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B1.2 · Represent integers on horizontal and vertical number lines

Learn to represent integers on horizontal and vertical number lines through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Number

Zero separates positive and negative numbers

Integers are whole numbers, zero, and their negative opposites. We use them for positions above and below a reference level, such as a building floor or a temperature relative to zero. A number line makes each position visible. The marks must be equally spaced: the distance from −4 to −3 is one unit, just like the distance from 2 to 3. The example below is a mathematical model, not a measured temperature record.

What you will learn

  • Locate positive and negative integers.
  • Read movement to the right or left.
  • Check a position by counting equal intervals.

Read the line

Zero is the reference point. Numbers to its right are positive; numbers to its left are negative. The greater of two integers appears farther right. Thus −2 is greater than −5, even though 5 is a larger counting number than 2.

Count intervals, not marks

To move from −4 six units right, make six one-unit jumps: −3, −2, −1, 0, 1, 2. Landing at zero is the fourth jump, not the final destination. A vertical number line works in the same way except positive values go upward.

Check the displacement

Subtract the starting position from the ending position: 2 − (−4) = 6. This verifies a movement of six units to the right. Label any real-world unit separately; a plain number line is just a position model.

Worked example

Six steps right from minus four

Start at −4 on an integer number line and move six equal steps to the right. Where do you land?
Movement from −4 to 2
Movement from −4 to 2The orange point is −4, the teal point is 2, and their separation is six equally spaced units.-6-5-4-3-2-101234+6 steps

The orange point is −4, the teal point is 2, and their separation is six equally spaced units.

  1. Find the start
    Mark −4, four units to the left of zero.
  2. Move right
    Count six intervals: −3, −2, −1, 0, 1, 2.
  3. Verify
    The difference between 2 and −4 is 6.
Answer: You land at 2.
Check: −4 + 6 = 2.

Common mistakes and how to avoid them

Counting −4 as the first step.
Correction: The first step ends at −3. Count spaces between positions, not the starting mark.

Lesson summary

  • Integers include negatives, zero, and positives.
  • Each equal interval is one unit.
  • Moving right increases the value.

Check your understanding

Question 1

From −2, move five steps to the right. Where do you land?
  1. 3
  2. −7
  3. 2
  4. 5
Show answer and explanation
3
−2 + 5 = 3; count −1, 0, 1, 2, 3.

Key terms

Integer
A whole number, zero, or a negative whole number.
Origin
The zero reference point on a number line.

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Published by DoAssignment. This reviewed lesson follows Ontario Grade 6 Mathematics, expectation B1.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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