Grade 6 Workbook — Chapter 2: Adding and Subtracting Integers

SOL 6.CE.2 a, b, d · Companion to Textbook Chapter 2

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 2 · Adding and Subtracting Integers

Standard 6.CE.2

In this chapter you will:

Model integer addition and subtraction with chips and number lines
Add any two integers
Subtract by adding the opposite
Solve one- and two-step problems in context

Words to know: integer chips · zero pair · addend · sum · additive inverse · difference · net change

Calculator note: 6.CE.2a and 6.CE.2b are assessed WITHOUT a calculator. Every page here is mental math, models, and estimation.

PAGE 2 — Chips and zero pairs

2.1 Modeling Integer Addition

FIGURE: fig6-chip-zero-pair.png (half width, top right)

Fill in the blanks.

A yellow chip is worth ________. A red chip is worth ________.

One yellow chip and one red chip make a ________ ________, worth ________.

Adding a zero pair to a pile ________ change what the pile is worth.

Complete the table. Model each sum with chips.

Addition sentence	Zero pairs formed	Sum
$-4 + (-3)$
$8 + (-5)$
$-9 + 4$
$-6 + 6$
$-2 + (-5)$
$6 + (-4)$

FIGURE: fig8-chip-addition-different-signs.png (full width, bottom)

PAGE 3 — Jumps on the number line

Adding on a Number Line

FIGURE: fig9-numberline-addition-jumps.png (full width)

Adding a POSITIVE jumps RIGHT. Adding a NEGATIVE jumps LEFT.

Find each sum by jumping.

$-3 + 7 =$ ______
$5 + (-9) =$ ______
$-2 + (-6) =$ ______
Start at $-1$ , jump 5 right. Sentence: __________________ Sum: ______
Start at $2$ , jump 6 left. Sentence: __________________ Sum: ______

Use the blank number line below to model $-6 + 4$ . Sum: ______

BLANK NUMBER LINE: -10 to 10, ticks unlabeled for student use

Write the addition sentence modeled by 3 yellow chips and 8 red chips.

__________________ Sum: ______

Apply it. At 5 a.m. the temperature was $-4$ °F. It rose 9 degrees by noon.

Sentence: __________________ Noon temperature: ______

PAGE 4 — Exit ticket 2.1

Exit Ticket · Lesson 2.1

Name: ________________________ Date: ____________

Use chips: $-5 + (-2) =$ ______
Use chips: $7 + (-4) =$ ______ Zero pairs formed: ______
Start at $-6$ and jump 4 right. Sentence: __________________ Sum: ______
What is a zero pair, and why does adding one not change a pile's value?

PAGE 5 — The two addition rules

2.2 Adding Integers

Fill in the rules.

Same signs: ________ the absolute values, then ________ the sign they share.

Different signs: ________ the smaller absolute value from the larger, then use the sign of the addend with the ________ absolute value.

Find each sum.

a) $-6 + (-9) =$ ______	b) $-12 + 5 =$ ______	c) $14 + (-6) =$ ______
d) $-20 + 20 =$ ______	e) $-7 + 18 =$ ______	f) $-25 + (-13) =$ ______
g) $-31 + 17 =$ ______	h) $42 + (-58) =$ ______	i) $-64 + 64 =$ ______

Sort. Circle the sums above that are NEGATIVE. Put a box around the sums that equal ZERO.

PAGE 6 — Estimate, then add

Estimating Sums

Round each addend, estimate, then compute exactly.

Problem	Estimate	Exact sum
$-197 + 88$
$-403 + 150$
$88 + (-312)$

Add three integers. Show both steps.

$-14 + 6 + (-5) =$ ______
$-9 + (-9) =$ ______ 3. $-45 + 60 =$ ______ 4. $30 + (-12) =$ ______

Find the missing addend.

$-8 + \underline{\ \ \ \ } = 3$ $\underline{\ \ \ \ } + (-6) = -14$ $-15 + \underline{\ \ \ \ } = 0$

Apply it. A team gained 7 yards, lost 12 yards, then gained 3 yards.

Sentence: __________________ Net result: ______________________

Think. Without computing, is $-56 + 43$ positive or negative? ______

Why? _______________________________________________

PAGE 7 — Exit ticket 2.2

Exit Ticket · Lesson 2.2

Name: ________________________ Date: ____________

$-7 + (-8) =$ ______
$-19 + 11 =$ ______
$23 + (-40) =$ ______
Two integers have different signs. How do you decide whether the sum is positive or negative?

PAGE 8 — Add the opposite

2.3 Subtraction as Adding the Opposite

To subtract an integer, ADD ITS OPPOSITE: $a - b = a + (-b)$

FIGURE: fig10-numberline-subtraction-adding-opposite.png (full width)

Rewrite each subtraction as an addition, then find the value.

Subtraction	Rewrite as addition	Value
$4 - 9$
$-3 - 5$
$-6 - (-10)$
$12 - (-7)$
$-4 - 11$
$-9 - (-4)$

FIGURE: fig11-chip-subtraction-remove.png (full width, bottom)

Explain. To model $-4 - (-6)$ with chips, why must you add zero pairs first?

