Unit 9 · Standard 6.NS.7
Integers and Absolute Value
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
... -3, -2, -1, 0, 1, 2, 3 ... shown on a number line with 0 in the center
Integer
A whole number that can be positive, negative, or zero.
+5 means 5 above zero, like 5 floors above ground level
Positive
A number bigger than zero, to the right of zero on a number line.
-3 means 3 below zero, like 3 floors underground
Negative
A number smaller than zero, to the left of zero on a number line.
|-5| = 5 and |5| = 5 — both are 5 units from 0
Absolute value
How far a number is from zero. It is never negative.
3 and -3 are opposites — both are 3 units from 0
Opposite
Two numbers the same distance from zero, on opposite sides, like 3 and -3.
Key Ideas & Notes
- Captain Vega's treasure map has clues hidden at different elevations!
- Some treasures are buried underground (below sea level) and some are on mountaintops (above sea level).
- Sea level is marked as 0.
- A treasure chest is at -4 (4 meters below sea level) and a lookout tower is at +6 (6 meters above sea level).
- Plot each integer on the number line and find its absolute value (distance from zero).
Think About It
- What does the negative sign tell you about the treasure chest's location?
- Which location is farther from sea level — the chest at -4 or the tower at +6?
- How can you find the distance from sea level without worrying about direction?
My Notes
Guided Examples
Example 1
What is the absolute value of -9?
Solution: Absolute value is the distance from zero. -9 is 9 units from zero, so |-9| = 9.
Answer: A. 9
Example 2
Which integer has the GREATEST absolute value: -3, 7, -5, 2?
Solution: |-3| = 3, |7| = 7, |-5| = 5, |2| = 2. The greatest absolute value is 7.
Answer: A. 7
Example 3
What is |0|?
Solution: Zero is 0 units from itself on the number line, so |0| = 0.
Answer: A. 0
Write About the Math The Writing Revolution
I can explain my reasoning using the words integer, positive, negative, absolute value, and opposite.
1. Kernel Sentence subject + verb
Model: Integer is a whole number that can be positive, negative, or zero.Número entero es un número entero que puede ser positivo, negativo o cero.
Write a kernel sentence about integer. Use a subject and a verb.Escribe una oración base sobre número entero. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Integer matters in mathNúmero entero importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Integer matters in math because ___.Número entero importa en matemáticas porque ___.
Integer matters in math, but ___.Número entero importa en matemáticas, pero ___.
Integer matters in math, so ___.Número entero importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about integer.Di un hecho verdadero sobre integer.
Integer ___.
Ask a question about integer.Haz una pregunta sobre integer.
How does ___ ?¿Cómo ___ ?
Show excitement about integer.Muestra entusiasmo sobre integer.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with integer.Dile a un compañero qué hacer con integer.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
The absolute value of ___ is ___.El valor absoluto de ___ es ___.
It means the distance from ___.Significa la distancia desde ___.
I see negatives when ___.Veo negativos cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is |0|?
- 0
- 1
- -1
- There is no answer
2. Which statement about absolute value is TRUE?
- |-4| = |4| because both are 4 units from zero
- |-4| = -4 because the number is negative
- |4| > |-4| because positive is always bigger
- |-4| = 0 because negatives cancel out
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A submarine is at -150 meters and a bird is flying at +150 meters. A student says the submarine is closer to sea level because -150 is less than 150. Is the student correct? Explain using absolute value.
Sentence starter: The student is ___ because absolute value measures ___. Since |-150| = ___ and |150| = ___, both are ___ from sea level. The student confused ___ with ___.
Reflect — Exit Ticket
Which integer has an absolute value of 8 and is located to the LEFT of zero on the number line?
- 8
- -8
- 0
- -80
Answer Key & Teacher Guide
- Try It 1: A. 0 — Zero is 0 units from itself on the number line, so |0| = 0.
- Try It 2: A. |-4| = |4| because both are 4 units from zero — Absolute value measures distance from zero. Both -4 and 4 are 4 units from zero, so |-4| = |4| = 4.
- Exit Ticket: B. -8 — To the left of zero means negative. The integer -8 has an absolute value of 8 because it is 8 units from zero.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Integer is a whole number that can be positive, negative, or zero.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).