CCSS.Math.Content.8.NS.A.1
The standard
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
Common Core State Standards for Mathematics · The Number System
What this standard means
Students need to tell the difference between rational and irrational numbers by looking at decimals and fractions. They should know that rational numbers can be written as fractions, and their decimals either end or repeat. They also need to turn repeating decimals into fractions.
Mastery looks like explaining why 0.375, -2/3, and 0.121212... are rational, while numbers like √2 or π are not rational. Students often get stuck thinking any long decimal is irrational, or missing the repeating pattern when it starts after a few digits.
Ways to teach it
- Use fraction cards and decimal cards, then have students sort them into terminating, repeating, and non-repeating groups with a partner.
- Ask students to explain in writing: How can a decimal go on forever but still be rational?
- Give five numbers, including 0.777..., 0.625, √5, π, and 1.232323..., and have students label each rational or irrational.
- Connect to calculators by having students enter 1/3, 1/7, and √2, then compare the decimal displays and what they mean.
Plan a lesson for CCSS.Math.Content.8.NS.A.1
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Related standards
- CCSS.Math.Content.8.NS.A
Know that there are numbers that are not rational, and approximate them by rational numbers.
- CCSS.Math.Content.HSN-RN.B
Use properties of rational and irrational numbers.
- CCSS.Math.Content.6.NS.C
Apply and extend previous understandings of numbers to the system of rational numbers.
- CCSS.Math.Content.7.NS.A.2d
Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.