PAGE 9 — Subtraction practice and error hunt

Subtracting Integers

Find each difference.

a) $3 - 15 =$ ______	b) $-14 - 6 =$ ______	c) $-21 - (-9) =$ ______	d) $18 - (-18) =$ ______
e) $-30 - (-45) =$ ______	f) $25 - 41 =$ ______	g) $-13 - 13 =$ ______	h) $-7 - (-7) =$ ______

Error hunt. Three of these are FALSE. Mark each and correct the false ones.

Statement	True or false?	Correction
$5 - 8 = 3$
$-2 - 6 = -8$
$-5 - (-9) = -14$
$10 - (-4) = 14$
$-6 - (-6) = -12$

Find the missing number. $-6 - \underline{\ \ \ \ } = -2$

Two steps. $5 - (-3) - 8 =$ ______

Challenge. Marcus says subtracting always makes a number smaller. Give an example that proves him wrong.

PAGE 10 — Exit ticket 2.3

Exit Ticket · Lesson 2.3

Name: ________________________ Date: ____________

$2 - 9 =$ ______
$-11 - 4 =$ ______
$-5 - (-12) =$ ______
State the subtraction rule and show it working on an example of your own.

PAGE 11 — Choosing the operation

2.4 Adding and Subtracting in Context

"What is the result after a change?" → ADD. "How far apart are two values?" → SUBTRACT.

FIGURE: fig12-thermometer-net-change.png (right third of page)

Complete the table.

Situation	Add or subtract?	Number sentence	Answer
Balance $-\$24$ , deposit $40
Temperature $-7$ °F rises 12 degrees
Hiker at $85$ ft descends 110 ft
How far apart are $6$ °F and $-14$ °F?
Team loses 8 yards, then gains 3

PAGE 12 — Two-step problems

Two Steps at a Time

Show both steps for each problem.

An elevator is on level $-3$ . It goes up 9 levels, then down 4 levels.

Step 1: ____________ Step 2: ____________ Ends on level: ______
An account is at $-\$58$ . A deposit of $120 is made, then $35 is withdrawn.

Step 1: ____________ Step 2: ____________ Final balance: ______
A diver at $-46$ ft rises 19 ft, then descends 33 ft.

Step 1: ____________ Step 2: ____________ Final depth: ______
Overnight lows were $-11$ °F, $4$ °F, $-6$ °F, and $9$ °F. Find the difference between the greatest and the least.

Sentence: ____________ Difference: ______
Mount Whitney is $14{,}505$ ft. Death Valley's low point is $-282$ ft. Find the difference in elevation.

Sentence: ____________ Difference: ______
Estimate, then compute: the temperature is $-18$ °C and rises 41 degrees.

Estimate: ______ Exact: ______

PAGE 13 — Exit ticket 2.4

Exit Ticket · Lesson 2.4

Name: ________________________ Date: ____________

A balance of $-\$30$ receives a deposit of $18. New balance: ______
The temperature goes from $-4$ °F to $11$ °F. Degrees risen: ______
A diver at $-25$ ft descends 15 more ft. New depth: ______
Estimate $-198 + 205$ , then compute exactly. Estimate: ______ Exact: ______

What did the estimate tell you? _______________________________________________

PAGE 14 — Chapter 2 review, part 1

Chapter 2 Review

Part A · Modeling

Chips: a) $-5 + (-3) =$ ______ b) $9 + (-4) =$ ______ c) $-7 + 7 =$ ______
Number line: a) $-6 + 10 =$ ______ b) $3 + (-8) =$ ______
Sentence modeled by 2 yellow and 7 red chips: __________________ Sum: ______
Model $-4 - (-6)$ with chips. Answer: ______

Why must zero pairs be added first? _______________________________________________

Part B · Adding and subtracting

a) $-17 + (-24) =$ ______ b) $-38 + 52 =$ ______ c) $29 + (-46) =$ ______ d) $-15 + 15 =$ ______
a) $8 - 19 =$ ______ b) $-22 - 7 =$ ______ c) $-16 - (-25) =$ ______ d) $14 - (-14) =$ ______
$-9 + 14 + (-20) =$ ______
$-6 - (-11) + (-8) =$ ______
Missing number: a) $-13 + \underline{\ \ \ \ } = -5$ b) $\underline{\ \ \ \ } - (-6) = 1$

PAGE 15 — Chapter 2 review, part 2

Chapter 2 Review (continued)

Part C · In context

Account at $-\$62$ , deposit $95, withdraw $18. Final balance: ______
High $7$ °F, low $-21$ °F. Degrees apart: ______
Diver at $-38$ ft rises 12 ft, then descends 27 ft. Final depth: ______

Part D · Application and reasoning

Estimate $-406 + 289$ : ______ Exact: ______
Using a number line, explain why $a - b$ equals $a + (-b)$ .
Always true? a) The sum of two negative integers is negative. ______

b) The sum of a positive and a negative integer is positive. ______

Counterexample for the false one: _______________________________________________
Write a real situation for $-15 + 40 = 25$ , and say what the $25$ means.

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
Chip figures: print in color if possible; if printing in grayscale, add a "+" inside yellow chips and a "−" inside red chips so the two are distinguishable
Blank number lines: page 3 needs an unlabeled number line from $-10$ to $10$
Figure widths: number-line figures full width; fig6-chip-zero-pair.png and fig12-thermometer-net-change.png are small and belong at one-third to one-half width
Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow