Wyoming Math 8.NS.1

Math8th GradeThe Number System

Standard Cluster

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. Understand that all real numbers have a decimal expansion. Model the hierarchy of the real number system, including natural, whole, integer, rational, and irrational numbers. Convert repeating decimals to fractions.

2023 Wyoming Mathematics Content and Performance Standards · Know that there are numbers that are not rational, and approximate them by rational numbers.

Cluster contents

Standards in This Cluster

8.NS.1 is a cluster heading. These are the individual standards under it.

Teacher's field guide

What This Cluster Means

What Students Need to Do: Students sort numbers into natural, whole, integer, rational, and irrational groups. They recognize that every real number has a decimal expansion, and that rational decimals terminate or eventually repeat. They turn repeating decimals into fractions and use rational estimates to compare irrational numbers.
What Mastery Looks Like: A student can place 4 in the natural, whole, integer, and rational groups, and √2 in the irrational group. They can write 0.1666... as 1/6, even though the repeating digits do not start right away. They can use 1.4² and 1.5² to show that √2 lies between 1.4 and 1.5.
Common Misconceptions: Students may call a negative number irrational just because it is negative. They may think 0.1666... is irrational because it does not repeat right away. They may mistake a calculator's short display of √2 for a terminating decimal.
How to Assess It: Exit ticket: Place -3, 4, 0.1666..., and √2 in all groups that apply: natural, whole, integer, rational, or irrational. Convert 0.1666... to a fraction, then use squares to show whether √2 lies between 1.4 and 1.5.

Lesson moves

Ways to Teach It

Give pairs nested circles labeled real, rational, integer, whole, and natural; have them place cards showing 4, 0, -3, 1/6, and √2.
Ask: Why is 0.1666... rational even though it never ends? Have students write its fraction and explain the repeating 6.
Play a matching game with cards showing 1/3, 1/6, 2/9, 0.333..., 0.1666..., and 0.222...
Sketch a square garden with area 2 square meters; compare 1.4 and 1.5 meters as estimates of its side.

Free download