CCSS.Math.Content.8.EE.A.3
The standard
Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.
Common Core State Standards for Mathematics · Expressions and Equations
What this standard means
Students need to write very large and very small numbers as a single digit times a power of 10, then use those forms to make estimates. They should compare two quantities by dividing the front numbers and powers of 10, not by counting zeros.
Mastery looks like saying 6 x 10^7 is about 20 times larger than 3 x 10^6, and explaining why. Students often mix up positive and negative powers, treat 10^8 as 8 zeros without checking size, or subtract exponents when they should compare by division.
Ways to teach it
- Give pairs population, distance, and cell-size cards, then have them sort each into scientific notation and order them from least to greatest.
- Ask students to explain which is larger, 4 x 10^9 or 7 x 10^8, and how many times larger it is.
- Use a three-question exit ticket: rewrite 52,000,000, rewrite 0.00063, and compare 8 x 10^5 to 2 x 10^3.
- Have students compare real data, such as Earth’s mass and the Moon’s mass, using scientific notation and a times-as-much statement.
Plan a lesson for CCSS.Math.Content.8.EE.A.3
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Related standards
- CCSS.Math.Content.4.NBT.A.1
Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right.
- CCSS.Math.Content.5.NBT.A.2
Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point whe...
- CCSS.Math.Content.5.NBT.A.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represen...
- CCSS.Math.Content.3.NBT.A.3
Multiply one-digit whole numbers by multiples of 10 in the range 10—90 (e.g., 9 × 80, 5 × 60) using strategies based on place value and properties of operations...