Maryland Math 8.NOS.A.2
The Standard
Use rational approximations of irrational numbers to estimate their locations on a number line, compare their size, and apply this understanding to estimate the value of expressions (e.g., π²) in context.
Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH IRRATIONAL NUMBERS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students estimate numbers such as π and √10 with decimals. They use those estimates to place the numbers on a number line, compare them, and calculate values such as π².
What Mastery Looks Like
- A student places π near 3.14 and √10 near 3.16, then explains why √10 is larger. They estimate the area of a square with side π cm as about 9.9 square centimeters.
Common Misconceptions
- Students may treat 3.14 as exactly π or round √10 to 3 before comparing it with π. Some mistake π² for 2π.
How to Assess It
- On an exit ticket, ask students to place π and √10 on a number line from 3.10 to 3.20 and circle the larger number. Then ask them to estimate the area of a square with side π cm to the nearest tenth.
Lesson moves
Ways to Teach It
Tape a number line from 3.10 to 3.20 on a desk, then have students place π and √10 cards at about 3.14 and 3.16.
Ask students to write which is greater, π or √10, and explain their choice using decimal estimates.
Hand out π, √10, √11, and 3.2 cards; pairs race to order them and defend each placement.
Tell students a square tile has sides of π cm, then have them estimate its area to the nearest tenth of a square centimeter.
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Printable 8.NOS.A.2 Worksheet
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Related Standards
- 4.NOS.A.1.b
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and rounding to any place.
- 2.NOS.A.5
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers (e.g. 10, 50, 100), and to assess reasonableness...
- 6.NOS.C.6.a
Estimate quantities by reasoning about their location on a number line, their relationship to benchmark numbers, and by rounding.
- 6.NOS.C.6.b
Locate and interpret the positions of rational numbers on a number line.
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