Want to help your eighth-grader master math? Here are some of the skills your child will be learning in the classroom.

## Numbers

**Rational and irrational Numbers**

Understand rational and irrational numbers. Know that a rational number can be written as a fraction or decimal (for example: ½, 0.5, 2, or -2), but that an irrational number – for example, the square root of 2, or √2 – cannot be written as a fraction. When written in decimal form, an irrational number does not repeat or end.

## Expressions & equations

**Working with radicals**

Work with radicals – mathematical expressions including square roots (symbol:√ ), cube roots (symbol: 3√), etc.

Determine the square roots of small perfect squares – for example: √49 = 7 (7 x 7 = 49).

Determine the cube roots of small perfect cubes – for example: 3√64 = 4 (4 x 4 x 4 = 64).

**Equations with exponents**

Solve simple equations involving exponents, including exponents with negative bases and exponents with decimal and fraction bases.

**Scientific notation**

Understand scientific notation as a way of writing numbers that are too big or too small to be easily written and read in decimal form – for example, convert 7,120,000,000 (standard decimal notation) to 7.12 x 10^9 (scientific notation). Add, subtract, multiply, and divide with numbers expressed in scientific notation.

**Proportional relationships**

Compare different proportional relationships, expressed in different forms: equations, graphs, verbal expressions, tables, etc.

**Graph proportional relationships**

Graph proportional relationships. Interpret the unit rate as the slope of the graph – how steep or flat the line is.

**Slope-intercept**

Work with the slope-intercept (or y-intercept) form of linear equations (equations that make a straight line when graphed): *y = mx + b.*

- Understand that the values of
*x*and*y*on the graph are the solutions of the equation, and*m*is the slope of the line. - Understand slope (
*m*) as the change in y over the change in*x*(called rise over run): if the*x*-coordinate changes by*A*, the*y*-coordinate changes by*m x A*.

**Linear equations**

Solve single-variable linear equations (both one-step and two-step).

**Simultaneous linear equations**

Solve simultaneous linear equations (linear equations involving the same set of variables). Find the point of intersection of two lines.

## Functions

**Functions as rules**

Understand functions as rules assigning to each value of x exactly one value of y (to each input exactly one output). Use functions to describe relationships between numbers (quantities) and situations where one quantity determines another. For example, y = 2x is a way to express the relationship between the numbers 3 and 6, or 4 and 8, or -2 and -4.

**Comparing function properties**

Using function tables, graphs, equations, or descriptions, compare the properties of two functions. Understand that linear equations are functions.

## Geometry

**Congruence and similarity**

For two-dimensional figures (including lines and angles), understand and determine congruence (objects of equal size and shape) and similarity (objects of the same shape but different sizes).

**The Pythagorean Theorem**

Understand the Pythagorean Theorem, a relationship unique to right triangles. The Pythagorean Theorem can be expressed as an equation to determine unknown side lengths in right triangles: a² +b² = c². In a right-angled triangle, the square of the hypotenuse (the longest side of the triangle, c) is equal to the sum of the squares of the other two sides (a and b).

**Distance between two points**

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

**Pythagorean Theorem problems**

Use the Pythagorean Theorem to solve real-world and mathematical problems.

Example:

The library is 8 miles south of the school. The rec center is 15 miles east of the library. What is the straight-line distance from the school to the rec center? Use a diagram to explain your answer.

**Transformations**

Recognize and identify transformations of two-dimensional figures

- translations – a sliding movement of the figure in any direction.
- dilations – shrinking or expanding the figure.
- rotations – turning the figure.
- reflections – mirror images of the figure.

For tips to help your eighth-grader in math class, check out our eighth grade math tips page.

*Parent Toolkit resources were developed by NBC News Learn with the help of subject-matter experts and align with the Common Core State Standards.*