8.NR.1Irrational Numbers Overview

Expectations

• 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.

Georgia Milestones coverage

• Mathematics Grade 8 (EOG) · Numerical Reasoning

  Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.

  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

Recognize irrational numbers as a category distinct from rational numbers. Identify whole-number values between which an irrational number belongs.

Developing

Classify real numbers as rational or irrational. Approximate irrational numbers by estimating or locating them on a number line.

Proficient

Convert a decimal expansion that repeats into a rational number. Compare an irrational number to another number (rational or irrational) by using a benchmark or number line. Estimate the values of expressions that contain both rational and irrational numbers.

Distinguished

Solve realistic problems involving rational approximations of irrational numbers, including using estimation.

The same standard across grades

1. Kindergarten · K.NR.1

   Demonstrate and explain the relationship between numbers and quantities up to 20; connect counting to cardinality (the last number counted represents the total quantity in a set).

2. Grade 1 · 1.NR.1

   Extend the count sequence to 120. Read, write, and represent numerical values to 120 and compare numerical values to 100.

3. Grade 2 · 2.NR.1

   Using the place value structure, explore the count sequences to represent, read, write, and compare numerical values to 1000 and describe basic place-value relationships and structures.

4. Grade 3 · 3.NR.1

   Use place value reasoning to represent, read, write, and compare numerical values up to 10,000 and round whole numbers up to 1,000.

5. Grade 4 · 4.NR.1

   Recognize patterns within the base ten place value system with quantities presented in real-life situations to compare and round multi-digit whole numbers through the hundred-thousands place and compare decimal numbers to the hundredths place.

6. Grade 5 · 5.NR.1

   Use place value understanding to solve real-life, mathematical problems.

7. Grade 6 · 6.NR.1

   Solve relevant, mathematical problems involving operations with whole numbers, fractions, and decimal numbers.

8. Grade 7 · 7.NR.1

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

9. Grade 8 · 8.NR.1 (this standard)

   Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.