8.NR.2Exponents and Scientific Notation

Expectations

• 8.NR.2.1

  Apply the properties of integer exponents to generate equivalent numerical expressions.

• 8.NR.2.2

  Use square root and cube root symbols to represent solutions to equations. Recognize that $x^2 = p$ (where p is a positive rational number and |x| ≤ 25) has two solutions and $x^3 = p$ (where p is a negative or positive rational number and |x| ≤ 10) has one solution. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ -1000 and ≤ 1000.

• 8.NR.2.3

  Use numbers expressed in scientific notation to estimate very large or very small quantities, and to express how many times as much one is than the other.

• 8.NR.2.4

  Add, subtract, multiply and divide numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Interpret scientific notation that has been generated by technology (e.g., calculators or online technology tools).

Georgia Milestones coverage

• Mathematics Grade 8 (EOG) · Numerical Reasoning

  Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.

  about 19% of the test · 11 points These points are shared with other standards, so count them once and never add them up per standard.

What mastery looks like

Georgia's Achievement Level Descriptors. The levels are cumulative: each includes the ones before it. Proficient is on grade level.

Beginning

Using only positive exponents, apply one property of exponents to identify equivalent expressions. Represent whole-number multiples of 10 in scientific notation. Interpret scientific notation.

Developing

Apply one property of exponents to generate equivalent numerical expressions. Evaluate square roots of perfect squares ≤ 625 and cube roots of perfect cubes ≥ −1,000 and ≤ 1,000. Use square root and cube root symbols to represent solutions to equations in the form x² = p and x³ = p, where p is a perfect square or perfect cube. Use scientific notation to estimate both very large and very small quantities. Add, subtract, multiply, or divide numbers expressed in scientific notation.

Proficient

Apply more than one property of exponents to generate equivalent numerical expressions. Use square root and cube root symbols to represent positive and negative solutions to equations in the form x² = p and x³ = p, where p is a positive rational number. Compare two numbers written in scientific notation in a real-life context to determine how much times one number is the other number. Solve relevant mathematical problems involving addition, subtraction, multiplication, or division of numbers expressed in scientific notation.

Distinguished

Determine whether multiple expressions both with and without exponents are equivalent. Solve realistic problems involving addition, subtraction, multiplication, or division of numbers expressed in both scientific notation and decimal notation.

The same standard across grades

1. Kindergarten · K.NR.2

   Use count sequences within 100 to count forward and backward in sequence.

2. Grade 1 · 1.NR.2

   Explain the relationship between addition and subtraction and apply the properties of operations to solve real-life addition and subtraction problems within 20.

3. Grade 2 · 2.NR.2

   Apply multiple part-whole strategies, properties of operations and place value understanding to solve real-life, mathematical problems involving addition and subtraction within 1,000.

4. Grade 4 · 4.NR.2

   Using part-whole strategies, solve problems involving addition and subtraction through the hundred-thousands place, as well as multiplication and division of multi-digit whole numbers presented in real-life, mathematical situations.

5. Grade 5 · 5.NR.2

   Multiply and divide multi-digit whole numbers to solve relevant, mathematical problems.

6. Grade 6 · 6.NR.2

   Apply operations with whole numbers, fractions and decimals within relevant applications.

7. Grade 8 · 8.NR.2 (this standard)

   Solve problems involving radicals and integer exponents including relevant application situations; apply place value understanding with scientific notation and use scientific notation to explain real phenomena.