Introduction to Multiplying Decimals

• Understanding the importance of decimal multiplication.
• Overview of the lesson objectives.
• Essential question: How do we know where the decimal point goes when multiplying decimals?

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What is a Decimal?

• A decimal is a number that has a whole number part and a fractional part, separated by a decimal point (e.g., 2.5, 0.75).
• Decimals can represent parts of a whole in real-life situations (e.g., money, measurements).

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Real-World Applications

• Decimals are commonly used in everyday life, like shopping.
• Example: If a pack of gum costs $1.25, how much would 4 packs cost?

{The image of a pack of gum with its price tag showing $1.25, placed on a grocery store shelf.}

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Problem of the Day

• Multiply these two numbers:
  • 25 × 36 = ?
  • Now, multiply 2.5 × 3.6 = ?
• Reflection: What do you notice about the answers?

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Brain Break: Decimal Snap

• Quick exercise to engage students:
• Teacher says a multiplication fact (e.g., 3 × 4 = 12), and students snap fingers that many times.
• For decimals, students show the decimal point with their hands (e.g., for 0.3 × 0.4).

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Setting the Purpose

• Objective: I can multiply decimals and place the decimal correctly in the product.
• Essential Question: Why does multiplying decimals change the size of the product compared to whole numbers?

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Activating Prior Knowledge

• Quick review of multiplying whole numbers.
• Class discussion:
  • What happens when you multiply a number by one?
  • What happens when you multiply by something greater or less than one?

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The Rule of Decimal Multiplication

• Ignore the decimal when multiplying (treat as whole numbers).
• Multiply the numbers as if there were no decimals.
• Count the total decimal places from both factors.
• Place the decimal point in the product accordingly.

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Example 1: Basic Multiplication

• Example Calculation:
  • 2.4 × 1.3 = 3.12
• Explanation of steps:
  • 24 × 13 = 312
  • Total decimal places = 2 (1 in 2.4 and 1 in 1.3)
  • Therefore, the product is 3.12.

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Example 2: Multiplying Small Decimals

• Example Calculation:
  • 0.06 × 0.5 = 0.03
• Explanation of steps:
  • Multiply as whole numbers: 6 × 5 = 30
  • Total decimal places = 3 (2 in 0.06 and 1 in 0.5)
  • The product is 0.03.

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Guided Practice: Try It Yourself

• Work with a partner on the following problems:
  • 3.2 × 0.4
  • 1.25 × 2.5
• Real-World Scenario:
  • A gallon of gas costs $3.75. How much for 0.8 gallons?

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Checks for Understanding

• Ask students:
  • What’s the first step when multiplying decimals? (DOK 1)
  • Why do we count decimal places from both factors? (DOK 2)
  • How can you estimate if your decimal placement is reasonable? (DOK 3)

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Readiness Check

• Students who successfully solve two practice problems can move to Independent Practice.
• Struggling students will work in a reteach group with the teacher using money-related examples.

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Independent Practice

• Worksheet with problems:
  • Multiply decimals with one decimal place.
  • Multiply decimals with two or more decimal places.
• Include real-world word problems related to shopping or area calculations.

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Closed Device Time (CDT)

• Whole group activity:
  • “Estimate First!” game.
  • Students estimate the result of a decimal multiplication before calculating the exact product.
• Discuss results and reasonableness of the products.

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Small Group Instruction (SGI)

• During Independent Practice:
  • Focus on a group struggling with decimal placement.
  • Use base-ten blocks or visuals (e.g., money) to reinforce decimal rules.
• Other students will continue working independently or peer check.

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Closure: Exit Ticket

• Assign Exit Ticket:
  • Multiply 4.8 × 0.6. Show your work and explain how you decided where to put the decimal.
• Emphasize the importance of estimation in checking the placement of decimals.

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Key Takeaways

• Review the critical steps in multiplying decimals:
  • Ignore the decimal initially, multiply, then place the decimal correctly.
• Remember: Estimation helps ensure that the decimal placement is reasonable.

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Final Thoughts

• Multiplying decimals can be fun and relevant to your daily life.
• Keep practicing, and this will become easier with time!

{The image of a happy group of children discussing and solving math problems together in a classroom setting.}