Combine Skills From Mathematics

Find the unique prime factorization for a whole number
Find the greatest common factor of two whole numbers less than or equal to 100
Use the greatest common factor and the distributive property to rewrite the sum of two whole numbers, each less than or equal to 100
Find the least common multiple of two whole numbers less than or equal to 12
Find the least common multiple of two whole numbers less than or equal to 12 to add and subtract fractions with unlike denominators

Number Lines

Add and subtract integers from -20 to 20
Position rational numbers on a horizontal number line
Write statements of order for rational numbers

Number Systems

Irrational Numbers

Identify numbers as rational or irrational
Evaluate perfect squares and cubes (positive numbers ≤ to 400)
Estimate the value of square roots to the tenths place
Estimate the value of cube roots to the tenths place
Locate numbers approximately on a number line
Compare the size of numbers by plotting them on a number line

Scientific Notation

Write numbers in scientific notation
Write numbers in decimal notation
Compare numbers written in scientific notation
Express how much larger numbers in scientific notation are
Multiply numbers in scientific notation
Divide numbers in scientific notation
Multiply numbers in scientific and decimal notation
Divide numbers in scientific and decimal notation

Ratio and Proportional Relationships

Ratios

Unit Conversions

Convert and manipulate measurements for distances in the customary system
Convert and manipulate measurements in the metric system
Convert time between different units

Ratios

Use ratios to solve problems
Complete missing values in ratio tables
Plot ratio values
Find equivalent unit ratios

Unit Rate

Identify the unit rate of a proportional relationship (given a description)
Identify the unit rate of a proportional relationship (given a table)
Identify the unit rate of a proportional relationship (given a graph)

Percents

Benchmark Percents

Find the part given the whole and the percent (benchmark percents)
Find the whole given the part and the percent (benchmark percents)
Find the percent given the whole and the part (benchmark percents)

Percents

Find the part given the whole and the percent
Find the whole given the part and the percent
Find the percent given the whole and the part
Write a percent of a quantity as a ratio per 100
Percent word problems

Percent Applications

Use proportional relationships to solve percent problems (percent increase)
Use proportional relationships to solve percent problems (percent decrease)
Use proportional relationships to solve percent problems (two-step)
Use proportional relationships to solve percent problems (backward)
Use proportional relationships to solve percent problems (mixed)

Proportional Relationships

Identifying Proportional Relationships

Recognize whether ratios are in a proportional relationship using tables
Recognize whether ratios are in a proportional relationship using graphs

Proportional Relationships

Represent proportional relationships using tables (given an equation)
Represent proportional relationships using tables (given a description)
Represent proportional relationships using graphs (given an equation)
Represent proportional relationships using graphs (given a description)
Represent proportional relationships using equations (given a table)
Represent proportional relationships using equations (given a graph)
Represent proportional relationships using equations (given a description)
Use proportional relationships to solve real-world problems

Expressions and Equations

Expressions

Expression Word Problems

Write expressions from mathematical descriptions
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Write expressions from real-world scenarios
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Write and solve expressions using real-world scenarios
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Expand and Factor Expressions

Expand linear expressions with rational coefficients (easy)
Expand linear expressions with rational coefficients (medium)
Expand linear expressions with rational coefficients (challenging)
Factor linear expressions with an integer GCF

Add and Subtract Expressions

Add linear expressions with rational coefficients (easy)
Add linear expressions with rational coefficients (medium)
Add linear expressions with rational coefficients (challenging)
Subtract linear expressions with rational coefficients (medium)
Subtract linear expressions with rational coefficients (challenging)

Simplify Expressions

Rewrite expressions into equivalent forms (easy)
Rewrite expressions into equivalent forms (medium)
Rewrite expressions into equivalent forms (challenging)

Exponential Expressions

Exponents (positive exponents only)

Simplify exponents with the product rule (positive exponents with integer bases)
Simplify exponents with the quotient rule (positive exponents with integer bases)
Simplify exponents with the power rule (positive exponents with integer bases)
Simplify exponents with the product rule (positive exponents with variable bases)
Simplify exponents with the quotient rule (positive exponents with variable bases)
Simplify exponents with the power rule (positive exponents with variable bases)

Exponents (single base)

