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CCSS 6.NS.C.5–7

Unit 7 — Integers & the Number Line

Dive the number line like a submarine. 0 is sea level. Going up is positive (+). Going down is negative (−).

Neft Teacher · Grade 6 Mathematics

Learning Target

I can describe positive and negative numbers in real-world contexts. (6.NS.C.5)
I can place integers on a number line and find their opposites. (6.NS.C.6)
I can compare and order integers and explain using absolute value. (6.NS.C.7)

📐 Standards: 6.NS.C.5 · 6.NS.C.6 · 6.NS.C.7 ⏱ Estimated time: 50 minutes 📦 Materials: pencil, this HyperDoc, optional number-line handout 👥 Format: individual or pair work

Teacher Notes (not for student display)

Pacing

Engage — 5 min: pose the submarine hook aloud; cold-call 2 students before they begin.
Explore — 10 min: 3D game + 5 min debrief on number-line placement.
Explain — 8 min: vocabulary card review with pair-share on absolute value.
Apply — 15 min (self-check) + 5 min NTKit auto-graded set.
Reflect — 7 min: individual writing; collect deliverable at class end.

Grouping

Pair students for Explore; individual for Apply and Reflect.
Small-group option: compare self-check answers before pressing "Check My Answers."

Differentiation — Support

Provide a printed number line from −20 to +20 for Q1 and Q6.
Allow students to draw the number line on scratch paper during Apply.
Reduce Apply to Q1–Q4 for students needing scaffolding.

Differentiation — Challenge

Ask: "If |a| = |b|, does a = b? Explain with examples."
Extension: place rational numbers (½, −¾) on the number line.

ESOL / Language Supports

Display a bilingual word wall: entero/integer, valor absoluto/absolute value, opuesto/opposite.
Use the submarine diagram as a non-linguistic representation throughout.
Accept numeric answers without written justification for emerging English learners.

Step 1 · Engage · Think

A submarine dives below the sea

A submarine sits at 0 (sea level). It dives to −30 meters. A bird flies +30 meters above the sea.

Question: Are −30 and +30 the same distance from 0? Which one is lower? You will find out in this HyperDoc.

−4 −3 −2 −1 0 +1 +2 +3 +4

Think: On the number line above, point to where −30 and +30 would go. Which direction is "down"?

Step 2 · Explore · Play

Try the Unit 7 tools

Open a link in a new tab. Play, then come back to finish.

3D Game: Submarine Dive Math Hub Graphic Novels

After playing: What was the deepest integer you used in the game? Write it on scratch paper.

Step 3 · Explain · Learn

What you need to know

Integer: a whole number that can be positive, negative, or zero. Like −3, 0, or +5.

Negative number: a number less than 0. It has a minus sign (−). Like −7.

Opposite: the same distance from 0, but the other side. The opposite of +6 is −6.

Absolute value: how far a number is from 0. We write it like |−8| = 8. It is never negative.

Worked example: Order −2, 3, −5 from least to greatest.

On a number line, numbers on the left are smaller. So: −5, −2, 3.

Absolute value: |−5| = 5 because −5 is 5 steps from 0.

Rule: the more negative a number is, the smaller it is. −5 is less than −2.

Step 4 · Apply · Do

Show what you know

Quick Self-Check

Answer each question, then press Check to see if you are right. Read the explanation!

A. A fish is at −8 meters. It swims 5 meters deeper. What integer tells the new depth?

−3 −13 +13

B. What is |−22|?

−22 0 22

C. Which list is in order from least to greatest?

−1, −4, 0, 3 −4, −1, 0, 3 3, 0, −1, −4

Graded Questions

Type your answers. Use a minus sign (−) or a dash (-) for negatives. Then press Check my answers.

First, write your name in the box below so your work can be saved.

1. A diver is at −12 meters. Write the integer for "8 meters lower than −12". (6.NS.C.5) Hint: going lower means more negative.

2. What is the opposite of +9? (6.NS.C.6a)

3. Find the absolute value: |−15| = ? (6.NS.C.7c)

4. Which number is the smallest? (6.NS.C.7a)

−8 −3 0 5

5. Which comparison is TRUE? (6.NS.C.7a–b)

−6 > −2 −2 > −6 −6 = −2

6. A temperature is −4°C. It gets 4 degrees colder. Write the new temperature as an integer. (6.NS.C.5)

Rubric

How Your Work Is Scored

Level	Score	What this looks like
4 — Exceeds	6/6	All 6 graded questions correct AND both reflection responses are detailed with examples. Self-check completed before graded section.
3 — Meets	5–6/6	At least 5 graded questions correct. Both reflections answered in complete sentences. Minor errors in absolute value or ordering.
2 — Approaching	3–4/6	Some correct answers; confuses positive/negative direction or absolute value sign. At least one reflection attempted.
1 — Beginning	0–2/6	Fewer than 3 correct; confuses negative integers with absolute value or ordering. Reflections missing or incomplete.

Step 5 · Reflect · Write

Think Back

Write in complete sentences. Use math vocabulary from the Explain section.

1. In your own words, what does absolute value mean? Give one real-world example.

2. Why is −5 less than −2? Use the number line idea to explain.

Deliverable: When you are done, press Save as PDF above and upload it to your class folder. Your two reflection responses and your score will be included in the document.

Your reflection is saved when you press "Save as PDF" or "Save as DOC" above.

Teacher Resource

Answer Key

Show / Hide Answer Key (Teacher Only)

#	Question	Correct Answer	Standard	Explanation
Self-Check A	Fish at −8, swims 5 deeper	−13	6.NS.C.5	−8 − 5 = −13; deeper = more negative.
Self-Check B	\|−22\|	22	6.NS.C.7c	Absolute value = distance from 0.
Self-Check C	Least to greatest	−4, −1, 0, 3	6.NS.C.7a	More negative = farther left on the number line.
Q1	8 meters lower than −12	−20	6.NS.C.5	−12 − 8 = −20.
Q2	Opposite of +9	−9	6.NS.C.6a	Opposites are equidistant from 0 on opposite sides.
Q3	\|−15\|	15	6.NS.C.7c	Distance from 0 is always non-negative.
Q4	Smallest: −8, −3, 0, 5	−8	6.NS.C.7a	−8 is farthest left on the number line.
Q5	True comparison	−2 > −6	6.NS.C.7b	−2 is to the right of −6, so −2 is greater.
Q6	−4°C, 4 degrees colder	−8	6.NS.C.5	−4 − 4 = −8.