Integers: Positive, Negative, and the Number Line
A 45-minute math lesson that builds integer addition and subtraction on the number line rather than on memorized sign rules, including the move students find hardest: subtracting a negative.
Math
Subject
Grades 6-8
Grade Level
45 minutes
Duration
Integers
Topic
On this page: Materials · Warm-Up · Direct Instruction · Guided Practice · Independent Practice · Assessment · Closure · Related Resources
Learning Objectives
By the end of this lesson, students will be able to:
- Locate positive and negative integers on a number line
- Compare and order integers, including two negatives
- Explain absolute value as distance from zero
- Add and subtract integers by modeling the movement on a number line
- Explain why subtracting a negative moves to the right
Materials
- Adding and Subtracting Integers Worksheet — one copy per student
- Negative Numbers on a Number Line Worksheet, for support or as a warm-up
- Comparing and Ordering Integers Worksheet, for the ordering practice
- A long number line across the board or a wall, marked from -10 to 10
- Individual number-line strips, one per student, same range
Vocabulary
- Integer — a whole number and its opposite, including zero — no fractions or decimals
- Negative number — a number less than zero, written with a minus sign
- Opposite — two numbers the same distance from zero on either side, like 6 and -6
- Absolute value — how far a number is from zero, ignoring direction
- Sum — the result of adding
- Difference — the result of subtracting
Preparation
Put the number line up before class and make it long. A line from -10 to 10 that spans most of the board lets you point at a single tick from anywhere in the room; a small one drawn during the lesson becomes something students copy rather than something they read.
Have a real-world context ready that students already reason about correctly — temperature below zero, or floors below ground in a parking garage. You are not teaching the context, you are borrowing the intuition students already have in it, so pick one your class actually knows.
Cut individual number-line strips. Students who model the move with a finger on their own strip get the answer; students watching you do it on the board get a memory of watching.
Warm-Up
5 minutes. Write four temperatures on the board — say 4°, -1°, -9°, and 0° — and ask the class to put them in order from coldest to warmest.
They will do it correctly, and quickly, because they are thinking about weather rather than about numbers. Then write the same four as bare numbers and ask which is smallest.
Some of the room will now say -1, because 1 is smaller than 9. Do not correct it yet. Put both answers on the board and say that by the end of the lesson everyone will be able to say which is right and why — the number line will settle it.
Direct Instruction
12 minutes. Point at the line and state the one rule that replaces all the guessing: further left is smaller, always. Not smaller-looking, not smaller-except-for-negatives. Order the warm-up temperatures on the line and let the picture settle the disagreement rather than settling it yourself.
Introduce opposites by pointing rather than defining: 6 and -6 are the same distance from zero on opposite sides. That distance has a name, absolute value, and it is why -9 can be a bigger distance and a smaller number at the same time. Say that out loud, because it is the sentence that resolves the warm-up split.
Now build addition as movement. Every problem starts somewhere and moves: a positive moves right, a negative moves left. Do -3 + 5 on the line — start at -3, move 5 right, land on 2 — and then do 5 + -3 and land on the same place, which is worth naming.
Do subtraction as movement the other way, and say the whole rule in one sentence: subtracting reverses the direction the sign tells you to go. Then walk straight into the hard case: 4 – (-3).
Take it slowly, on the line, twice. Subtracting reverses; the number is negative, which means left; reversed, it goes right. Land on 7. Then ask the question that makes it stick: 4 – 3 gave us 1, and 4 – (-3) gave us 7 — why did taking something away make it bigger? Let the class answer with the garage or the thermometer.
Close direct instruction by writing the four sign rules on the board and crossing them out. Tell the class they are welcome to memorize them later, but that anything they can find on the line they never have to memorize at all.
Guided Practice
13 minutes. Pairs work eight problems with their number-line strips, one modeling while the other reads the problem aloud, then swapping. The rule for this block is that the finger moves before the pencil writes.
Choose the eight to walk deliberately through the cases, in this order:
- a positive plus a negative, landing positive (7 + -2)
- a positive plus a negative, landing negative (2 + -7)
- a negative plus a negative (-4 + -3)
- a negative minus a positive (-2 – 6)
- a positive minus a negative (4 – -3)
- a negative minus a negative (-5 – -8)
The last two are the lesson. Everything before them is confidence-building for the last two, and a pair that gets the first four fast should be at the last two early rather than doing more of the first four.
Circulate with one question and only one: show me on the line. A student who can point can be left alone even if the arithmetic slipped; a student with the right answer and no movement is the one to stop at.
Pairs then start the Adding and Subtracting Integers Worksheet together, still with the strips available.
Independent Practice
10 minutes. Students finish the worksheet alone. Strips stay on the desk — not taken away as a reward for being ready, because the student who stops using the line and starts guessing signs is exactly the failure mode this lesson exists to prevent.
Add one written item: explain to someone in the year below you why 3 – (-5) is 8. The explanation is the assessment of understanding; the eight answers above it are the assessment of accuracy, and they are not the same thing.
Assessment
3 minutes. Exit ticket, three items. Order -6, 2, -1, and 0 from least to greatest. Find -8 + 5. Then: find 2 – (-6), and mark the movement on the line printed on the ticket.
The third item is the one that discriminates. A student can get the first two right by pattern-matching problems they have just done; only the third asks them to produce the reversal, and the marked line shows whether they did it or guessed it.
Closure
2 minutes. Go back to the warm-up temperatures and ask the question again: which is smallest. Now the room agrees. Close on the sentence the lesson earns — every integer problem is a starting point and a movement, and if you can find both on the line, you never have to remember a sign rule.
Differentiation and Accommodations
- Extra support: stay on the line and drop subtraction for the day. Placing and comparing negatives is a real result on its own, and the negative numbers on a number line worksheet gives that skill a full page before any arithmetic is asked for.
- Extension: absolute value is the natural next page — students who noticed that -9 is far from zero and small at the same time have already met the idea and are ready for the notation.
- Common difficulty: a student who applies the multiplication rule to addition and writes -3 + -4 = 7. Do not re-teach the rule; put them on the line, start at -3, and ask which way a negative moves. The wrong answer disappears without ever being argued about.
- Watch for: students reading the minus sign in 4 – (-3) as one thing instead of two. Have them say it aloud — "four, subtract, negative three" — because the sentence separates the operation from the sign and the notation does not.
Extension Activities
Comparing and ordering integers is the cleanest follow-up lesson: it takes the further-left-is-smaller rule and works it hard, including sets that mix negatives, zero, and positives.
Multiplying and dividing integers comes next, and it is worth flagging to students that the sign rules there really are different from the ones here — the confusion between the two is the single most common integer error, and naming it in advance helps.
Keep the number line on the wall for the rest of the unit. Every time a student asks about a sign, point at it rather than answering, and by the end of the unit most of them stop asking.
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