Pre-Algebra

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Percents

6.RP.37.RP.3

Convert Percents to Fractions--

Find Equivalent Fractions (Denominator of 100)--

Convert Percents to Reduced Fractions--

Convert Fractions to Percents--

Divide 100--

Convert Unit Fractions to Mixed Number Percents--

Find a Percent of a Number--

What Percent Is It?--

Percent Increase and Decrease--

Coordinate Plane

6.NS.66.NS.76.NS.8

Evaluate Absolute Value of Integers--

Evaluate Expressions Inside Absolute Value--

Identify Points in First Quadrant--

Plot Points in First Quadrant--

Identify Points in All Quadrants--

Plot Points in All Quadrants--

Identify Points on the Axes--

Plot Points on the Axes--

Plot Reflections Across the x-axis--

Plot Reflections Across the y-axis--

Mixed Reflections Practice--

Identify Δx Between Two Points--

Identify Δy Between Two Points--

Identify Slope from Two Points--

Integer Operations

6.NS.57.NS.17.NS.27.NS.3

Below Zero--

Add to Negative--

Subtract From Negative--

Add Negatives--

Subtract Negatives--

Add/Subtract Negatives--

Multiply Integers--

Divide Integers--

Compare Integers--

Order Integers (Least to Greatest)--

Mixed Integer Operations--

Exponents, Roots, and Order of Operations

6.EE.18.EE.18.EE.2

Square Numbers--

Cube Numbers--

Square and Cube Numbers--

Exponents of 2--

Exponents of 3--

Exponents with 0 and 1--

Find Missing Base in Square Numbers--

Find Missing Base in Cube Numbers--

Square Roots of Perfect Squares--

Cube Roots of Perfect Cubes--

Negative Exponents--

Product Rule (Same Base)--

Quotient Rule (Same Base)--

Power of a Power Rule--

2 Step MDAS--

3 Step MDAS--

Parentheses--

2 Step EMDAS--

3 Step EMDAS--

PEMDAS--

Radicals

8.EE.2HSN-RN.1HSN-RN.2

Evaluate Square Roots--

Simplify Square Roots (Intro)--

Simplify Square Roots--

Multiply Radicals--

Divide Radicals--

Add and Subtract Radicals--

Add/Subtract Radicals (Simplify First)--

Mixed Radical Operations--

Evaluate Cube Roots--

Simplify Cube Roots--

Scientific Notation

8.EE.38.EE.4

Exponents of 10--

Convert Standard Form to Scientific Notation--

Convert Scientific Notation to Standard Form--

Compare Values in Scientific Notation--

Multiply Scientific Notation by Powers of Ten--

Scientific Notation with Small Numbers--

Add Numbers in Scientific Notation--

Expressions

6.EE.26.EE.36.EE.47.EE.1HSA-SSE.1HSA-SSE.2

Combine Like Terms--

Combine Like Terms with Constants--

Distributive Property--

Linear Equations

6.EE.56.EE.77.EE.37.EE.48.EE.7HSA-REI.1HSA-REI.3

One-Step Equations: Add & Subtract (Positives)--

One-Step Equations: Multiply & Divide (Positives)--

One-Step Equations: Add & Subtract--

One-Step Equations: Multiply & Divide--

Two-Step Equations (Positives)--

Two-Step Equations--

Distributive Property Equations--

Equations with Variables on Both Sides--

Solving Inequalities

6.EE.56.EE.87.EE.4

One-Step Inequalities (Add & Subtract)--

One-Step Inequalities (Multiply & Divide)--

Two-Step Inequalities--

Inequalities with Negative Coefficients--

Functions

8.F.18.F.28.F.38.F.4

Is It a Function?--

Evaluate a Linear Function--

Evaluate a Quadratic Function--

Linear vs. Nonlinear Functions--

Identify Slope from y = mx + b--

Identify y-intercept from y = mx + b--

Rate of Change from a Table--

Write Equation from Slope and y-intercept--

Common Core Standards

Grade 6

RP — Ratios & Proportional Relationships

Understand ratio concepts and use ratio reasoning to solve problems.

