CCSS.Math.Content.8.NS.A
The standard
Know that there are numbers that are not rational, and approximate them by rational numbers.
Common Core State Standards for Mathematics
What this standard means
Students need to know that some numbers cannot be written as fractions. They should recognize examples like square roots of non-perfect squares and decimals that never end or repeat. They also need to place these numbers on a number line and estimate their value using nearby rational numbers.
Mastery looks like estimating values such as √2 or √50 without a calculator, explaining why they fall between two whole numbers, and comparing them to decimals or fractions. Students often get stuck thinking every decimal is rational, or that a long decimal must be exact.
Ways to teach it
- Hands-on activity: Give students square tiles and grid paper to build squares, then estimate side lengths for areas like 2, 5, and 10.
- Discussion prompt: Ask, “Can every decimal be written as a fraction?” and have students defend their answer using examples and nonexamples.
- Quick assessment: Ask students to place √3, √9, π, 1.7, and 5/3 on a number line and justify two placements.
- Real-world connection: Use a diagonal path across a rectangular park map and have students estimate its length with the Pythagorean theorem.
Plan a lesson for CCSS.Math.Content.8.NS.A
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Related standards
- CCSS.Math.Content.HSN-RN.B
Use properties of rational and irrational numbers.
- CCSS.Math.Content.8.NS.A.2
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate th...
- CCSS.Math.Content.8.NS.A.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that t...
- CCSS.Math.Content.6.NS.C
Apply and extend previous understandings of numbers to the system of rational numbers.