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Keystone Algebra
Concepts
Competencies
Assessment
Standards
Arithmetic
Readiness
Whole Numbers : Rounding – Estimating a sum - Writing expressions using
exponents - Order of operations - Evaluating an algebraic expression
Factors - Prime numbers - Prime factorization - Greatest common factor - Least
common multiple - Equivalent fractions
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CC.2.1.HS.F.1
Fractions : Equivalent fractions - Simplifying a fraction - Ordering fractions Finding the LCD of two fractions - The reciprocal of a number - Writing an
improper fraction as a mixed number - Writing a mixed number as an improper
fraction – Perform Fraction operations (+ - x /) - Fractional part of a circle
Decimals : Tenths and hundredths decimal place value - Rounding decimals Ordering fractions and decimals - Perform decimal operations (+ - x /) - Word
problems with decimal operations
Geometry – Find perimeter or area of a polygon, square, triangle, or a rectangle.
Find the area between two rectangles. Find circumference and area of a circle. Finding the missing length in a figure - Area of a piecewise rectangular figure Area between two rectangles - Find the volume of a rectangular prism
Demonstrate knowledge on Arithmetic Readiness
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CC.2.2.HS.D.6
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CC.2.1.8.E.1
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CC.2.3.HS.A.3
Real Numbers
Classify Integers, rational and irrational numbers. Plotting integers, fractions, and
rational numbers on a number line. Ordering integers and real numbers.
Perform operations with signed numbers. Word problems with integers.
Exponents and order of operations - Evaluating a linear expression in two
variables. Evaluating a quadratic expression in one variable. Find the absolute
value of a number. Perform operations with absolute value
Properties of Real Numbers - Distributive property - Combining like terms
Demonstrate knowledge of Real Numbers
Linear
Equations
Solve One-Step Linear Equations.
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CC.2.1.6.E.3
CC.2.1.8.E.1
CC.2.1.HS.F.2
CC.2.2.HS.D.2
CC.2.2.8.B.1
CC.2.2.8.B.3
CC.2.2.HS.D.8
Solving two-step equations
Solving a multi-step equation given in fractional form.
Solving a simple equation with parentheses.
Solving a linear equation with several occurrences of the variable.
Solving equations with zero, one, or infinitely many solutions
Identifying properties used to solve a linear equation
Algebraic symbol manipulation
Writing Expressions and Equations
Writing a variable expression for a real-world situation
Translating a sentence into an expression
Solving a fraction word problem using a linear equation
Solving a word problem with two unknowns using a linear equation
Solving a decimal word problem using a linear equation with the variable on both
sides
Finding a side length given the perimeter and side lengths with variables
Finding the side length of a rectangle given its perimeter or area
Finding the perimeter or area of a rectangle given one of the values
Finding the value for a new score that will yield a given mean
Proportions : Solving a proportion of the form x/a = b/c. Solving a proportion of the
form (x+a)/b = c/d. Solving a proportion of the form (x+a)/b = x/c. Solving word
problem on proportions, similar polygons and indirect measurement
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CC.2.2.8.B.3
CC.2.2.HS.D.8
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CC.2.2.HS.C.3
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CC.2.2.HS.D.7
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CC.2.2.HS.D.10
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CC.2.2.8.B.3
CC.2.2.HS.D.8
CC.2.1.HS.F.3
CC.2.1.HS.F.3
CC.2.1.HS.F.3
CC.2.1.HS.F.3
CC.2.1.HS.F.9
Percents: Converting between percentages and decimals, a percentage to a
fraction, or a fraction to a percentage. Writing a ratio as a percentage. Find
percentage of a whole number. Finding the sale price given the original price and
percent discount.
Solving an equation involving absolute value.
Demonstrate knowledge of linear equations
Linear
Inequalities
Translating a sentence into an inequality
Writing an inequality for a real-world situation.
Graphing a linear inequality on the number line.
Writing an inequality given a graph on the number line
Writing a compound inequality.
Graphing a compound linear inequality on the number line.
Writing a compound inequality given a graph on the number.
Identifying solutions to a linear inequality in one variable
Solve a two-step linear inequality.
Solving a two-step linear inequality with a fractional coefficient.
Solving a linear inequality with multiple occurrences of the variable.
Writing an absolute value inequality given a graph on the number line.
Solving an inequality involving absolute value.
