Mr. S Teaches
Sign inRequest Tutoring
Menu
Sign inRequest Tutoring

Grade 6 · Mathematics · 30 minutes

Unit 1 · Number relationships and rates · Lesson 3 of 3

Rational Numbers Above and Below Zero

Use signed coordinates and absolute value to interpret elevation.

Mr. S Teaches · Original starter mini-lesson · MS6-MATH-03

Learning objective

Order four rational numbers and distinguish a number’s value from its distance to zero.

Before you begin

  • Fractions and decimal equivalents
  • Number lines

Gather your materials

  • Paper and pencil
  • Ruler and graph paper

Language to know

rational number
A number expressible as a fraction of integers with a nonzero denominator.
opposite
A number equally far from zero in the other direction.
absolute value
A number’s distance from zero.

Understand the concept

Zero is a reference point, such as sea level. Positive and negative numbers describe opposite directions from it. A number farther right on a horizontal line is greater, even when it has a smaller absolute value. Absolute value answers a distance question and is never negative; it is not a replacement for the original signed value.

Teach it step by step

  1. Draw a horizontal line from −5 to 5 and label zero as sea level.
  2. Place a point at −2.5 meters and its opposite at 2.5 meters. Count equal intervals on both sides.
  3. Add points at −3/2 and 1/2; convert them to decimals to compare positions.
  4. Compare −2.5 and −1.5 using an inequality, then compare their absolute values separately.
  5. Ask a learner to describe what zero, a sign and an absolute value mean in this elevation model.

Make the thinking visible

Worked example or model response

−3/2 = −1.5. In increasing order the elevations are −2.5, −1.5, 0.5 and 2.5 meters. Although −2.5 < −1.5, |−2.5| = 2.5 > 1.5 = |−1.5|.

Guided practice

Place −4, −0.75, 0 and 1.25 on a number line. Circle the point farthest from zero and identify the opposite of −0.75.

Independent practice

1. Order −1/4, −0.8 and 0.1. 2. A diver is at −6 meters and a platform is at +4 meters. Which location has the greater elevation? Which is farther from sea level?

Quick assessment

A learner says −9 is greater than −2 because 9 is greater than 2. Explain the error with a number line.

Answer key & assessment criteria

Answers and teaching guidance

  1. Guided: −4 is farthest from zero; the opposite of −0.75 is 0.75.
  2. Independent 1: −0.8 < −1/4 < 0.1. 2: The platform is higher, but the diver is farther from sea level.
  3. Quick check: −9 lies left of −2, so −9 < −2. Comparing unsigned distances confuses absolute value with number order.

Look for: Look for an explanation of the choices, not only a final answer. Require units and a check against the context.

Make it work for your learner

More support

Use a vertical thermometer and mark half-unit increments before using quarters.

Extension challenge

Find two signed elevations with equal absolute value and two unequal absolute values whose elevations have the reverse order.

Selected contributions · Official sources

Standards connections

Contributes to Common Core standard

6.NS.C.7.a

Common Core · Grade 6

Interpret inequalities by the positions of rational numbers on a number line.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.

Contributes to Common Core standard

6.NS.C.7.c

Common Core · Grade 6

Interpret absolute value as distance from zero in a real context.

Read the official standard ↗

This lesson contributes selected skills; it does not fully address the standard.

Source and mapping checked 2026-11-04. This mini-lesson contributes selected skills; it does not claim full attainment.