Content Category |
Skills |
Example |
Lessons |
Operations with Integers
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Order of operations, adding, subtracting, multiplying, and dividing basic integers
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$72+4÷2+5$
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Intro to PEMDAS
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Operations with Fractions
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Adding, subtracting, multiplying, and dividing fractions
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$2/3+(3/4×1/2)+(3/4-1/3)$
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Adding & Subtracting Fractions
Multiplying & Dividing Fractions
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Operations with Decimals
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Adding,subtracting,multiplying,and dividing decimals
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$7.46+1.85+2.5×3$
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Decimals
Decimals rounding
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Operations between mixed numbers and improper fractions
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Adding, subtracting, multiplying,and dividing using mixed numbers and improper fractions
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$7(1/2)+ 18.85+4(2/3)$
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Improper Fractions and Mixed Numbers
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Exponents
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Raising numbers to "a power" (how many times a number is multiplied by itself)
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$2^4+3^2$
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Intro to Exponents
Exponent Rules, Like Bases, & Negative Exponents
Scientific Notation
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Square Roots
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A number that produces a specified quantity when multiplied by itself.
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$√4+√81$
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Simplifying Roots & Radicals
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Ratios and Proportions
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"Part over whole" or fractions that equals a similar fraction
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$X/2=12/8$
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Ratios & Proportions
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Percentages |
"A part" of a certain value which is used in operations.
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20% of 100 + 30% of 60
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Percents as Ratios
Percent Increase & Decrease
Percents As Decimals
Hard Multi-Step Percent Problems
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Averages
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Another word for the "mean" which is a sum of all numbers in a set of data divided by the amount of numbers
|
Steve tried to compute the average of his 5 test scores. He scored 86 on one, 55 on the next one, then 99, 77, and 90. What is Steve's average test score?
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Calculating The Mean (Average)
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Geometry |
Knowing both the area and the perimeter of triangles, quadrilaterals, and circles
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If one angle of a triangle is 95 degrees and another is 35 degrees, what is the third angle of the triangle?
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180 Triangle Rule Problems
Areas of Rectangles & Squares
Rectangles & Squares
Basic Circle Area Problems
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Substituting values for x
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Being given a value for x and plugging in |
What is the value at $(x^2-2)/(x-1)$ for x=2?
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Intro to Variables & Expressions
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Setting up an Equation
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Translating an equation from words into numbers and variables
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A car's distance is determined by the velocity multiplied by the amount of time the car is at that speed.If a car can go at a maximum velocity of 225 meters per second, what equation shows how far the car has travelled at its maximum speed?
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How to Translate Words Into Equations
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Operations with Polynomials
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Adding,subtracting,multiplying,and dividing equations with multiple variables
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Simplify: $2a+3b-(-6a+4b)$
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Adding Polynomials (a.k.a. Combining Like Terms)
Distribution (a.k.a. "multiplying stuff out")
Solving Equations With Distribution
Basic FOIL on 2-by-2 parentheses
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Factoring
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Undoing a polynomial and simplifying it into its most basic equations as well as using it to find certain input values
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What is one possible factor of $x^2+4x+3$ ?
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Factoring Stuff Out (a.k.a. "distrubution in reverse")
Easier Factoring Problems
Factoring Difference of Squares
Hard Factoring Problems
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Linear Equations to One Variable
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An input which leads to an output and using the output to solve for the input
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Solve for x when $2(x-2)=-10$
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Solving Equations With Addition & Subtraction Only]
Solving Equations With Multiplication & Division]
Solving Two Step Equations
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Exponent Properties
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Multiplying, dviding, or taking the power of a number or variable to a power
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$(x^2)((x^5)^2)/ x^9$ =?
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Basic Exponent Rules & Rational Expressions
Negative Exponents
Common Algebraic Canceling Mistakes
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Irrational functions and multiplying by the Complex Conjugate
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Simplifying a polynomial over a polynomial and being able to simplify roots in a denominator.
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$ √x/(3√x- √y)$
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Dividing Roots & Rationalizing Denominators
Solving Rational Equations (x's in denominators)
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System of Equations
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Solving for an intersection point of two equation at a designated x or y value.
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Solve for x and y: $2x+3y=6$
$8x-4y=-12$
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Solving Systems of Simultaneous Equations with Elimination
Solving Systems of Simultaneous Equations with Substitution
Solving 3 Simultaneous Equations with 3 Unknowns
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Inequalities
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Solving for the range of a functions x or y value using manipulation of a number line
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What is the range of x for the function $2x+5<6$ ?
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Solving "Linear" Inequalities
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