Curated Skills for Mathematics

Long Division (No Remainder)

• Use long division (dividend ≤ 100)
• Use long division (dividend ≤ 1000)
• Use long division (dividend ≥ 1000)

Long Division (With Remainder)

• Use long division with a remainder (dividend ≤ 100)
• Use long division with a remainder (dividend ≤ 1000)
• Use long division with a remainder (dividend ≥ 1000)

Long Division Applications

• Solve real-world problems involving long division
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Decimal Addition

• Apply the standard algorithm for the addition of decimals (easy)
• Apply the standard algorithm for the addition of decimals (medium)
• Apply the standard algorithm for the addition of decimals (challenging)

Decimal Subtraction

• Apply the standard algorithm for the subtraction of decimals (easy)
• Apply the standard algorithm for the subtraction of decimals (medium)
• Apply the standard algorithm for the subtraction of decimals (challenging)

Decimal Multiplication

• Apply the standard algorithm for the multiplication of decimals (easy)
• Apply the standard algorithm for the multiplication of decimals (medium)
• Apply the standard algorithm for the multiplication of decimals (challenging)

Decimal Division

• Apply the standard algorithm for the division of decimals (easy)
• Apply the standard algorithm for the division of decimals (medium)
• Apply the standard algorithm for the division of decimals (challenging)

Operations with Decimals

• Apply the standard algorithm for all operations on decimals (easy)
• Apply the standard algorithm for all operations on decimals (medium)
• Apply the standard algorithm for all operations on decimals (challenging)

Fraction Division (fractions < 1)

• Foundational - Division of fractions with denominators ≤ 6
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• Progressive - Division of fractions with denominators ≤ 9
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• Elevated - Division of fractions with denominators ≤ 12
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Fraction Division (fractions < 4)

• Foundational - Division of fractions with denominators ≤ 6
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• Progressive - Division of fractions with denominators ≤ 9
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• Elevated - Division of fractions with denominators ≤ 12
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Fraction Division (fractions < 12)

• Foundational - Division of fractions with denominators ≤ 6
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• Progressive - Division of fractions with denominators ≤ 9
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• Elevated - Division of fractions with denominators ≤ 12
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Fraction Division Applications

• Solve real-world problems involving the division of fractions
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Operations with Rational Numbers

• Add and subtract rational numbers
• Multiply rational numbers
• Divide rational numbers
• Conduct all operations on rational numbers
• Convert fractions to decimals using long division

Number Theory

• 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

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

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)

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)

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

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)

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)

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 (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)

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)

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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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

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)

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

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

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 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)

Area of Figures

• Find the area of squares
• Find the area of rectangles
• Find the area of triangles
• Find the area of trapezoids
• Find the area of rhombuses
• Find the area of kites
• Find the area of special quadrilaterals
• Find the area of triangles (with measurements for area and perimeter)
• Find the area of trapezoids (with measurements for area and perimeter)
• Find the area of rhombuses (with measurements for area and perimeter)
• Find the area of kites (with measurements for area and perimeter)
• Find the area of special quadrilaterals (with measurements for area and perimeter)

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 on Points

• Translate points on graphs
• Describe translations shown on graphs
• Reflect points over the x-axis
• Reflect points over the y-axis
• Reflect points over both axes
• Identify reflections shown on graphs
• Rotate points 90 degrees CW
• Rotate points 180 degrees
• Rotate points 270 degrees CCW
• Rotate points in multiples of 90 degrees
• Identify rotations shown on graphs
• Dilate points on graphs
• Describe dilations shown on graphs

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)

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

Circles (circumference)

• Find circumference of a circle (given diagram with radius)
• Find circumference of a circle (given diagram with diameter)
• Find circumference of a circle (given description of radius or diameter)

Circles (area)

• Find area of a circle (given diagram with radius)
• Find area of a circle (given description of radius or diameter)
• Apply the formula for the area of a circle (mixed r and d)

Circles (working backward)

• Find the radius of a circle given the circle's area
• Find the radius of a circle given the circle's circumference
• Find the area of a circle given the circle's circumference
• Find the circumference of a circle given the circle's area

Prisms

• Find the volume of right rectangular prisms with fractional edge lengths
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• Divide prisms
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• Find the volume of prisms
• Find the surface area of prisms
• Find the height of a prism by using the volume

Pyramids

• Find the volume of pyramids
• Find the surface area of pyramids
• Find the height of a pyramid by using the volume

Cylinders

• Calculate the volume of cylinders
• Calculate missing heights of cylinders
• Calculate missing radii of cylinders

Cones

• Calculate the volume of cones
• Calculate missing heights of cones
• Calculate missing radii of cones

