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Integer Ops: Multiply!

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Lesson Plan

Integer Ops: Multiply!

Students will be able to confidently multiply positive and negative integers by applying the correct sign rules and performing calculations accurately.

Understanding how to multiply integers is a crucial skill for advanced mathematics, including algebra and problem-solving in real-world contexts like finances or temperature changes.

Audience

7th Grade

Time

30 minutes

Approach

Direct instruction, guided practice, and independent assessment.

Materials

Whiteboard or Projector, Integer Ops: Multiply! Slide Deck, Multiplying Integers Quiz, and Multiplying Integers Answer Key

Prep

Teacher Preparation

10 minutes

Step 1

Introduction: The Integer Puzzle

5 minutes

  • Begin by projecting the first slide of the Integer Ops: Multiply! Slide Deck.
    - Engage students with a quick warm-up question: "What happens when you multiply two positive numbers?" (e.g., 3 x 4).
    - Introduce the concept of multiplying integers by posing a scenario like "What if we owe three friends two dollars each? How much money do we 'owe' in total?" (relates to negative numbers).
    - Briefly explain that today's lesson will unlock the mystery of multiplying positive and negative numbers.

Step 2

Direct Instruction: Rules of the Game

10 minutes

  • Use the Integer Ops: Multiply! Slide Deck to teach the rules for multiplying integers.
    - Rule 1: Same Signs, Positive Product (e.g., positive x positive = positive; negative x negative = positive).
    - Rule 2: Different Signs, Negative Product (e.g., positive x negative = negative; negative x positive = negative).
    - Provide clear examples for each rule, walking through the steps.
    - Encourage students to ask questions and clarify any confusion.

Step 3

Guided Practice: Try It Out!

5 minutes

  • Display a few practice problems from the Integer Ops: Multiply! Slide Deck.
    - Work through these problems together as a class, asking students to identify the signs and predict the product's sign before calculating.
    - Provide immediate feedback and correct misunderstandings.
    - Optionally, have students work in pairs to solve one or two problems and share their answers.

Step 4

Independent Practice: Show What You Know

8 minutes

  • Distribute the Multiplying Integers Quiz to each student.
    - Instruct students to complete the quiz independently, applying the rules they just learned.
    - Circulate around the room to provide support and answer individual questions without giving direct answers.
    - Remind students to show their work if applicable.

Step 5

Wrap-Up: Quick Check

2 minutes

  • Collect the Multiplying Integers Quiz from students.
    - Briefly reiterate the main rules for multiplying integers.
    - Conclude by emphasizing the importance of these rules in future math concepts.
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Slide Deck

Integer Ops: Multiply!

What happens when you multiply two positive numbers? (e.g., 3 x 4)

What if we owe three friends two dollars each? How much money do we 'owe' in total?

Today, we're going to unlock the mystery of multiplying positive and negative numbers!

Greet students. Ask an engaging question to activate prior knowledge about multiplication. Introduce the day's topic.

Rule #1: Same Signs, Positive Product

  • When you multiply two numbers with the SAME sign, the answer is ALWAYS positive.

  • Positive (+) x Positive (+) = Positive (+)
    Example: 5 x 3 = 15

  • Negative (-) x Negative (-) = Positive (+)
    Example: -4 x -2 = 8

Introduce the first rule: same signs result in a positive product. Provide clear examples.

Rule #2: Different Signs, Negative Product

  • When you multiply two numbers with DIFFERENT signs, the answer is ALWAYS negative.

  • Positive (+) x Negative (-) = Negative (-)
    Example: 6 x -3 = -18

  • Negative (-) x Positive (+) = Negative (-)
    Example: -7 x 2 = -14

Introduce the second rule: different signs result in a negative product. Provide clear examples.

Practice Time!

Let's try these together:

  1. 8 x -2 =
  2. -5 x -6 =
  3. -9 x 3 =
  4. 10 x 4 =

Present a few practice problems. Guide students through solving them step-by-step, emphasizing the sign rules.

Time for Your Quiz!

Now it's your turn to show what you've learned!

Remember the rules:

  • Same signs, positive product!
  • Different signs, negative product!

Good luck!

Prepare students for the independent quiz. Remind them to apply the rules.

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Quiz

Multiplying Integers Quiz

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Answer Key

Multiplying Integers Answer Key

Here are the answers and explanations for the Multiplying Integers Quiz.

Question 1: What is 7 x (-4)?

  • Thought Process: We are multiplying a positive number (7) by a negative number (-4). When multiplying two numbers with different signs, the product is always negative.
  • Answer: B) -28

Question 2: Calculate -6 x -5.

  • Thought Process: We are multiplying a negative number (-6) by a negative number (-5). When multiplying two numbers with the same sign (both negative), the product is always positive.
  • Answer: C) 30

Question 3: What is -9 x 3?

  • Thought Process: We are multiplying a negative number (-9) by a positive number (3). When multiplying two numbers with different signs, the product is always negative.
  • Answer: -27

Question 4: Solve: 12 x (-2)

  • Thought Process: We are multiplying a positive number (12) by a negative number (-2). When multiplying two numbers with different signs, the product is always negative.
  • Answer: -24

Question 5: Which expression has a positive product?

  • Thought Process:
    • A) 4 x (-5) = -20 (different signs, negative product)
    • B) -8 x 2 = -16 (different signs, negative product)
    • C) -3 x -7 = 21 (same signs, positive product)
    • D) 10 x (-1) = -10 (different signs, negative product)
      Therefore, -3 x -7 is the only expression with a positive product.
  • Answer: C) -3 x -7

Question 6: Find the product: -11 x -3

  • Thought Process: We are multiplying two negative numbers (-11) and (-3). When multiplying two numbers with the same sign (both negative), the product is always positive.
  • Answer: 33

Question 7: If a submarine descends 3 feet per minute for 5 minutes, what is its total change in depth?

  • Thought Process: Descending 3 feet can be represented as -3. For 5 minutes, we multiply -3 by 5. A negative number multiplied by a positive number results in a negative product.
  • Answer: B) -15 feet

Question 8: Calculate: (-2) x 4 x (-3)

  • Thought Process: First, multiply -2 by 4, which gives -8 (different signs, negative product). Then, multiply -8 by -3. When multiplying two numbers with the same sign (both negative), the product is always positive.
  • Answer: 24
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Integer Ops: Multiply! • Lenny Learning