Georgia 8.NR.1

8.NR.1 is a Georgia mathematics standard. These are the expectations under it.

• 8.NR.1.1

  Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.

• 8.NR.1.2

  Approximate irrational numbers to compare the size of irrational numbers, locate them approximately on a number line, and estimate the value of expressions.

01

What Students Need to Do

Students use rational decimals or fractions to approximate values such as square roots and π in realistic problems. They calculate, choose sensible precision, and explain what the approximate answer means.

02

What Mastery Looks Like

A student can bound an irrational number between two rational values, then use a suitable approximation in a multistep problem. The student labels units, rounds reasonably, and distinguishes an exact expression from an estimate.

03

Common Misconceptions

Students may treat a rounded decimal as exactly equal to an irrational number. They may assume every nonterminating decimal is irrational or round too early during calculations. Some confuse a calculator display with the complete decimal value.

04

How to Assess It

Exit ticket: A circular table has a diameter of 1.2 meters. Write its exact circumference using π, estimate using 3.14, and label each answer exact or approximate.

1. 01

   Measure the circumference and diameter of three round objects with string, calculate each ratio, and compare the results with 3.14.

2. 02

   Write a response to: Why can a calculator show only an approximation of √2, and when would that approximation be useful?

3. 03

   Play a matching game pairing √2, √10, and π with decimal approximations, number-line intervals, and contextual measurements.

4. 04

   Use a classroom floor plan to estimate the diagonal distance, then decide what tape-measure precision is reasonable for ordering cable.

• 6.NR.3

  Solve a variety of problems involving whole numbers and their opposites; model rational numbers on a number line to describe problems presented in relevant, mat...

• 7.NR.1.6

  Make sense of multiplication of rational numbers using realistic applications.

• 7.NR.1

  Solve relevant, mathematical problems, including multi-step problems, involving the four operations with rational numbers and quantities in any form (integers, ...