Explore Integers and Their Opposites
I can use integers to represent quantities in everyday life, explain what 0 means in each situation, and name the opposite of an integer on the number line.
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🎯 Content Objective / Objetivo de contenido
I can use integers to represent quantities in everyday life, explain what 0 means in each situation, and name the opposite of an integer on the number line.
Today's Flow
Total pacing: ~45 min · Progress bar at top tracks your place
LAUNCH
⏱ ~10 min
⏱️ 3 MIN · THINK-PAIR-SHARE
Why does 0 represent sea level instead of meaning 'nothing at all'?
Check for Understanding #1
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Below Sea Level
The lowest elevation in North America is Badwater Basin in Death Valley: 86 meters below sea level. When we measure elevation, sea level is defined as 0. So 86 meters below sea level cannot be written as plain 86 — that would put it ABOVE the water. Numbers less than zero are negative numbers, written with a − sign, so the elevation of Badwater Basin is −86 meters. On a number line, −86 is 86 units to the LEFT of 0, while 86 is 86 units to the RIGHT of 0. Those two numbers are opposites.
Concept Launch
💡 How do you use integers to describe quantities above and below zero?
Counting numbers, their opposites, and 0 are integers. A negative integer is less than zero and is written with a − sign. Opposites are the same distance from 0, but on opposite sides of the number line.
Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a
Check for Understanding #2
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Now it's your turn
VOCABULARY
⏱ ~8 min
| Term / Término | Meaning / Significado | Example / Ejemplo | Visual |
|---|---|---|---|
| Integer Número entero |
The counting numbers, their opposites, and 0. Los números para contar, sus opuestos y el 0. |
..., -3, -2, -1, 0, 1, 2, 3, ... | |
| Opposite Opuesto |
A number that is the same distance from 0 as another number, but on the other side of 0. Un número que está a la misma distancia de 0 que otro número, pero del otro lado del 0. |
86 and -86 are both 86 units from 0, on opposite sides | |
| Negative number Número negativo |
A number less than 0, written with a − sign. On a number line it sits to the left of 0. Un número menor que 0, escrito con un signo −. En la recta numérica queda a la izquierda del 0. |
-86 meters means 86 meters BELOW sea level | |
| Positive number Número positivo |
A number greater than 0. On a number line it sits to the right of 0. Un número mayor que 0. En la recta numérica queda a la derecha del 0. |
9°C is 9 degrees ABOVE zero | |
| Number line Recta numérica |
A straight line where numbers are placed in order. It extends to the left of 0 to show values less than 0. Una recta donde los números se colocan en orden. Se extiende a la izquierda del 0 para mostrar valores menores que 0. |
-3, -2, -1, 0, 1, 2, 3 marked in order from left to right |
Which Word Fits?
A counting number, its opposite, or 0 is an ___.
Use It In a Sentence
Check for Understanding #3
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Turn & Talk — Launch
Why does 0 represent sea level instead of meaning 'nothing at all'?
👂 Listen For
Student explains 0 is a chosen reference point (sea level), so values above it are positive and values below it are negative.
Extend: Ask students to name another situation where 0 is a chosen starting point rather than 'nothing'.
EXPLORE & PRACTICE
⏱ ~18 min
Visual Modeling Workspace
Use the drawing tray below to annotate the visual model. Teacher: say "Click to reveal" on key steps.
Explore Activity
Each card names a real quantity. Sort it by whether the integer that represents it is BELOW zero, ABOVE zero, or exactly AT zero.
✍️ Explore Discourse
How did you decide what 0 meant in each situation, and how did that decide the sign of the integer?
Whiteboard Moment
Show your work clearly. Be ready to explain your thinking to a partner.
Turn & Talk — Explore
How can you tell from the words in a situation whether the integer will be negative or positive?
👂 Listen For
Student links direction words (below, loss, under) to negative integers and left of 0, and (above, gain) to positive integers and right of 0.
Extend: Ask students what a quantity of exactly 0 would sound like in each of these situations.
Practice Check A
Which list of integers is ordered from LEAST to GREATEST?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Practice Check B
Badwater Basin is at -86 meters. Which elevation is FARTHER below sea level than Badwater Basin?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Coordinate Treasure Hunt
Plot points to find the treasure! Target: (4, 3)
✍️ Justify Your Thinking
Sort each integer by which side of 0 it sits on when you graph it on a number line.
A classmate turned in the work below. One step has a mistake. Read every step, find it, name it, and fix it.
Choose ONE option to show what you know — then do it in the workspace below.
Use evidence from today's lesson to complete each frame.
Today's key idea is: "Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a" — and it works because ___.
Because Integer means ___, but a tricky part is ___, so I have to ___.
A common mistake with Integer is ___. It happens because ___, and the fix is ___.
I can prove my answer is correct by ___, using Opposite to check my work.
