Wyoming Math 8.NS.1a
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. Make comparisons between 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 tell rational and irrational numbers apart using fractions, roots, and decimal patterns. They turn repeating decimals into fractions and use decimal estimates to compare numbers on a number line.
What Mastery Looks Like
- A student converts 0.272727... to 3/11 and places √2 between 1.4 and 1.5. They explain that 1.41 is rational but √2 is not.
Common Misconceptions
- Students may call any long decimal irrational, including 0.333.... Some treat 1.41 as the exact value of √2 or assume every square root is irrational.
How to Assess It
- Exit ticket: Classify 0.272727... and √2, convert 0.272727... to a fraction, and place √2 between two tenths on a number line.
Lesson moves
Ways to Teach It
Have pairs draw a 10 cm square on grid paper, measure its diagonal, and mark the length on a number line.
Ask students to write whether 1.414 m is the exact diagonal of a 1 m square table, and explain why.
Play a sorting relay with cards labeled 3/8, 0.333..., √9, √2, and π; teams sort them and defend one choice.
Give students a 30 cm square tile diagram and ask for the diagonal strip length, rounded to the nearest millimeter.
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Printable 8.NS.1a Worksheet
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Related Standards
- 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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