Montana Math MT.CORE.NUM.REAL.3
The Standard
Define, manipulate, interpret, and compare real numbers presented through different representations, including both rational and irrational numbers, and apply comparisons in context. This standard should incorporate cultural context relating to Montana Indigenous Peoples and local communities.
2026 Montana Mathematics Content Standards · Numeric Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students compare numbers written as fractions, decimals, and square roots. They identify rational and irrational numbers, use estimates when needed, and explain what a comparison means in a real situation.
What Mastery Looks Like
- A student orders 5/4, 1.3, and √2 by using 1.25 and an estimate of 1.414. They can explain why √2 is greater than 1.3 without treating the estimate as exact.
Common Misconceptions
- Students may call every decimal irrational, including the repeating decimal 0.333.... They may assume √9 is irrational because it has a radical sign, or treat 1.4 as equal to √2.
How to Assess It
- Exit ticket: Order 5/4, 1.3, and √2 from least to greatest, label each rational or irrational, and decide whether a 1.3-mile route is shorter than a √2-mile route.
Lesson moves
Ways to Teach It
Give pairs fraction strips, square grids, and a number line; have them place 5/4, 1.3, and √2 and explain each placement.
Ask: “Does writing √2 as 1.414 make it rational?” Have students explain the difference between the number and its estimate.
Give groups cards showing 0.75, 3/4, √2, 1.4, and 3/2; award a point for each correctly justified comparison.
Use an online map to measure two routes near Salish Kootenai College, a tribal college in Pablo; compare their lengths as decimals and fractions.
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Printable MT.CORE.NUM.REAL.3 Worksheet
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