8.2.B
The Standard
approximate the value of an irrational number, including π and square roots of numbers less than 225, and locate that rational number approximation on a number line
Texas Essential Knowledge and Skills for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use nearby perfect squares or known decimal values to estimate irrational numbers. They round each estimate to a requested place and place it correctly between labeled values on a number line.
What Mastery Looks Like
- A student can explain why √70 lies between 8 and 9, estimate it as about 8.4, and plot that value accurately. The student treats 3.14 as an approximation of π, not an exact value.
Common Misconceptions
- Students may treat √70 as 35 or assume it sits halfway between √64 and √81. They may write π = 3.14 as an exact equality. They may also ignore the scale when plotting decimal estimates.
How to Assess It
- Exit ticket: Without a calculator, estimate √70 to the nearest tenth, explain your bounds using perfect squares, and mark the estimate on a number line from 8 to 9.
Lesson moves
Ways to Teach It
Use square tiles to build largest squares below 50, 80, and 130, then estimate each root and place cards on a floor number line.
Ask, “Which is closer to √50, 7.0 or 7.1?” Have students defend their answer by squaring both decimals.
Play Estimate and Place: teams draw an irrational-number card, choose a decimal estimate, and earn points for correct order on a shared line.
Measure a circular lid, use 3.14 and 3.1416 to estimate its circumference, then compare both results with a string measurement.
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Printable 8.2.B Worksheet
A ready-to-print activity worksheet aligned to 8.2.B, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Related Standards
- 2.2.E
locate the position of a given whole number on an open number line
- 2.9.C
represent whole numbers as distances from any given location on a number line
- 3.7.A
represent fractions of halves, fourths, and eighths as distances from zero on a number line
- 6.2.C
locate, compare, and order integers and rational numbers using a number line
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