Simplify exponents with the product rule (single integer base)
Simplify exponents with the quotient rule (single integer base)
Simplify exponents with the power rule (single integer base)
Simplify exponents with the product rule (single variable base)
Simplify exponents with the quotient rule (single variable base)
Simplify exponents with the power rule (single variable base)

Exponents (multiple bases)

Simplify exponents with the product rule (multiple bases)
Simplify exponents with the quotient rule (multiple bases)
Simplify exponents with the power rule (multiple bases)

Exponents (combined rules)

Simplify complex exponential expressions (single integer base)
Simplify complex exponential expressions (mixed integer bases)
Rewrite exponential expressions without exponents
Simplify complex exponential expressions (single variable base)
Simplify complex exponential expressions (multiple variable bases)

Equations (One Solution)

One-Step Equations

Solve one-step equations (integers)
Solve one-step equations (decimals)
Solve one-step equations (fractions)
Solve one-step equations (all)
Use substitution to determine whether a given number makes an equation true

Two-Step Equations

Solve two-step equations (easy)
Solve two-step equations (medium)
Solve two-step equations (challenging)

Multi-Step Equations

Solve multi-step equations (easy)
Solve multi-step equations (medium)
Solve multi-step equations (challenging)

Equations with Variables on Both Sides

Solve linear equations with the same variable on both sides (easy)
Solve linear equations with the same variable on both sides (medium)
Solve linear equations with the same variable on both sides (challenging)
Solve linear equations with the same variable on both sides (proportional)

Equations (All Solution Types)

Equations (one, none, or infinitely many solutions)

Recognize linear equations as having one, none, or infinite solutions (easy)
Recognize linear equations as having one, none, or infinite solutions (medium)
Recognize linear equations as having one, none, or infinite solutions (challenging)

Inequalities

Inequality Basics

Represent solutions of inequalities on number lines
Use substitution to determine whether a given number makes an inequality true
Write inequalities from number lines

Two-Step Inequalities

Solve two-step inequalities (easy)
Solve two-step inequalities (medium)
Solve two-step inequalities (challenging)

Multi-Step Inequalities

Solve multi-step inequalities (easy)
Solve multi-step inequalities (medium)
Solve multi-step inequalities (challenging)

Inequalities with Variables on Both Sides

Solve linear inequalities with the same variable on both sides (easy)
Solve linear inequalities with the same variable on both sides (medium)
Solve linear inequalities with the same variable on both sides (challenging)
Solve linear inequalities with the same variable on both sides (proportional)

Functions

Function Basics

Identifying Functions

Recognize functions given scatter plots
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Recognize functions given a map
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Recognize functions given tables
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Recognize functions given ordered pairs
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Representing Relationships

List the ordered pairs for each relationship given its mapping
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Create mappings given ordered pairs
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Create scatter plots given mappings of relationships
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Create mappings given scatter plots
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Linear Functions

Slope

Find slope from a graph
Find slope from two points
Find slope from a table

Slope-Intercept Form

Find slope from the slope-intercept form equation
Graph lines using slope-intercept form
Write the slope-intercept form equation from a graph
Write the slope-intercept form equation using a point and the slope
Write the slope-intercept form equation from two points
Write the slope-intercept form equation from a table
Compare slopes of linear functions shown in different ways

Forms of Linear Functions

Convert equations from slope-intercept form to standard form
Convert equations from standard form to slope-intercept form
Convert equations from point-slope form to standard form
Convert equations from point-slope form to slope-intercept form
Graph linear functions from various forms and find intercepts

Sequences

Arithmetic Sequences

Represent arithmetic sequences in recursive form (function notation)
Represent arithmetic sequences in recursive form (subscript notation)
Represent arithmetic sequences in explicit form (function notation)
Represent arithmetic sequences in explicit form (subscript notation)
Translate between explicit and recursive forms of arithmetic sequences (subscript notation)

Geometric Sequences

Represent geometric sequences in recursive form (function notation)
Represent geometric sequences in recursive form (subscript notation)
Represent geometric sequences in explicit form (function notation)
Represent geometric sequences in explicit form (subscript notation)
Translate between explicit and recursive forms of geometric sequences (subscript notation)

Sequence Applications

Identify a sequence as arithmetic or geometric
Build arithmetic and geometric sequences given a table (subscript notation)

Quadratic Functions

Quadratics

Solve quadratics by taking square roots
Factor quadratics with integral roots (a=1)
Factor quadratics with integral roots and GCFs
Solve for the real solutions of quadratic equations by factoring

