Mastering Decimals

Introduction

Objective

Students will develop a solid understanding of multiplying and dividing decimals using both multiples of ten and whole decimal numbers. By the end of the lesson, students will confidently solve both numeric problems and word problems involving decimals.

Curriculum Alignment

• California Common Core Standards:
  • Grade 7: CCSS.MATH.CONTENT.7.NS.A.2.D – Apply properties of operations as strategies to multiply and divide rational numbers.
  • Grade 8: CCSS.MATH.CONTENT.8.NS.A.1 – Know that numbers that are not rational are called irrational.

Materials Needed

• Whiteboard and markers
• Calculator (optional)
• Exit tickets (provided at the end of the lesson plan)
• Printed word problems (for student groups)

Lesson Outline

1. Warm-up (5 minutes)

• Activity: Quick mental math

  • Ask students quick mental multiplication and division questions involving whole numbers (e.g., 25 x 10, 50 ÷ 5) to warm up.

• Discussion: Briefly review place value concepts involved in multiplying and dividing by 10, 100, etc., focusing on shifting decimal places.

2. Direct Instruction (10 minutes)

• Demonstration: Calculating with Decimals

  • Using the whiteboard, demonstrate multiplying a decimal by a whole number (e.g., 2.34 x 10).
  • Explain the movement of decimal places during multiplication and division.
  • Highlight how to handle decimals in divisors (e.g., 4.56 ÷ 2).

• Practical Example:

  • Multiply: 1.75 x 10
  • Divide: 5.40 ÷ 0.5

3. Guided Practice (8 minutes)

• Interactive Activity:

  • Provide students with practice problems to solve in pairs:
    • Multiply: 3.8 x 100, 0.75 x 10
    • Divide: 9.6 ÷ 1.2, 10.5 ÷ 0.5

• Monitor and Support:

  • Walk around, check for understanding, and provide support where needed.
  • Encourage students to verbalize their thought process and strategies.

4. Independent Practice (5 minutes)

• Students independently solve a set of problems on paper:
  • Grade 7 Example: Multiply 6.2 by 0.1, Divide 7.5 by 2.5.
  • Grade 8 Example: Multiply 0.9 by 10.5, Divide 12.8 by 0.4.

5. Wrap-Up and Exit Ticket (2 minutes)

• Review key points and strategies.

• Distribute Exit Tickets:

  • Grade 7 Exit Ticket:

    • Multiply 3.6 by 10.
    • Divide 45.0 by 10.
    • Word Problem: If a pencil costs $2.50, how much do 10 pencils cost?
    • Word Problem: A ribbon is 9.6 metres long. It is cut into pieces each 1.2 metres long. How many pieces?

  • Grade 8 Exit Ticket:

    • Multiply 4.56 by 10.
    • Divide 108.0 by 0.9.
    • Word Problem: A pack of 6 apples costs $3.60. What is the cost of one apple?
    • Word Problem: A fabric roll is 11.25 metres long. If each section requires 1.25 metres, how many sections can be cut?

Assessment

• Collect and review exit tickets to assess student understanding.
• Identify common errors or misconceptions for future lessons and address them in the next class.

Reflection

This lesson sharpens students' skills in decimal multiplication and division, moving beyond rote computation into practical application. Encourage students to share strategies that work for them and explore different problem-solving pathways.