Grade 6 Workbook — Chapter 1: Integers and the Number Line

SOL 6.NS.2 · Companion to Textbook Chapter 1

Each page below is one Canva page. Headings are sized for direct paste: page title as H1, section labels as H2. Figures referenced by filename live in ../figures/.

PAGE 1 — Chapter opener

Chapter 1 · Integers and the Number Line

Standard 6.NS.2

In this chapter you will:

• Represent integers on a number line and in real situations
• Compare and order integers
• Use the symbols <, >, and =
• Find the absolute value of an integer

Words to know: integer · positive · negative · opposites · absolute value

Calculator note: this chapter is fully mental-math. No calculator needed.

PAGE 2 — Integers all around us

1.1 Representing Integers

FIGURE: fig1-integer-number-line.png (full width)

Fill in the blanks.

Positive integers are ________ than zero and sit to the ________ of zero.

Negative integers are ________ than zero and sit to the ________ of zero.

Zero is ____________ positive nor negative.

Write an integer for each situation.

PAGE 3 — Opposites

Opposites

FIGURE: fig3-opposites.png (full width)

Two integers are opposites when they are the same distance from zero, on opposite sides.

Write the opposite of each integer.

Circle the integers. Cross out anything that is not an integer.

$$-6 \qquad 2.5 \qquad 0 \qquad -\tfrac{3}{4} \qquad 18 \qquad -41 \qquad 7.0 \qquad \tfrac{1}{2}$$

Explain. Why is zero its own opposite?

PAGE 4 — Integers in real situations

Integers in Context

FIGURE: fig5-elevation.png (right half of page)

Complete the table.

Write a sentence for each integer without using the words "negative" or the minus sign.

$-9$ °F: _______________________________________________

$-55$ ft elevation: _______________________________________________

$-30$ dollars: _______________________________________________

Challenge. An elevator starts at 0, goes down 3 floors, then up 8 floors. Write an integer for each move and name the ending floor.

Move 1: ______ Move 2: ______ Ends on floor: ______

PAGE 5 — Exit ticket 1.1

Exit Ticket · Lesson 1.1

Name: ________________________ Date: ____________

1. Write an integer for "35 feet below sea level." ______

2. What is the opposite of $8$? ______

3. Circle the integers: $-3$ · $0.5$ · $0$ · $-\tfrac{1}{2}$ · $12$

4. In the integer $-14$, what does the sign tell you? What does the 14 tell you?

PAGE 6 — The left–right rule

1.2 Comparing and Ordering

The rule

On a number line, the number farther to the RIGHT is always GREATER.

FIGURE: fig4-ordering-integers.png (full width)

Circle the greater integer in each pair.

Watch out. Which is greater, $-20$ or $-2$? ______

Why is this the answer, even though 20 is a bigger digit than 2?

PAGE 7 — Ordering practice

Ordering Integers

Order from LEAST to GREATEST.

1. $-2$, $-11$, $5$, $0$, $-7$

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2. $-4$, $7$, $-12$, $0$, $-1$

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Order from GREATEST to LEAST.

3. $-1$, $-13$, $8$, $-6$

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4. $-15$, $-2$, $-20$, $-9$

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List all integers between:

5. $-5$ and $-1$: _______________________________________________

6. $-3$ and $2$: _______________________________________________

Plot and label $-6$, $-2$, $0$, $3$, $5$ on the number line below, then list them least to greatest.

BLANK NUMBER LINE: -8 to 8, ticks unlabeled for student use

PAGE 8 — Exit ticket 1.2

Exit Ticket · Lesson 1.2

Name: ________________________ Date: ____________

1. Which is greater, $-9$ or $-2$? ______

2. Order least to greatest: $3$, $-5$, $0$, $-8$

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3. Name an integer between $-4$ and $-2$. ______

4. A friend says $-6 > -1$. Correct it and explain the error.

PAGE 9 — Comparison symbols

1.3 Comparing with Symbols

The open end always faces the GREATER number.

Fill in $<$, $>$, or $=$.

Rewrite each statement the other way.

$-3 < 8$ becomes _______________

$5 > -2$ becomes _______________

PAGE 10 — Find and fix the errors

Error Hunt

Three of these are FALSE. Cross out the false ones and rewrite them correctly.

