Montana Math MT.6.NS.6
The Standard
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 indicating locations on opposite sides of 0 on the number line, recognizing that the opposite of the opposite of a number is the number itself, and that 0 is its own opposite. Understanding signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane and recognizing that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes, and Finding and positioning integers and other rational numbers on a horizontal or vertical number line diagram and finding and positioning pairs of integers and other rational numbers on a coordinate plane.
2026 Montana Mathematics Content Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students place positive and negative integers, fractions, and decimals on horizontal and vertical number lines. They plot ordered pairs in all four quadrants and use signs to describe opposites and reflections.
What Mastery Looks Like
- Students place −1.5 and 1.5 the same distance from 0 on opposite sides. They explain that changing a sign twice returns the starting number and that 0 is its own opposite. They plot (−2, 3) and its reflections across each axis.
Common Misconceptions
- Students may put −3 to the right of −1 because 3 is larger than 1. Some swap x and y when plotting, or change both signs when reflecting across one axis. Others think 0 has a different opposite.
How to Assess It
- Exit ticket: Mark −1.5 and 1.5 on a vertical number line, then plot (−2, 3) and its reflection across each axis. Write the opposite of the opposite of −1.5 and the opposite of 0.
Lesson moves
Ways to Teach It
Tape a vertical number line to the wall, then have students place cards labeled −1.5, −1/2, 0, 1/2, and 1.5.
Have partners sketch (−2, 3) and discuss why reflecting it across the y-axis changes only the first sign.
Play coordinate bingo with quadrant grids: call points such as (−1/2, 2) and have students mark their positions.
On a street grid centered on school, plot a store two blocks west and three blocks north, then write its coordinates.
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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.7.NS.1
Add and subtract rational numbers, represent addition and subtraction on a horizontal or vertical number line diagram, and understand subtraction as adding the ...
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