CCSS.Math.Content.8.NS.A.2
The standard
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., π²).
Common Core State Standards for Mathematics · The Number System
What this standard means
Students need to use decimals and fractions they know to pin down irrational numbers. They should compare values like square roots and pi, place them on a number line, and estimate expressions without a calculator doing all the thinking.
Mastery looks like a student saying, “√18 is between 4 and 5, closer to 4, because 4.2² is 17.64 and 4.3² is 18.49.” Common trouble spots are treating square roots as simple division, rounding too early, and not checking estimates by squaring or comparing benchmarks.
Ways to teach it
- Have students place cards like √2, √7, √20, and π on a taped number line using benchmark squares and decimal checks.
- Ask students to write: How can you prove √50 is between 7 and 8, then narrow it to the nearest tenth?
- Give an exit ticket with three values, √13, 3.6, and π, and ask students to order them with one reason.
- Use tape measures to estimate the diagonal of a square tile, then compare the measurement to a decimal approximation of its square root.
Plan a lesson for CCSS.Math.Content.8.NS.A.2
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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.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.