Georgia 8.NR.1.1
The Standard
Distinguish between rational and irrational numbers using decimal expansion. Convert a decimal expansion which repeats eventually into a rational number.
Georgia's K-12 Mathematics Standards · Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students examine decimal expansions and decide whether the numbers are rational or irrational. They convert decimals with repeating digit patterns, including delayed repeats, into fractions using place value and subtraction.
What Mastery Looks Like
- Students correctly classify terminating and eventually repeating decimals as rational, and nonterminating, nonrepeating decimals as irrational. They use place-value shifts and subtraction to convert an eventually repeating decimal into a simplified fraction.
Common Misconceptions
- Students may think every nonterminating decimal is irrational, overlooking repeating decimals. They may also subtract the wrong place values when converting a decimal with nonrepeating digits before the repeating block.
How to Assess It
- Classify 0.125, 0.272727..., and 0.1010010001... as rational or irrational. Then convert 0.1666... to a fraction and show each algebra step.
Lesson moves
Ways to Teach It
Sort cards showing terminating, eventually repeating, and nonrepeating decimals, then match each rational decimal to a fraction card.
Write a response to: How does a decimal’s digit pattern tell you whether it can be written as a fraction?
Play Decimal Detective: teams classify projected decimals, earning a bonus point by converting each repeating decimal to a fraction.
Measure circular objects, calculate circumference divided by diameter, and discuss why each measured value only approximates pi.
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Printable 8.NR.1.1 Worksheet
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Related Standards
- 7.NR.1.7
Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is 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.
- 7.NR.1.10
Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that th...
- 8.NR.1
Solve problems involving irrational numbers and rational approximations of irrational numbers to explain realistic applications.
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