6.RP.1Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
6.RP.3Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

NS — The Number System

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

6.NS.1Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions.

Compute fluently with multi-digit numbers and find common factors and multiples.

6.NS.2Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12.

Apply and extend previous understandings of numbers to the system of rational numbers.

6.NS.5Understand that positive and negative numbers are used together to describe quantities having opposite directions or values; use positive and negative numbers to represent quantities in real-world contexts.
6.NS.6Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
6.NS.7Understand ordering and absolute value of rational numbers.
6.NS.8Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane.

EE — Expressions & Equations

Apply and extend previous understandings of arithmetic to algebraic expressions.

6.EE.1Write and evaluate numerical expressions involving whole-number exponents.
6.EE.2Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.3Apply the properties of operations to generate equivalent expressions.
6.EE.4Identify when two expressions are equivalent.

Reason about and solve one-variable equations and inequalities.

6.EE.5Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true?
6.EE.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
6.EE.8Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Represent and analyze quantitative relationships between dependent and independent variables.

6.EE.9Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable.

G — Geometry

Solve real-world and mathematical problems involving area, surface area, and volume.

6.G.1Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
6.G.2Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism.
6.G.3Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate.
6.G.4Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures.

SP — Statistics & Probability

Develop understanding of statistical variability.

6.SP.1Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers.
6.SP.2Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
6.SP.3Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.

Summarize and describe distributions.

6.SP.4Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
6.SP.5Summarize numerical data sets in relation to their context.

Grade 7

RP — Ratios & Proportional Relationships

Analyze proportional relationships and use them to solve real-world and mathematical problems.

7.RP.1Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.
7.RP.2Recognize and represent proportional relationships between quantities.
7.RP.3Use proportional relationships to solve multistep ratio and percent problems.

NS — The Number System

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

7.NS.1Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
7.NS.2Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
7.NS.3Solve real-world and mathematical problems involving the four operations with rational numbers.

EE — Expressions & Equations

Use properties of operations to generate equivalent expressions.

7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

7.EE.3Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

G — Geometry

Draw, construct, and describe geometrical figures and describe the relationships between them.

7.G.1Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.G.2Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
7.G.3Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

7.G.4Know the formulas for the area and circumference of a circle and use them to solve problems.
7.G.5Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
7.G.6Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

SP — Statistics & Probability

Use random sampling to draw inferences about a population.

7.SP.1Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.
7.SP.2Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions.

Draw informal comparative inferences about two populations.

7.SP.3Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability.
7.SP.4Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Investigate chance processes and develop, use, and evaluate probability models.

7.SP.5Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood.
7.SP.6Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability.
7.SP.7Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
7.SP.8Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

Grade 8

NS — The Number System

Know that there are numbers that are not rational, and approximate them by rational numbers.

8.NS.1Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
8.NS.2Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions.

EE — Expressions & Equations

Work with radicals and integer exponents.

8.EE.1Know and apply the properties of integer exponents to generate equivalent numerical expressions.
8.EE.2Use square root and cube root symbols to represent solutions to equations of the form x² = p and x³ = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes.
8.EE.3Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
8.EE.4Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used.

Understand the connections between proportional relationships, lines, and linear equations.

8.EE.5Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
8.EE.6Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

Analyze and solve linear equations and pairs of simultaneous linear equations.

8.EE.7Solve linear equations in one variable.
8.EE.8Analyze and solve pairs of simultaneous linear equations.

F — Functions

Define, evaluate, and compare functions.

8.F.1Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
8.F.2Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
8.F.3Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

Use functions to model relationships between quantities.

8.F.4Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph.
8.F.5Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

G — Geometry

Understand congruence and similarity using physical models, transparencies, or geometry software.

8.G.1Verify experimentally the properties of rotations, reflections, and translations.
8.G.2Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8.G.3Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
8.G.5Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

Understand and apply the Pythagorean Theorem.

8.G.6Explain a proof of the Pythagorean Theorem and its converse.
8.G.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
8.G.8Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

8.G.9Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

SP — Statistics & Probability

Investigate patterns of association in bivariate data.

8.SP.1Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
8.SP.2Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
8.SP.3Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept.
8.SP.4Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects.