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# 8th Grade Skills in Math

The 8th Grade Skills below are based on the Common Core Standards For Mathematics. You can find out more about the Common Core Standards here.

You will also find a listing of related math resources (worksheets, charts, etc) here.

Note: Math standards and curricula can vary by location or school. Check with your child’s school to determine what 8th grade math skills are expected in your location.

## The Number System

Understanding that all numbers have a decimal expansion and, for rational numbers, showing that this expansion repeats.
Using rational approximations to compare irrational numbers and being about to position these on a number line.

## Expressions & Equations

Knowing and using exponent rules. e.g. 45 x 4-3 = 42

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 x 3-5 = 3-3 = 1/33 = 1/27.

### Example/Guidance

Solving equations by using the square and cubic root symbols and know square roots for perfect squares.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Use 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. Know that ?2 is irrational.

### Example/Guidance

Using and understanding scientific notation. e.g. 5 x 109

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Use numbers expressed in the form of a single digit times a whole-number power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 times 108 and the population of the world as 7 times 109, and determine that the world population is more than 20 times larger.

### Exponents

Adding, subtracting, multiplying, and dividing with numbers shown in scientific notation and use appropriate units for both very large and very small quantities.
Understanding and drawing graphical representations of proportional relationships recognizing that the slope shows the unit rate.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

### Coordinate Geometry

Explaining slope and determining the equation, y =mx for a line that intersects the origin and determining the equation y = mx + c for one which intersects the y-axis at c.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Use 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.

### Worksheet

Solving linear equations in one variable.
Solving simultaneous linear equations.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Analyze and solve pairs of simultaneous linear equations.
1. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.
2. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
3. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

## Functions

Recognizing functions as rules that maps each output from exactly one input.
Comparing and contrasting two functions both shown in different ways (graphic, tabular, algebraic) e.g. be able to tell which one shows a greater rate of change.
Identifying and distinguishing between equations that define linear functions and those that define non-linear functions. e.g. y = mx + a is linear and H = r2 is non-linear.
Generating functions to represent linear relationships between two quantities.
Describing the characteristics of a functional relationship by examining its graphical representation.

## Geometry

Experimenting to confirm the properties of translations, rotations, and reflections.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.

### Similarity, Congruence and Transformations

Identifying the congruence of two figures and the sequence of transformations that connects them.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Understand 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.

### Worksheet

Expressing the changes caused by dilations, translations, rotations, and reflections with the coordinate system.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

### Worksheet

Understanding similarity of triangles and other 2-D figures e.g. how similar figures can be generated through a series of transformations.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Understand 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.

### Similarity, Congruence and Transformations

Establishing facts about the sum of angles in a triangle and its exterior angles.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Use 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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

### Lines and Angles

Describing a proof for Pythagoras’ Theorem.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Explain a proof of the Pythagorean Theorem and its converse.

### Shapes and Figures

Using Pythagoras’ Theorem to find unknown dimensions in right-angled triangles.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

### Worksheet

Using Pythagoras’ Theorem to find the distance between two sets of coordinates.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

### Coordinate Geometry

Recalling and using the formulas for volume of 3-D objects. e.g. cylinders, cones, spheres.

## Statistics & Probability

Generating and analyzing scatter plots for bivariate measurement data to determine patterns of association. e.g. clustering, outliers, linear, and non-linear association.
Using “best fit” straight lines to identify linear association on scatter plots.
Solving bivariate measurement data problems using the equation of a linear model.

The listing of worksheets and other math resources below are related to the following standard extracted from the Common Core Standards For Mathematics:

Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.

### Example/Guidance

Understanding that a 2-way table can list frequency and relative frequency to show patterns of association for bivariate categorical data.

Browse for skills and worksheets at other grade levels by clicking in the table below.