✍️ TWR · WRITE 3 SENTENCES · 7 MIN
Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a because ___
Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a but ___
Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a so ___
🌱 TWR · GROW THE KERNEL · 6 MIN
Answer these to add detail
Sentence starters (tap to use)
Student Workspace
Each card names a real quantity. Sort it by whether the integer that represents it is BELOW zero, ABOVE zero, or exactly AT zero.
| Column A | Column B |
|---|---|
✏️ Sketch Your Strategy
Differentiation Paths
Step-by-step with a worked model and sentence frames.
Badwater Basin is 86 meters below sea level, and sea level is 0. Which integer represents that elevation?
Which list of integers is ordered from LEAST to GREATEST?
At 6 a.m. in Reykjavik the temperature was -12°C. At 2 p.m. it was the opposite of the 6 a.m. temperature, and at 11 p.m. it was the opposite of the 2 p.m. temperature. What were the temperatures at 2 p.m. and 11 p.m.?
Partner Activity
Work with your partner on the practice problems at your differentiation path level. Explain each step using math vocabulary.
Check for Understanding #4
Teacher: If >30% thumbs down, re-teach with a fresh example before moving on.
Real-World Connection
🌍 Math in the Wild
To make a first down, a football team must gain at least 10 yards from where they started, a spot called the line of scrimmage. The line of scrimmage is 0: a gain moves the team above 0 and a loss moves the team below 0. During one series, a team had a 10-yard loss, a 4-yard gain, a 3-yard loss, and a 21-yard gain.
✍️ Connection Reasoning
Write each play as an integer, then decide: did the team make a first down, and how far are they from the line of scrimmage?
The 10-yard loss is the integer ___ and the 3-yard loss is the integer ___. Combining all four plays leaves the team ___ yards from where they started, which is ___ the line of scrimmage. Because they needed at least 10 yards, the team ___ make a first down.
Turn & Talk — Connect
Two numbers are opposites. What is always true about them, and what is always different?
👂 Listen For
Student says opposites are the same distance from 0 but on opposite sides of 0.
Extend: Push students to explain what happens when you take the opposite of an opposite.
Summarize: Explore Integers and Their Opposites
Integers & Opposites. 1. Integers: Positive whole numbers, negative whole numbers, and zero (..., -2, -1, 0, 1, 2, ...). 2. Opposites: Numbers that are the same distance from 0 in opposite directions (e.g. -5 and 5). 3. The opposite of the opposite of a number is the number itself: -(-a) = a
In your own words:
CLOSURE & REFLECT
⏱ ~8 min
Today I learned that ___ because ___.
One thing I am still not sure about is ___.
Which situation is best represented by the integer -15?
Bonus Exit Check
Which statement about 0 is TRUE?
✍️ Show Your Work
Explain why your answer is correct using today's vocabulary.
Reflection & Self-Assessment
Continue Learning
Launch the Full Interactive Activity
Students continue practice in the HTML lesson engine with auto-check, hints, and differentiation.
Family Connection
Share tonight's family homework and discuss one vocabulary word at home.
Open Family Homework ↗Teacher Notes
⏱️ Pacing Guide
- Launch & vocab: 12 min
- I Do / We Do / You Do: 15 min
- Explore & practice: 15 min
- Connect & closure: 8 min
Total: ~45 min
🎯 Listen For · Common Errors
• Student explains 0 is a chosen reference point (sea level), so values above it are positive and values below it are negative.
• Student links direction words (below, loss, under) to negative integers and left of 0, and (above, gain) to positive integers and right of 0.
• Student says opposites are the same distance from 0 but on opposite sides of 0.
• Student says the opposite of 0 is 0, because 0 is zero units from itself and has no other side to move to.
Common mistake: The most common mistake in this lesson is thinking that the opposite of a negative integer is still negative — for example, saying the opposite of -7 is -7, or that the opposite of -12 is -24. Opposites are the same DISTANCE from 0 but on OPPOSITE sides of 0, so taking an opposite always changes the direction and never changes the distance: the opposite of -7 is 7 and the opposite of -12 is 12. The one exception is 0, which is 0 units from itself and is therefore its own opposite. Before you submit, count the units from 0 and check that your answer is on the other side.
Answer Key (Teacher Appendix)
Hide this slide during presentation or move to the end of your copy.
✓ Practice 1: -8, -3, 0, 5 — Least to greatest reads left to right on the number line: -8, then -3, then 0, then 5.
✓ Practice 2: -120 meters — Farther below sea level means farther to the left of 0. -120 is 120 units below 0, which is deeper than 86 units below 0.
✓ Practice 3: 0 is an integer, and it is its own opposite — Integers are the counting numbers, their opposites, and 0. Zero is 0 units from itself, so it is its own opposite.
✓ Practice 4: -86 — Below sea level means less than 0, so the elevation is written with a negative sign: -86 meters.
✓ Exit ticket: A diver 15 meters below the surface of the water — A negative integer represents a quantity below the chosen 0. With the water surface as 0, a diver 15 meters below it is -15.