NY Next Generation Math NY-8.NS.2
The Standard
Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students replace irrational numbers with nearby rational decimals. They use those approximations to compare irrational values, place them on a number line, and estimate expressions.
What Mastery Looks Like
- A student bounds √10 between 3.1 and 3.2 by comparing their squares, then places it near 3.16. The student uses that approximation to estimate 2 + √10 near 5.16.
Common Misconceptions
- Students may treat a square-root symbol as division or place √10 at 5 because 5 is half of 10. They may also round too early and reverse a comparison between close values.
How to Assess It
- Ask students to approximate √7 to the nearest tenth, place it on a number line, and estimate 1 + √7. Require rational bounds that support the approximation.
Lesson moves
Ways to Teach It
Mark decimal tenths on a floor number line, then place radical cards between rational bounds supported by nearby squares.
Ask students how 2.6² and 2.7² help locate √7 without a square-root key.
Play closest bound by drawing an irrational-number card and choosing the tightest valid pair of rational approximations.
Estimate a square patio’s diagonal with the Pythagorean Theorem, then choose a practical decimal length for materials.
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