Intercept form4-2 Slope intercept form
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i Define and use the standard form and point-slope form for linear equations.7-2 Point-Slope form4-3 Point slope form
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j Identify parallel lines and perpendicular lines by comparing their slopes7-7 Parallel and perpendicular lines4-4 Parallel and perpendicular lines
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k Write equations of lines that are parallel or perpendicular to given lines.7-7 Parallel and perpendicular lines4-4 Parallel and perpendicular lines
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2 Apply the Pythagorean theorem to solve problems involving right trianglesa Define the Pythagorean theorem
8-7 Pythagorean theorem
10-5 Pythagorean theorem
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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
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c Apply the Pythagorean theorem to real world problems
8-7 Pythagorean theorem
10-5 Pythagorean theorem
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d Perform an angle bisector to any equilateral triangle to find the length of the shorter leg.10-5 Pythagorean theorem
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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
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3 Develop an understanding of the distance formulaa Use the distance formula, d=√[(x₂−x₁)²+(y₂−y₁)²] to find the distance between two points in a coordinate plane10-5 Extend
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b Determine whether a triangle is a right triangle10-5 Pythagorean theorem
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c Apply the midpoint formula: ½(x₂+x₁)², ½(y₂+y₁)²
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4 Apply different geometric propertiesa Define and use the equation of a circle
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b Use the coordinate plane to investigate the diagonals of a rectangle and the mid-segment of a triangle
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c Use given information about a focus and directrix to write an equation describing a parabola
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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.
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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
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c Graph and describe how changes to the rule of a function stretch or compress its graph (vertical or horizontal stretch or compress)
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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)
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e Study real world application of transformed functions
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f Graph functions that involve more than one transformation (order of vertical transformations)
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6 Explore the basic trigonometric functions
a Identify and use the tangent ratio in a right triangle10-6 Trigonometric ratios
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b Find the unknown side and angle measures in right triangles using the tangent ratio10-6 Trigonometric ratios
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c Define sine and cosine ratios in a right triangle10-6 Trigonometric ratios
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d Find unknown side and angle measures in right triangles using sine and cosine ratios10-6 Trigonometric ratios
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3 Patterns and Algebra1 Determine if a linear pattern exists in a set of data and represent the data algebraically and graphicallya Use an organized table of the data and/or a graph of the data to justify whether a linear pattern exists or not7-4 Scatter plots4-5 Scatter plots and lines of fit, 4-6 Regression and median fit lines
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2 Represent mathematical situations as algebraic expressions and equations, and describe algebraic expressions using words
a Compare and contrast algebraic expressions and equations
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b Translate algebraic expressions and equations into words, or word back into expressions and equations
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c Translate mathematical sentences into algebraic expressions and equations
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3 Solve linear equations or inequalities in one variable using a variety of methodsa 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 equations2-2, 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
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4 Apply different strategies to solve systems of equations and inequalitiesa 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 equations6-1, 6-2, 6-3, 6-4, 6,6 Solving systems of equations and inequalities
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5 Perform operations on polynomialsa Add (or subtract or multiply) polynomials (or divide polynomials by monomials) by selecting and applying appropriate strategies15-1 Simplifying rational expressions, 15-2 Multiplying and dividing rational expressions, 15-3 Dividing polynomials8-1 Adding and subtracting polynomials, 8-2 Multiplying a polynomial by a monomial, 8-3 Multiplying polynomials
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6 Identify functions as linear or nonlinear and contrast their properties from tables and graphsa Define functions including input and output concept in a function6-4 Functions1-7 Functions
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b Explain one-to-one functions6-4 Functions1-7 Functions
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c Identify linear functions and justify when a relation (presented as ordered pairs, in a table, algebraic expressions, or a a graph) is a function1-6 Relations, 1-7 Functions
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d Identify, create, analyze, and graph linear and nonlinear functions7-5 Graphing linear equations, 11-1 Graphing quadratic functions3-1 Graphing linear equations, 9-1 Graphing quadratic functions
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7 Represent data involving linear relationship from tables as graphs and equations, and vice versaa Draw graphs using data from data tables4-5 Scatter plots and lines of fit, 4-6 Regression and median fit lines
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b Draw the graph of a linear equation7-5 Graphing linear equations
3-1 Graphing linear equations
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c Use graphing paper and a calculator to graph linear equations7-5 Graphing linear equations
3-1 Graphing linear equations
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4 Statistics and probability1 Investigate probabilitya Find the experimental probability that an event will occur using P(E)=(number of favorable outcomes/total number of outcomes)5-6 Probability and odds0-11 Simple probability and odds
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b Experiment by tossing coins, rolling number cubes, etc.5-6 Probability and odds0-11 Simple probability and odds
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c List and describe the sample space of an experiment
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d Find the theoretical probability of a favorable outcome5-6 Probability and odds0-11 Simple probability and odds
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e Find the union and intersection of sets
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f Count the elements of a sets
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g Apply the addition of probabilities principle5-6 Probability and odds0-11 Simple probability and odds
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h Use a tree diagram to count the number of choices that can be made from sets
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i Use the fundamental counting principle to count the number of choices that can be made from sets
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j Find the probability of independent events5-7 Compound events0-11 Simple probability and odds
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k Design and perform simulations to find experimental probabilities
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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.
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3 Apply proportional reasoning and percent problemsa Identify the means and extremes of a proportion
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b Use proportions to solve problems5-1 Solving proportions0-6 Percent proportion
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c Find equivalent fractions, decimals, and percents5-3 Percent proportion0-6 Percent proportion
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d Interpret step (stem?)-and-leaf plots, histograms, and box-and-whisker plots12-3 Distributions of data, 12-4 comparing sets of data
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e Represent data with stem-and-leaf plots, histograms, and box-and-whisker plots12-3 Distributions of data, 12-4 comparing sets of data
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