Grade 6 Workbook — Chapter 3: Multiplying and Dividing Integers; Absolute Value Expressions

SOL 6.CE.2 a, b, c, d · Companion to Textbook Chapter 3

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 3 · Multiplying and Dividing Integers

Standard 6.CE.2

In this chapter you will:

Model integer multiplication and division with chips and number lines
Multiply and divide any two integers
Simplify expressions with absolute value bars and show the result on a number line
Solve one- and two-step problems in context

Words to know: factor · product · dividend · divisor · quotient · fact family · absolute value bars · rate

Calculator note: 6.CE.2a and 6.CE.2b are assessed WITHOUT a calculator. Estimate before you compute, every time.

PAGE 2 — Multiplication as groups

3.1 Modeling Integer Multiplication

FIGURE: fig13-chip-multiplication-groups.png (full width)

First factor = HOW MANY GROUPS. Second factor = WHAT IS IN EACH GROUP. A negative first factor means REMOVE groups instead of adding them.

Complete the table.

Product	Model in words	Value
$3 \times (-5)$	3 groups of 5 red chips
$-4 \times 2$	remove 4 groups of 2 yellow chips
$-2 \times (-6)$	remove 2 groups of 6 red chips
$5 \times (-4)$
$-6 \times 3$
$-3 \times (-7)$

Repeated addition. Write $5 \times (-2)$ as an addition and find the product.

__________________________________ = ______

Follow the pattern. Fill in the missing values and describe the step.

$-4 \times 2 =$ ______ $-4 \times 1 =$ ______ $-4 \times 0 =$ ______ $-4 \times (-1) =$ ______ $-4 \times (-2) =$ ______

Each product goes ________ by ________ as you read down.

FIGURE: fig15-pattern-table-negative-times-negative.png (half width, right)

PAGE 3 — Division as sharing

Modeling Integer Division

FIGURE: fig16-chip-division-sharing.png (full width)

Find each quotient. Say whether you shared or measured.

a) $-18 \div 6 =$ ______	b) $-20 \div (-5) =$ ______	c) $-24 \div 8 =$ ______
d) $-30 \div (-6) =$ ______	e) $28 \div (-7) =$ ______	f) $-21 \div 7 =$ ______

Fact family. Write all four facts using $-6$ , $4$ , and $-24$ .

FIGURE: fig14-numberline-multiplication-jumps.png (full width, bottom)

Apply it. A well's water level drops 3 feet each week for 6 weeks.

Sentence: __________________ Total change: ______ What it means: ______________________

PAGE 4 — Exit ticket 3.1

Exit Ticket · Lesson 3.1

Name: ________________________ Date: ____________

$6 \times (-2) =$ ______
$-3 \times (-5) =$ ______
$-21 \div 7 =$ ______
How does the chip model show that removing groups of red chips raises a pile's value?

PAGE 5 — The sign rules

3.2 Multiplying and Dividing Integers

Fill in the rules.

Same signs → the result is ____________.

Different signs → the result is ____________.

These rules work for ____________ and for ____________.

Find each answer.

a) $-9 \times 4 =$ ______	b) $-7 \times (-8) =$ ______	c) $-56 \div 7 =$ ______
d) $-45 \div (-9) =$ ______	e) $-11 \times 6 =$ ______	f) $-13 \times (-4) =$ ______
g) $15 \times (-8) =$ ______	h) $-1 \times (-25) =$ ______	i) $-144 \div 12 =$ ______
j) $-81 \div (-9) =$ ______	k) $100 \div (-25) =$ ______	l) $-20 \times (-3) =$ ______

PAGE 6 — Many factors, and estimating

Counting the Negatives

Even number of negative factors → POSITIVE. Odd number → NEGATIVE.

Predict the sign, then find the product.

Expression	Negative factors	Sign	Product
$-3 \times (-2) \times (-5)$
$(-4) \times (-3) \times (-2)$
$-2 \times 3 \times (-4)$
$(-2) \times (-3) \times (-4) \times (-5)$

Sign only. Do not compute.

$(-1) \times (-2)$ : ______ $(-1) \times (-2) \times (-3)$ : ______ $(-2) \times 5 \times (-3)$ : ______ $4 \times (-1) \times (-2) \times (-3)$ : ______

Estimate, then compute.

Problem	Estimate	Exact
$-38 \times 21$
$-296 \div 4$
$-19 \times 31$

Find the missing number.

$-7 \times \underline{\ \ \ \ } = 63$ $\underline{\ \ \ \ } \div (-6) = -5$ $-8 \times \underline{\ \ \ \ } = -96$

PAGE 7 — Exit ticket 3.2

Exit Ticket · Lesson 3.2

Name: ________________________ Date: ____________

$-8 \times 9 =$ ______
$-6 \times (-12) =$ ______
$-75 \div (-5) =$ ______
Using a fact family, explain why a negative divided by a negative is positive.

PAGE 8 — Inside the bars first

3.3 Expressions with Absolute Value Bars

Step 1: simplify INSIDE the bars. Step 2: take the absolute value. Step 3: apply anything OUTSIDE the bars, such as a negative sign.

FIGURE: fig17-absolute-value-expression-numberline.png (full width)

Show all three steps.

Expression	Inside the bars	Absolute value	Final value
$\lvert 3 - 7 \rvert$
$-\lvert 3 - 7 \rvert$
$\lvert -2 + 10 \rvert$
$-\lvert -5 - 5 \rvert$
$\lvert 6 \times (-3) \rvert$
$-\lvert 36 \div (-6) \rvert$

Compare. Simplify each and notice which ones match.

