# Eighth-Grade Mathematics Standards Eighth-grade students connect their understanding of rates and relationships to points on a line, using linear equations and functions to analyze and solve problems. They also learn about the Pythagorean Theorem. Here are a few examples of what your child will study throughout the year, questions to ask his or her teachers and tips for reinforcing math skills at home.

### Number System

1. Understand the difference between rational and irrational numbers; for example, rational numbers can be expressed as fractions and decimals, but irrational numbers can only be written as an unending decimal.
Pi: (π = 3.14159265359…) is an irrational number because it is an unending decimal. A number such as 1.5 is rational because it can be written as a fraction: ### Expressions and Equations

1. Work problems that involve radical numbers, including square roots and cube roots.
2 + 2(√7)2
= 2 + 2(7)
= 2 + 14
= 16
2. Write and solve linear equations.
5x + 3x = 8
8x = 8
x = 1
3. Solve basic equations that use exponents. ### Functions

1. Comprehend functions as rules that assign one input to one output and that can be expressed using tables, graphs and equations.
 X 0 1 2 2 3 4 Y 1 2 1 3 0 5

This is not a function because “2” is an X value more than once.

2. Complete word problems that involve proportional relationships; be able to illustrate the solution using a graph.

### Geometry

1. Understand the Pythagorean Theorem and how it is used as an equation to solve problems.
Q: A: a2 + b2 = c2
a2 + 42 = 52
a2 + 16 = 25
a2 = 9
a = √9
a = 3
2. Gain knowledge of the difference between congruent and similar two-dimensional objects.
Q: A: These two triangles are similar triangles because the second triangle increases by a factor of 2.
(6 × 2 = 12); (2 × 2 = 4)

### Statistics and Probability

1. Learn and use the best-fit line method to compare two values.
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