Key Features of Quadratics

Graph quadratic functions using factors (a=1)
Graph quadratic functions from the standard form equation (a=1)
Identify key features of quadratic functions from graphs
Identify key features of quadratics in standard form
Write the factored form of quadratics from graphs (a=1)
Write the factored form of quadratics from graphs

Vertex Form

Convert perfect square trinomials (with/without GCFs) from standard form into vertex form
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Convert quadratics (with rational solutions) from standard form into vertex form
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Find the vertex of quadratics by completing the square (easy)
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Find the vertex of quadratics by completing the square
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Solve quadratics by completing the square (integer solutions)
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Solve quadratics by completing the square (rational solutions)
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Solve quadratics by completing the square (irrational solutions)
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Solve quadratics by completing the square (imaginary solutions)
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Exponential Functions

Find growth/decay rates from exponential equations
Find growth/decay rates for exponential functions given a table
Write exponential functions using regression
Complete tables using exponential equations
Sketch graphs of exponential functions
Sketch graphs of exponential functions (quadrant I)

Mixed Functions

Graph functions given in function notation
Evaluate functions expressed in function notation
Calculate average of rate of change over a specified interval for a function represented symbolically

Algebra

Literal Equations

Solve for a quantity of interest in formulas and equations (easy)
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Solve for a quantity of interest in formulas and equations (medium)
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Systems of Linear Functions

Solve systems by graphing lines
Solve systems with substitution
Solve systems with elimination
Solve systems with substitution or elimination
Solve systems with substitution (mixed forms)

Linear Inequalities

Graph a linear inequality (slope-intercept form)
Graph a linear inequality (standard form)
Check solutions to linear inequalites
Create linear inequalities from graphs (slope-intercept form)

Systems of Linear Inequalities

Graph a system of linear inequalities (standard form)
Check solutions to systems of linear inequalites (standard form)
Create systems of linear inequalities from graphs (slope-intercept form)

Operations with Polynomials

Add and subtract linear expressions
Multiply linear expressions
Add quadratic expressions
Subtract quadratic expressions
Add and subtract quadratic expressions

Geometry

Coordinate Planes

Coordinate Basics

Understand signs of numbers in ordered pairs as indicating locations in quadrants
Find and position pairs of rational numbers on a coordinate plane

Coordinate Applications

Reflect ordered pairs (on graph)
Reflect ordered pairs (no graph)
Find vertical/horizontal distances between points (on a graph)
Find vertical/horizontal distances between points (with ordered pairs)
Solve mathematical perimeter problems by graphing points in all four quadrants of the coordinate plane
Solve mathematical area problems by graphing points in all four quadrants of the coordinate plane
Find the coordinates of missing vertices in rectangles

Area of Polygons

Area on Coordinate Planes

Find the area of triangles (using coordinate planes)
Find the area of squares (using coordinate planes)
Find the area of rectangles (using coordinate planes)
Find the area of trapezoids (using coordinate planes)
Find the area of rhombuses (using coordinate planes)
Find the area of kites (using coordinate planes)
Find the area of special quadrilaterals (using coordinate planes)

Coordinate Geometry

Parallel and Perpendicular Lines

Determine if two lines are parallel, perpendicular, or neither (slope-intercept form)
Determine if two lines are parallel, perpendicular, or neither (mixed forms)
Determine if two lines are parallel, perpendicular, or neither (standard form)
Find the equation of lines parallel to given lines
Find the equation of lines perpendicular to given lines

Endpoints and Midpoints

Use a graph to find the midpoint of a line segment
Use coordinates to find the midpoint of a line segment
Use a graph to find the endpoint of a line segment
Use coordinates to find the endpoint of a line segment

Transformations

Transformations on Figures

Translate figures on graphs
Reflect figures on graphs (over both axes)
Rotate figures on graphs (by multiples of 90 degrees)
Dilate figures on graphs
Conduct transformations with figures (on graphs)
Use transformations on graphs to define congruence
Identify transformations (from ordered pairs)
Conduct a sequence of transformations (on ordered pairs)
Determine if two figures are congruent (from ordered pairs)

Triangles

Triangle Formation

Determine how many triangles can be created given the angle measures
Determine how many triangles can be created given the side lengths
Determine how many triangles can be created given the side lengths or angle measures