8.2.C

Math8th Grade

The Standard

convert between standard decimal notation and scientific notation

Texas Essential Knowledge and Skills for Mathematics

Teacher's field guide

What Students Need to Do: Students rewrite very large and very small decimals using a number from 1 up to, but not including, 10 multiplied by a power of 10. They also expand scientific notation into decimal form by moving the decimal according to the exponent.
What Mastery Looks Like: Students correctly write 0.00072 as 7.2 × 10^-4 and 6.3 × 10^5 as 630,000. They use a coefficient from 1 up to, but not including, 10 and choose the correct exponent sign.
Common Misconceptions: Students often move the decimal correctly but give the exponent the wrong sign. They may also write a coefficient greater than or equal to 10, or drop needed zeros when returning to decimal form.
How to Assess It: Use an exit ticket with two items: rewrite 0.000072 in scientific notation and rewrite 3.8 × 10^6 in decimal notation. Ask students to show each decimal shift.

Lesson moves

Give students digit cards and a place-value chart to build 0.00056, then shift the decimal and record 5.6 × 10^-4.
Ask students to explain why 4.2 × 10^-3 is smaller than 4.2 × 10^3, using decimal forms as evidence.
Play a matching relay where teams pair decimal cards with scientific notation cards and correct any mismatched coefficients or exponents.
Compare distances between planets and sizes of bacteria, then have students rewrite each measurement in both decimal and scientific notation.

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