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.