Maryland Math 8.NOS.B.5

8.NOS.B.5 is a cluster heading. These are the individual standards under it.

• 8.NOS.B.5.a

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

• 8.NOS.B.5.b

  Use scientific notation to model and compute with real-world quantities, choose appropriate units, and interpret their meaning based on the context.

01

What Students Need to Do

Students write very large and very small measurements in scientific notation. They round to one nonzero digit times a power of ten to estimate and compare sizes. They use a calculator to compute, choose useful units, and explain what their answers mean.

02

What Mastery Looks Like

They write 0.0000045 as 4.5 × 10^-6 and explain why it is less than 3 × 10^-5. They use a calculator to find the mass of 2 × 10^5 cells at 3 × 10^-6 grams per cell. They report 0.6 grams and explain why grams suit the result.

03

Common Misconceptions

Students may think 10^-6 is larger than 10^-5 because 6 is larger than 5. They may move the decimal the wrong way or leave 45 × 10^-7 as finished scientific notation. They may compare grams with kilograms without converting either value.

04

How to Assess It

Exit ticket: A sample has 2 × 10^6 cells, each with a mass of 3 × 10^-9 grams. Use a calculator to write the total mass in grams in scientific notation, compare it with 1 × 10^-2 grams, and convert it to milligrams.

1. 01

   Give pairs digit cards and a place-value chart; have them build 4,500,000 and 0.0000045, then write each in scientific notation.

2. 02

   Ask pairs which is larger, 6 × 10^-7 meters or 2 × 10^-6 meters, and have them defend their answer using powers of ten.

3. 03

   Have pairs race to match cards labeled 0.000008, 8 × 10^-6, eight millionths, 5,000,000, 5 × 10^6, and five million.

4. 04

   Give students a medicine dose of 2 × 10^-6 kilograms; have them convert it to milligrams and explain which unit fits a label.

• 6.AT.B.5

  Write numerical expressions involving whole number exponents and positive rational number bases. Use technology to evaluate numerical expressions involving whol...