Montana Math MT.8.NS.1
The Standard
Know real numbers are made up of rational and irrational numbers, understand informally that every number has a decimal expansion, and convert a decimal expansion which repeats eventually into a rational number.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students tell which numbers are rational and which are irrational. They write numbers as decimals and turn decimals with repeating tails into fractions.
What Mastery Looks Like
- A student can explain why 0.75 and 0.2333... are rational, while √2 is irrational. They can write 0.2333... as 7/30 and show how they got it.
Common Misconceptions
- Students may call every long decimal irrational, even when its digits repeat. They may write 23/99 for 0.2333..., treating the first 2 as part of the repeating block.
How to Assess It
- Exit ticket: Classify √2 and 0.2333... as rational or irrational. Write 0.2333... as a fraction and show your work.
Lesson moves
Ways to Teach It
Give pairs cards marked 0.75, 0.333..., √2, and π; have them sort the cards and explain each placement.
Ask, “Is 0.333... equal to 1/3, or just close to it?” Have students defend an answer using division.
Play fraction match with 0.333..., 0.1666..., and 0.1222... and cards marked 1/3, 1/6, and 11/90.
Show a tape measure reading 1/3 inch; students write its decimal and explain why 0.33 inch is not exact.
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Printable MT.8.NS.1 Worksheet
A ready-to-print activity worksheet aligned to MT.8.NS.1, with an answer key for the teacher on its own page. No account needed.
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Related Standards
- MT.6.NS.7
Understand ordering and absolute value of rational numbers by: Interpreting statements of inequality as statements about the relative position of two numbers on...
- MT.6.NS.6
Understand a rational number as a point on the number line and extend number line diagrams and coordinate axes by: Recognizing opposite signs of numbers as indi...
- MT.7.NS.3
Write any rational number as a fraction, decimal, and percent using long division, and know that the decimal form of a rational number terminates or repeats.
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