Spheres

• Calculate the volume of spheres
• Calculate missing radii of spheres

Cylinders, Cones, and Spheres

• Calculate the volume of cylinders, cones, and spheres
• Calculate missing heights of cylinders and cones
• Calculate missing radii of cylinders and cones

Pythagorean Theorem

• Find the missing hypotenuse in a right triangle
• Find the missing leg in a right triangle (hypotenuse rounded)
• Find the missing hypotenuse (in radical form)
• Find the missing leg in a right triangle (hypotenuse in radical form)

Pythagorean Theorem Applications

• Find the length of a rectangle's diagonal
• Find the distance between two points
• Find the perimeter of a right triangle on a coordinate plane
• Find the perimeter of triangles on a coordinate plane
• Find the perimeter of a quadrilateral on a coordinate plane
• Find diagonals of rectangular prisms
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• Find diagonals of rectangular prisms (in radical form)
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Interior Angles

• Solve mathematical problems involving interior angles (easy)
• Solve mathematical problems involving interior angles (medium)
• Solve mathematical problems involving interior angles (challenging)

Exterior Angles

• Solve mathematical problems involving exterior angles (easy)
• Solve mathematical problems involving exterior angles (medium)
• Solve mathematical problems involving exterior angles (challenging)

Vertical Angles

• Find vertical angles using a diagram (easy)
• Find vertical angles using a diagram (medium)
• Find vertical angles using a diagram (challenging)

Complementary Angles

• Find complementary angles using a diagram (easy)
• Find complementary angles using a diagram (medium)
• Find complementary angles using a diagram (challenging)

Adjacent Angles

• Find adjacent angles using a diagram (easy)
• Find adjacent angles using a diagram (medium)
• Find adjacent angles using a diagram (challenging)

Supplementary Angles

• Find supplementary angles using a diagram (easy)
• Find supplementary angles using a diagram (medium)
• Find supplementary angles using a diagram (challenging)

Angle Relationships

• Find missing angles in angle relationships from descriptions (easy)
• Find missing angles in angle relationships from descriptions (medium)
• Find missing angles in angle relationships from descriptions (challenging)

Transversals

• Solve mathematical problems involving transversals (easy)
• Solve mathematical problems involving transversals (medium)
• Solve mathematical problems involving transversals (challenging)

Summarize Data Sets

• Summarize numerical data sets
• Summarize numerical data sets from dotplots

Measures of Center

• Determine the measures of center of a data set
• Determine the measures of center of a dot plot
• Calculate measures of center and spread

Data Displays

• Display numerical data on dot plots
• Display numerical data on box plots
• Represent data with box plots

Shape of Data

• Describe the shape of data from dot plots
• Describe the shape of data from box plots

Measures of Spread

• Calculate the range of a data set
• Calculate the mean absolute deviation of a data set
• Calculate the interquartile range of a data set

Extreme Data Points

• Identify outliers
• Examine the effects of extreme data points on center
• Examine the effects of extreme data points on spread

Probability Basics

• Calculate samples spaces (word problems)

Coin Flips

• Calculate probabilities using coin flips
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• Calculate probabilities using coin flips (union/or)
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• Calculate probabilities using coin flips (intersection/and)
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• Calculate probabilities using coin flips (mixed)
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Die Roll - Basic

• Calculate probabilities using a single die
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• Calculate probabilities using a single die (challenging)
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Die Roll - OR

• Calculate probabilities using a single die (union/or - easy)
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• Calculate probabilities using a single die (union/or - medium)
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• Calculate probabilities using a single die (union/or - challenging)
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Die Roll - AND

• Calculate probabilities using a single die (intersection/and - easy)
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• Calculate probabilities using a single die (intersection/and - medium)
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• Calculate probabilities using a single die (intersection/and - challenging)
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Dice Roll - Basic

• Calculate probabilities using dice rolls
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Dice Roll - OR

• Calculate probabilities using dice rolls (union/or - easy)
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• Calculate probabilities using dice rolls (union/or - medium)
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• Calculate probabilities using dice rolls (union/or - challenging)
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Dice Roll - AND

• Calculate probabilities using dice rolls (intersection/and - easy)
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• Calculate probabilities using dice rolls (intersection/and - medium)
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• Calculate probabilities using dice rolls (intersection/and - challenging)
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Deck of Cards (Single Draw)

• Calculate probabilities for single card draws
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• Calculate probabilities for single card draws (intersection/and)
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• Calculate probabilities for single card draws (union/or)
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Deck of Cards (Two Draws)

• Calculate probabilities for double card draws (replacement)
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• Calculate probabilities for double card draws (without replacement)
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