$|9 - 4| =$ ______ $|4 - 9| =$ ______ $-|4 - 9| =$ ______ $-|9 - 4| =$ ______

PAGE 9 — Showing the result on a number line

Graphing the Result

FIGURE: fig18-numberline-negative-abs-result.png (full width)

Simplify, then plot each result on the number line below with a solid dot.

$-|2 - 11| =$ ______
$|-8 + 3| =$ ______ 3. $-|-8 + 3| =$ ______
$|-7 - 6| =$ ______ 5. $-|-7 - 6| =$ ______
$|-4 \times 5| =$ ______

BLANK NUMBER LINE: -15 to 25, ticks unlabeled for student use

Which is greater? $|-3 - 4|$ or $-|3 + 4|$ ? ______

Show both values: ______ and ______

Apply it. A stock's price moved from $52 to $45.

Size of the change (use bars): __________________ = ______

Signed change: __________________ = ______

PAGE 10 — Exit ticket 3.3

Exit Ticket · Lesson 3.3

Name: ________________________ Date: ____________

$|7 - 12| =$ ______
$-|7 - 12| =$ ______
$-|-9 + 2| =$ ______
Mark the answer to item 3 on the number line, then explain why the sign outside the bars is applied last.

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

PAGE 11 — Choosing the operation

3.4 Problems in Context

The question asks	Operation
result after one change	add
how far apart two values are	subtract
a repeated change	multiply
a change split into equal parts	divide

Complete the table.

Situation	Operation(s)	Number sentence	Answer
Temperature $-3$ °C falls 5 degrees per hour for 4 hours
An account loses $12 each week for 7 weeks
A balloon 240 ft up descends 30 ft per minute until it lands
72 points lost, spread equally over 6 rounds
A diver at $-15$ ft descends 6 ft per minute for 9 minutes

PAGE 12 — Two steps, and a check

Two-Step Problems

Solve. Show each step and write what the answer means.

A debt of $150 is shared equally among 5 people. Each share: ______
At midnight it was $-8$ °F. It rose 3 degrees each hour for 6 hours.

Step 1: ____________ Step 2: ____________ At 6 a.m.: ______
A player takes 5 penalties of $-4$ points and earns one $30$ -point bonus.

Sentence: __________________ Total change: ______
An elevator starts on floor 12 and goes down 3 floors at each of 6 stops.

Sentence: __________________ Ending level: ______
Estimate, then compute: $-296 \div 4$ . Estimate: ______ Exact: ______

Challenge. Two students simplify $-6 \times 4 + 10$ . One gets $-14$ ; the other gets $-84$ .

Who is correct? ______ What mistake did the other student make?

PAGE 13 — Exit ticket 3.4

Exit Ticket · Lesson 3.4

Name: ________________________ Date: ____________

The temperature is $2$ °F and falls 5 degrees each hour for 3 hours. Final temperature: ______
A penalty of 84 points is spread equally over 7 rounds. Change each round: ______
Estimate $-51 \times 19$ : ______ Exact: ______
How do you decide whether a problem calls for multiplication or division?

PAGE 14 — Chapter 3 review, part 1

Chapter 3 Review

Part A · Modeling

a) $4 \times (-6) =$ ______ b) $-5 \times 3 =$ ______ c) $-3 \times (-4) =$ ______
a) $-20 \div 4 =$ ______ b) $-27 \div (-9) =$ ______
Sentence modeled by 6 groups of 2 red chips: __________________ Product: ______
Use $-5 \times 2$ , $-5 \times 1$ , $-5 \times 0$ , $-5 \times (-1)$ to explain why two negatives multiply to a positive.

Part B · Multiplying and dividing

a) $-14 \times 5 =$ ______ b) $-9 \times (-11) =$ ______ c) $16 \times (-7) =$ ______ d) $-20 \times (-3) =$ ______
a) $-132 \div 11 =$ ______ b) $-64 \div (-8) =$ ______ c) $91 \div (-7) =$ ______
$(-2) \times (-5) \times (-3) =$ ______
Missing number: a) $-8 \times \underline{\ \ \ \ } = -96$ b) $\underline{\ \ \ \ } \div (-7) = 9$

PAGE 15 — Chapter 3 review, part 2

Chapter 3 Review (continued)

Part C · Absolute value expressions

a) $|6 - 14| =$ ______ b) $-|6 - 14| =$ ______
a) $|-5 + (-9)| =$ ______ b) $-|-5 + (-9)| =$ ______
a) $|-9 \times 3| =$ ______ b) $-|48 \div (-6)| =$ ______
$-|3 - 10| =$ ______ Where does it go on a number line? ______________________

Part D · In context

A diver at $-20$ ft descends 7 ft each minute for 6 minutes. Final depth: ______
A loss of $144 is shared equally among 8 people. Each share: ______
Estimate $-42 \times 29$ : ______ Exact: ______
The temperature is $-20$ °F and rises 4 degrees each hour. Hours until it reaches $0$ °F: ______

Which operation did you use, and why? _______________________________________________

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; in grayscale, add a "+" inside yellow chips and a "−" inside red chips
Blank number lines: page 9 needs an unlabeled line from $-15$ to $25$ ; page 10 needs one from $-10$ to $10$
Absolute value bars: set the vertical bars at full cap height so they do not read as the letter l or the digit 1
Answer blanks: keep every blank on the same line as its prompt so the Canva text box does not reflow