Wyoming Math 8.NS.1c
The Standard
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Explore the real number system and its appropriate usage in real-world situations. Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers.
2023 Wyoming Mathematics Content and Performance Standards · Know that there are numbers that are not rational, and approximate them by rational numbers.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students sort numbers into counting, whole, integer, rational, and irrational groups. They recognize that terminating and eventually repeating decimals are rational, and convert repeating decimals to fractions. They use decimal estimates when measuring irrational lengths.
What Mastery Looks Like
- A student can place 0, -3, 3/4, and √2 in the smallest fitting groups on a number-set diagram. They can show that 0.1666... equals 1/6 and explain why its endless digits do not make it irrational.
Common Misconceptions
- Students may think any decimal that goes on forever is irrational, so they mislabel 0.1666.... They may call -3 irrational because it is negative. They may also miss that a terminating decimal can continue with repeating zeros.
How to Assess It
- On an exit ticket, ask students to convert 0.1666... to a fraction and place 0, -3, 0.1666..., and √2 in their smallest fitting number sets.
Lesson moves
Ways to Teach It
Sort cards labeled 1, 0, -3, 0.75, and √2 into paper loops for counting, whole, integer, rational, irrational, and real numbers.
Write why 0.1666... belongs with fractions even though its digits never end, using 1/6 in the explanation.
Play a matching game with cards 0.333..., 0.1666..., 0.272727..., 1/3, 1/6, and 3/11; require a written conversion for each match.
Sketch a square room with 1-meter sides, find its diagonal as √2 meters, and decide whether a 1.4-meter rod reaches corner to corner.
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Printable 8.NS.1c Worksheet
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Related Standards
- 8.NS.1a
Make comparisons between rational and irrational numbers.
- 7.NS.3
Solve real-world and mathematical problems involving the four arithmetic operations with rational numbers. (Computations with rational numbers extend the rules ...
- 8.NS.1
Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that t...
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