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Multiplying & Dividing Integers

Seventh graders master the sign rules for multiplying and dividing integers — same signs make a positive, different signs make a negative — building fluency with positive and negative numbers.

Grade 7Integers50 minutes1 class periodGradual ReleaseExplicit teaching4 StandardsCommon Core
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Lesson at a Glance

Everything you need before the bell rings

Learning Objectives

Students will be able to…

  • ✓Multiply integers.
  • ✓Divide integers.
  • ✓Apply the sign rules.
  • ✓Explain why same signs give positive.
Essential Question

A negative times a negative equals a positive? It seems strange — but there’s a clear rule. How do signs behave when you multiply and divide?

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Lesson Phases
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Vocabulary Terms
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Standards Aligned
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Interactive Task
Model · Interactive Tool

The Sign Machine

Project this and change the signs and operation. Watch the result sign — same signs make positive, different signs make negative!

± Change the signs — see the result!Try it
1st sign
operation
2nd sign

The Lesson · Gradual Release (I Do · We Do · You Do)

50 minutes, five moves

Tap any phase to open the teacher moves and student actions.

1

Launch — Negative Times Negative

5 min

A negative times a negative equals a POSITIVE? How can that be?

👩‍🏫 Teacher Moves

  • Show (−)(−).
  • Ask what the sign should be.
  • Set the goal: sign rules.

🎒 Student Actions

  • See the signs.
  • Predict the result.
  • Wonder why.
2

I Do — The Sign Rules

10 min

Teacher models.

👩‍🏫 Teacher Moves

  • Same signs → positive.
  • Different signs → negative.
  • Show it for × and ÷.

🎒 Student Actions

  • Learn same-sign.
  • Learn different-sign.
  • See both.
3

We Do — Explore Together

13 min

Class uses the Sign Machine.

👩‍🏫 Teacher Moves

  • Change the signs.
  • Read the result sign.
  • State the rule.

🎒 Student Actions

  • Set the signs.
  • Read the sign.
  • Say the rule.
4

You Do — On Your Own

12 min

Students compute.

👩‍🏫 Teacher Moves

  • Multiply and divide integers.
  • Apply the sign rules.
  • Solve mixed problems.

🎒 Student Actions

  • Compute them.
  • Use the rules.
  • Solve them.
5

Close — Close

5 min

One problem.

👩‍🏫 Teacher Moves

  • Give an integer product/quotient.
  • Find it.
  • Hand out the exit ticket.

🎒 Student Actions

  • Find it.
  • Explain the sign.
  • Complete the exit ticket.
Standards Alignment

Built to the standards you report on

Aligned to the Common Core State Standards for Mathematics.

CCSS
7.NS.2

Apply properties of operations to multiply and divide rational numbers.

CCSS
7.NS.2a

Understand that products of integers follow sign rules.

CCSS
7.NS.2b

Understand integer division and its sign rules.

SMP
MP.7

Use structure in the sign rules.

Differentiation

One lesson, every learner

Multilingual Learners

ELL / EMERGING READERS
  • Sign-rule reference card.
  • Sentence frame: “Same signs make ___.”
  • Use a rule chart.

Support & Access

IEP / 504
  • Start with positive integers.
  • Use the sign chart.
  • Do one sign at a time.

Stretch & Extend

GIFTED / EARLY FINISHERS
  • Multiply and divide rationals.
  • Evaluate expressions with signs.
  • Explain the rule with patterns.
Materials

What to gather

  • 📽️Projector / board
  • 🧮Calculators
  • 💻The Sign Machine
  • 📄Sign-rule charts
  • ✏️Pencils
  • 🎫Exit-ticket slips
Vocabulary

Key terms — hover for a quick definition

integera positive or negative whole numberpositivegreater than zeronegativeless than zerosignpositive or negativeproductthe answer to multiplicationquotientthe answer to divisionoppositesame distance from zero, other siderational numbera number that can be written as a fraction
Evaluate

Exit Ticket

Preview the three formative checks. Tap “Sample answer” to see what mastery looks like — hide them before you print for students.

QUESTION 1
What is (−4) × (−5)?
20 (same signs make a positive).
QUESTION 2
What is (−18) ÷ (3)?
−6 (different signs make a negative).
QUESTION 3
What is the sign of a negative number times a positive number?
Negative (different signs).

Going deeper? Order of operations with signs.

Have students evaluate expressions that mix negative numbers with order of operations, like −2 × (3 − 7). A printable integer-operations sheet is in the Math library.

Study · Flashcards

Study the key terms

Tap a card to flip it, then rate whether you knew it. Built from this lesson’s vocabulary.

🃏 Multiplying & Dividing IntegersFlip
Card 1
Term
Tap to flip →
Meaning
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Practice · Quiz

Check your understanding

A quick self-check with instant feedback, drawn from this lesson’s key terms.

📝 Multiplying & Dividing IntegersQuiz
Score: 0
1 / 6
Question 1
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Practice · Worksheet

Printable worksheet

A print-and-go review sheet with a built-in answer key. Tap “Show answer key” to reveal answers, or print the clean version for students.

🖨️ Multiplying & Dividing IntegersPrint
Name: ________________________
Date: ____________

Part A · Write the word that matches each meaning

Word bank: integer, negative, opposite, positive, product, quotient, rational number, sign
  1. greater than zero
  2. the answer to multiplication
  3. less than zero
  4. same distance from zero, other side
  5. positive or negative
  6. a number that can be written as a fraction
  7. a positive or negative whole number
  8. the answer to division

Part B · Show what you learned

  1. What is (−4) × (−5)?
  2. What is (−18) ÷ (3)?
  3. What is the sign of a negative number times a positive number?
Answer key — Part A: 1) positive · 2) product · 3) negative · 4) opposite · 5) sign · 6) rational number · 7) integer · 8) quotient
Part B: 1) 20 (same signs make a positive). 2) −6 (different signs make a negative). 3) Negative (different signs).