Looking for free content that’s aligned to your standards? You’ve come to the right place!

## Get Free 8th Grade Math Content

Khan Academy is a nonprofit with thousands of free videos, articles, and practice questions for just about every standard.

No ads, no subscriptions – just 100% free, forever.

### 2 Number and operations

- 2 The student applies mathematical process standards to represent and use real numbers in a variety of forms.
- A extend previous knowledge of sets and subsets using a visual representation to describe relationships between sets of real numbers;
- B approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line;
- C convert between standard decimal notation and scientific notation; and
- D order a set of real numbers arising from mathematical and real-world contexts.
- Checkpoint opportunity

### 3-5 Proportionality

- 3 The student applies mathematical process standards to use proportional relationships to describe dilations.
- A generalize that the ratio of corresponding sides of similar shapes are proportional, including a shape and its dilation;
- B compare and contrast the attributes of a shape and its dilation(s) on a coordinate plane; and
- C use an algebraic representation to explain the effect of a given positive rational scale factor applied to two-dimensional figures on a coordinate plane with the origin as the center of dilation.
- Checkpoint opportunity

- 4 The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope.
- A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y
_{2}– y_{1})/ (x_{2}– x_{1}), is the same for any two points (x_{1}, y_{1}) and (x_{2}, y_{2}) on the same line; - B graph proportional relationships, interpreting the unit rate as the slope of the line that models the relationship; and
- C use data from a table or graph to determine the rate of change or slope and y-intercept in mathematical and real-world problems.
- Checkpoint opportunity

- A use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y
- 5 The student applies mathematical process standards to use proportional and non-proportional relationships to develop foundational concepts of functions.
- A represent linear proportional situations with tables, graphs, and equations in the form of y = kx;
- B represent linear non-proportional situations with tables, graphs, and equations in the form of y = mx + b, where b ≠ 0;
- C contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation;
- D use a trend line that approximates the linear relationship between bivariate sets of data to make predictions;
- E solve problems involving direct variation;
- F distinguish between proportional and non-proportional situations using tables, graphs, and equations in the form y = kx or y = mx + b, where b ≠ 0;
- G identify functions using sets of ordered pairs, tables, mappings, and graphs;
- H identify examples of proportional and non-proportional functions that arise from mathematical and real-world problems; and
- I write an equation in the form y = mx + b to model a linear relationship between two quantities using verbal, numerical, tabular, and graphical representations.
- Checkpoint opportunity

### 6-9 Expressions, equations, and relationships

- 6 The student applies mathematical process standards to develop mathematical relationships and make connections to geometric formulas.
- A describe the volume formula V = Bh of a cylinder in terms of its base area and its height;
- B model the relationship between the volume of a cylinder and a cone having both congruent bases and heights and connect that relationship to the formulas; and
- C use models and diagrams to explain the Pythagorean theorem.

- 7 The student applies mathematical process standards to use geometry to solve problems.
- A solve problems involving the volume of cylinders, cones, and spheres;
- B use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders;
- C use the Pythagorean Theorem and its converse to solve problems; and
- D determine the distance between two points on a coordinate plane using the Pythagorean Theorem.
- Checkpoint opportunity

- 8 The student applies mathematical process standards to use one-variable equations or inequalities in problem situations.
- A write one-variable equations or inequalities with variables on both sides that represent problems using rational number coefficients and constants;
- B write a corresponding real-world problem when given a one-variable equation or inequality with variables on both sides of the equal sign using rational number coefficients and constants;
- C model and solve one-variable equations with variables on both sides of the equal sign that represent mathematical and real-world problems using rational number coefficients and constants; and
- D use informal arguments to establish facts about the angle sum and exterior angle of triangles, the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.
- Checkpoint opportunity

- 9 The student applies mathematical process standards to use multiple representations to develop foundational concepts of simultaneous linear equations.
- The student is expected to identify and verify the values of x and y that simultaneously satisfy two linear equations in the form y = mx + b from the intersections of the graphed equations.
- Checkpoint opportunity

### 10 Two-dimensional shapes

- 10 The student applies mathematical process standards to develop transformational geometry concepts.
- A generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane;
- B differentiate between transformations that preserve congruence and those that do not;
- C explain the effect of translations, reflections over the x- or y-axis, and rotations limited to 90°, 180°, 270°, and 360° as applied to two-dimensional shapes on a coordinate plane using an algebraic representation; and
- D model the effect on linear and area measurements of dilated two-dimensional shapes.
- Checkpoint opportunity

### 11 Measurement and data

- 11 The student applies mathematical process standards to use statistical procedures to describe data.
- A construct a scatterplot and describe the observed data to address questions of association such as linear, non-linear, and no association between bivariate data;
- B determine the mean absolute deviation and use this quantity as a measure of the average distance data are from the mean using a data set of no more than 10 data points; and
- C simulate generating random samples of the same size from a population with known characteristics to develop the notion of a random sample being representative of the population from which it was selected.
- Checkpoint opportunity

### 12 Personal financial literacy

- 12 The student applies mathematical process standards to develop an economic way of thinking and problem solving useful in one’s life as a knowledgeable consumer and investor.
- A solve real-world problems comparing how interest rate and loan length affect the cost of credit;
- B calculate the total cost of repaying a loan, including credit cards and easy access loans, under various rates of interest and over different periods using an online calculator;
- C explain how small amounts of money invested regularly, including money saved for college and retirement, grow over time;
- D calculate and compare simple interest and compound interest earnings;
- E identify and explain the advantages and disadvantages of different payment methods;
- F analyze situations to determine if they represent financially responsible decisions and identify the benefits of financial responsibility and the costs of financial irresponsibility; and
- G estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college.