Demonstrate knowledge of linear inequalities
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CC.2.1.8.E.1
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CC.2.1.HS.F.2
CC.2.2.HS.D.7
CC.2.2.HS.D.7
CC.2.2.HS.D.7
CC.2.2.HS.D.7
CC.2.2.HS.D.7
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CC.2.2.HS.D.7
CC.2.2.HS.D.10
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CC.2.2.HS.D.10
CC.2.1.HS.F.1
CC.2.1.HS.F.2
Functions
Function tables - Domain and range from ordered pairs - Identifying functions
from relations - Vertical line test
Writing a function rule given a table of ordered pairs: One-step rules.
Writing a function rule given a table of ordered pairs: Two-step rules.
Reading and plotting a point in the coordinate plane.
Identifying solutions to a linear equation in two variable.
Finding a solution to a linear equation in two variables
Demonstrate knowledge of functions
Graphing
Lines
Graphing a linear equation of the form y = mx
Graphing a line given its equation in slope-intercept form: Integer slope.
Graphing a line given its equation in slope-intercept form: Fractional slope.
Graphing a line given its equation in standard form.
Graphing a line given the x- and y-intercepts.
Graphing a line by first finding its x- and y-intercepts.
Graphing a line through a given point with a given slope.
Graphing a line by first finding its slope and y-intercept.
Graphing a line given its equation in point-slope form.
Graphing a vertical or horizontal line
Demonstrate knowledge of functions
Equations of
Lines
Identifying linear functions given ordered pairs.
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CC.2.2.HS.C.2
CC.2.2.HS.C.1
CC.2.2.HS.C.3
CC.2.2.HS.D.10
CC.2.2.HS.D.10
CC.2.2.HS.D.7
CC.2.2.HS.C.2
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CC.2.2.HS.D.7
CC.2.2.HS.D.7
CC.2.2.HS.C.2
CC.2.2.HS.D.7
CC.2.2.HS.C.2
CC.2.2.HS.C.1
Rewriting a linear equation in the form Ax + By = C.
Finding x- and y-intercepts given the graph of a line on a grid.
Finding x- and y-intercepts of a line given the equation.
Classifying slopes given graphs of lines.
Finding slope given the graph of a line on a grid.
Finding slope given two points on the line.
Finding the slope of horizontal and vertical lines.
Finding the coordinate that yields a given slope.
Finding the slope and y-intercept of a line given its equation in the form y = mx + b
or the form Ax + By = C.
Writing an equation and graph a line given its slope and y-intercept or given the yintercept and another point.
Writing an equation in slope-intercept form given the slope and a point.
Writing an equation in point-slope form given the slope and a point.
Writing the equation of the line through two given points.
Writing the equations of vertical and horizontal lines through a given point.
Writing and evaluating a function that models a real-world situation.
Writing an equation and drawing its graph to model a real-world situation.
Identifying parallel and perpendicular lines from equations.
Identifying slopes of parallel and perpendicular lines.
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CC.2.2.HS.C.2
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CC.2.2.HS.C.2
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CC.2.2.HS.C.3
CC.2.2.HS.C.3
CC.2.2.HS.C.1
CC.2.2.HS.C.2
Interpreting direct variation from a graph. Identifying direct variation equations and
writing direct variation equations. Word problem on direct variation.
Finding the next terms of an arithmetic sequence. Finding a specified term of an
arithmetic sequence given the first terms. Finding a specified term of an arithmetic
sequence given the common difference and first term. Writing an explicit rule for
an arithmetic sequence. Finding the next terms of a geometric sequence
Scatter plots, correlation and sketching the line of best fit. Approximating the
equation of a line of best fit and making predictions.
Demonstrate knowledge of equations of lines.
Systems of
Linear
Equations
Identifying solutions to a system of linear equations.
Classifying systems of linear equations from graphs.
Solving a simple system using substitution.
Solving a system of linear equations using elimination.
Solving a system of linear equations with fractional coefficients.
Solving a system of linear equations with decimal coefficients.
Interpreting the graphs of two functions.
Solving a word problem using a system of linear equations.
Solving a value mixture problem using a system of linear equations.
Solving a distance, rate, time problem using a system of linear equations.
Demonstrate knowledge of systems of linear equations
Graphing
Linear
Inequalities
Identifying solutions to a linear inequality in two variables.
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CC.2.2.HS.C.2
CC.2.2.HS.C.3
CC.2.2.HS.C.2
CC.2.2.HS.C.3
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CC.2.4.HS.B.2
CC.2.4.HS.B.3
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CC.2.2.HS.D.10
CC.2.2.HS.D.10
CC.2.2.HS.D.10
CC.2.2.HS.D.10
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CC.2.2.HS.D.10
Graphing a linear inequality in the plane.
Graphing a system of linear inequalities
Solving a word problem using a system of linear inequalities.
Demonstrate knowledge of graphing linear inequalities
Exponents
Evaluating expressions with exponents of zero.
Powers of 10: Negative exponent.
Writing a positive number without a negative exponent.
Writing a negative number without a negative exponent.
Writing a simple algebraic expression without negative exponents.
Understanding the product rule of exponent.
Product rule with negative exponents.
Quotients of expressions involving exponents.
Quotient rule with negative exponents.
Power rule with positive exponents.
Power rule with negative exponents.
Using the power and product rules to simplify expressions with positive exponents.
Using the power and quotient rules to simplify expressions with negative
exponents:
Scientific notation with positive exponent. Scientific notation with negative
exponent. Multiplying and dividing numbers written in scientific notation
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CC.2.2.HS.D.7
CC.2.2.HS.D.10
CC.2.2.HS.D.10
CC.2.2.8.B.1
CC.2.2.8.B.1
CC.2.2.HS.D.2
CC.2.2.8.B.1
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CC.2.2.HS.D.2
CC.2.2.8.B.1
CC.2.1.HS.F.1
Demonstrate knowledge of Exponents.
Polynomials
Degree and leading coefficient of a polynomial in one variable.
Simplifying a sum or difference of polynomials.
Multiplying polynomials.
Find special products of polynomials.
Find greatest common factor of two monomials.
Factoring polynomials.
Solving equations written in factored form.
Finding the roots of a quadratic equation.
Solving a word problem using a quadratic equation.
Demonstrate knowledge of polynomials
Radical
Expressions
Find the square root of a perfect square.
Estimating a square root.
Find the cube root of an integer.
Simplifying a radical expression.
Simplifying a sum of radical expressions.
Simplifying a product of radical expressions.
Demonstrate knowledge of radical expressions
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CC.2.2.HS.D.1
CC.2.2.HS.D.3
CC.2.2.HS.D.3
CC.2.2.HS.D.3
CC.2.2.HS.D.3
CC.2.2.HS.D.2
CC.2.2.HS.D.3
CC.2.2.HS.D.6
CC.2.2.HS.D.5
CC.2.1.HS.F.1
CC.2.1.HS.F.1
CC.2.1.HS.F.1
CC.2.1.HS.F.1
CC.2.1.HS.F.1
CC.2.1.HS.F.1
Rational
Expressions
Restriction on a variable in a denominator.
Simplifying a ratio of polynomials.
Least common multiple of two monomials.
Demonstrate knowledge of rational expressions
Graphical
Displays
Line plots
Histograms for numerical data
Interpreting bar graphs, line graphs, and circle graphs or pie charts.
Computations from circle graphs.
Interpret a stem-and-leaf plot.
Using back-to-back stem-and-leaf plots to compare data sets.
Box-and-whisker plots
Using box-and-whisker plots to compare data sets.
Demonstrate knowledge of graphical displays
Data Analysis
Finding the mode and range of a data set.
Finding mean and median of a data set.
How changing a value affects the mean and median.
Choosing the best measure to describe data.
Computing a percentage from a table of values.
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CC.2.2.HS.D.2
CC.2.2.HS.D.3
CC.2.2.HS.D.2
CC.2.2.HS.D.2
CC.2.2.HS.D.3
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.1
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CC.2.4.HS.B.1
CC.2.4.HS.B.1
CC.2.4.HS.B.3
CC.2.4.HS.B.3
CC.2.4.HS.B.3
Calculating relative frequencies in a contingency table.
Five-number summary and interquartile range.
Demonstrate knowledge of data analysis
Probability
Probability and odds of an event
Outcomes and event probability
Die rolling
Introduction to expectation
Probability of independent events
Probability of dependent events
Demonstrate knowledge of probability
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CC.2.4.HS.B.3
CC.2.4.HS.B.5
CC.2.4.HS.B.4
CC.2.4.HS.B.4
CC.2.4.HS.B.4
CC.2.4.HS.B.4
CC.2.4.HS.B.7
CC.2.4.HS.B.7
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