Maryland Math 8.NOS.B.5.a

Math8th GradeNumber and Operation Sense

The Standard

8.NOS.B.5: Apply scientific notation to represent and compare very large and very small quantities in context, and use technology to compute with numbers in scientific notation.

Express numbers as a single digit times an integer power of 10 to estimate and compare magnitudes.

Maryland College and Career Ready Standards for Mathematics (2025) · REASON WITH EXPONENTS TO EXPRESS AND INTERPRET QUANTITIES.

Teacher's field guide

What Students Need to Do: Students round numbers to one nonzero digit and write each estimate as that digit times a power of 10. They use the estimates to compare large numbers and numbers smaller than one.
What Mastery Looks Like: A student estimates 0.0048 as 5 × 10^-3 and 0.00062 as 6 × 10^-4. They can explain why the first is about eight times as large.
Common Misconceptions: Students may think a negative exponent makes the number negative. Some reverse the order of 10^-3 and 10^-4, or write 43 × 10^5 instead of using a single digit.
How to Assess It: Exit ticket: Estimate 0.0072 and 0.00093 as a single digit times a power of 10. Circle the larger number and estimate how many times larger it is.

Lesson moves

Give pairs decimal number cards to place on a tape number line marked with powers of 10.
Ask students to explain in writing why 6 × 10^-3 is about eight times 8 × 10^-4.
Play estimate match: students flip decimal cards and power-of-10 cards, then keep pairs that agree to one nonzero digit.
Compare a city population of 3,000,000 with a stadium capacity of 40,000, and estimate how many stadiums would hold the city.

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