Apply it. Two hikers are at elevations $-15$ ft and $-6$ ft. Write a comparison using a symbol, then say which hiker is higher.

Comparison: _______________ Higher hiker: _______________

Explain. Why is $-100 < -1$, even though 100 is greater than 1?

PAGE 11 — Exit ticket 1.3

Exit Ticket · Lesson 1.3

Name: ________________________ Date: ____________

1. Fill in: $-7 \ \square \ -2$

2. Fill in: $-9 \ \square \ 0$

3. Rewrite $-4 < 5$ using $>$: _______________

4. How do you decide which way the symbol points?

PAGE 12 — Absolute value

1.4 Absolute Value

Absolute value = the DISTANCE from zero. Distance is never negative.

FIGURE: fig2-absolute-value.png (full width)

$$|-5| = 5 \qquad |5| = 5$$

Evaluate.

Name BOTH integers with each absolute value.

Absolute value $3$: ______ and ______

Absolute value $12$: ______ and ______

Absolute value $20$: ______ and ______

Think. Is there an integer whose absolute value is $-4$? Explain.

PAGE 13 — Greater vs. farther from zero

Two Different Questions

"Which is greater?" asks about position on the number line. "Which is farther from zero?" asks about absolute value. The answers can be different.

Complete the table.

Order from least to greatest: $|-7|$, $|3|$, $|-2|$, $|5|$

Challenge. Lena says: "If $a < b$, then $|a| < |b|$." Give two integers that prove her wrong and explain.

Counterexample: $a =$ ______, $b =$ ______

Explanation: _______________________________________________

PAGE 14 — Exit ticket 1.4

Exit Ticket · Lesson 1.4

Name: ________________________ Date: ____________

1. Find $|-13|$. ______

2. Name both integers whose absolute value is $9$. ______ and ______

3. Which is farther from zero, $-15$ or $12$? ______

4. Explain why absolute value can never be negative.

PAGE 15 — Chapter 1 review, part 1

Chapter 1 Review

Part A · Representing integers

1. Write an integer: a) 22 ft below sea level ______ b) a gain of 14 yards ______ c) 5 min before start ______

2. Opposites: a) $-17$ ______ b) $6$ ______ c) $0$ ______

3. Circle the integers: $-8$ · $3.2$ · $0$ · $-\tfrac{2}{5}$ · $41$

4. A point is 6 units left of zero. Name the integer. ______

Part B · Comparing and ordering

5. Least to greatest: $-4$, $7$, $-12$, $0$, $-1$

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6. Greatest to least: $-8$, $-19$, $2$, $-3$

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7. Fill in: a) $-6 \ \square \ -13$ b) $-2 \ \square \ 0$ c) $-10 \ \square \ -10$

8. Rewrite $-5 < 9$ using $>$: _______________

9. All integers between $-6$ and $-2$: _______________

PAGE 16 — Chapter 1 review, part 2

Chapter 1 Review (continued)

Part C · Absolute value

10. Evaluate: a) $|-16|$ ______ b) $|0|$ ______ c) $|-45|$ ______

11. Both integers with absolute value $20$: ______ and ______

12. Farther from zero, $-9$ or $7$? ______

Part D · Application and reasoning

13. Order coldest to warmest: $-7$°F, $4$°F, $-15$°F, $0$°F

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    Which is farthest from zero? ______

14. A submarine at $-90$ ft, a drone at $60$ ft. Which is farther from sea level? ______ Which elevation is greater? ______

    Why are these different answers?

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15. Using a number line, explain why the integer with larger digits is not always greater.

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16. Two integers are opposites and one is 13 units from zero. Name both and write a comparison.

    ______ and ______ Comparison: _______________

Canva production notes

• Page size: 8.5 × 11 in, 0.75 in margins
• Type: headings 24–28 pt, body 12–14 pt, answer blanks 14 pt with 1.5 line spacing
• Blank number lines: pages 7 and any reteach page need an unlabeled number line from $-8$ to $8$; generate with figures/make_grade6_ch01.py if a blank variant is added
• Figure widths: number-line figures full width; fig5-elevation.png is portrait, place at half width
• Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow