Montana Math MT.6.NS.7
The Standard
Understand ordering and absolute value of rational numbers by: Interpreting statements of inequality as statements about the relative position of two numbers on a number line diagram, Writing, interpreting, and explaining statements of order for rational numbers in problems in context, Understanding the absolute value of a rational number as its distance from 0 on the number line and interpreting absolute value as magnitude for a positive or negative quantity in problems in context, and Distinguishing comparisons of absolute value from statements about order.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students place positive and negative fractions and decimals on a number line and compare them. They explain what those comparisons mean for temperatures, balances, or other quantities. They use absolute value to show distance from 0, which is different from deciding which number is greater.
What Mastery Looks Like
- A student can place −2.5 to the left of 1.5 and explain why −2.5 < 1.5. They can also explain why |−2.5| > |1.5|, even though −2.5 is the smaller number.
Common Misconceptions
- Students may think −8 is greater than −3 because 8 is greater than 3. Some treat the absolute value of a negative number as negative. Others assume the number farther from 0 must be greater.
How to Assess It
- Exit ticket: The temperatures are −2.5°C and 1.5°C. Plot both, write and explain an inequality comparing them, then compare their absolute values and explain what those values mean.
Lesson moves
Ways to Teach It
Tape a number line to the floor; place cards for −1.5, −0.5, 0, and 1, then measure each card's distance from 0.
Ask students to write why −2.5°C is colder than 1.5°C but farther from 0°C.
Give pairs cards marked −3/4, −1/2, 1/4, and 3/4; have them rank the cards by value, then by distance from 0.
Plot bank balances of −$12 and $5; compare which balance is greater and which is farther from $0.
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