Dividing Decimals Easily

Lesson Overview

• Year Group: Year 7
• Subject: Mathematics
• Curriculum Area: Key Stage 3 – Fractions, Decimals, and Percentages
• Specific Aim: Develop fluency in dividing decimals by decimals and build confidence in choosing efficient methods to simplify calculations.
• Level: UK National Curriculum, Year 7 Mathematics – Pupils should be able to "solve problems involving numbers with up to three decimal places."
• Unit Context: This is the fifth and final lesson in the unit Decimals in Division. Students will consolidate their understanding of previously learned skills and apply them to solve more complex problems involving division of decimals.

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Lesson Objectives

By the end of this 60-minute lesson, students will:

1. Understand and apply strategies to simplify division problems involving decimals.
2. Confidently divide decimals by decimals, up to three decimal places.
3. Reflect on and articulate their progress across the unit through structured group discussions.
4. Apply their skills to solve real-world problems involving decimal division.

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Lesson Structure

1. Starter Activity – Mental Maths Challenge (10 minutes)

Objective: Activate prior learning and warm up decimal division skills.

• Teacher Instructions: Display 5 rapid-fire questions on the board for students to solve independently, e.g.:

  1. 8 ÷ 2
  2. 12.4 ÷ 4
  3. 7 ÷ 0.2
  4. 0.98 ÷ 7
  5. 3.6 ÷ 1.2

• Use a timer (visible on the board) to create a sense of urgency and fun. Students write answers in their maths exercise books.

• Discuss answers: Elicit strategies students used and highlight efficiency (e.g., multiplying both numbers by 10 to eliminate decimals).

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2. Mini-Teach: Simplifying Division of Decimals (15 minutes)

Objective: Teach a concrete method for dividing decimals by decimals using visual examples.

1. Introduction: Begin by writing "1.8 ÷ 0.6" on the board. Ask students whether this can be solved easily and what might make it tricky.

2. Explain the Strategy:

   • If we multiply both the dividend (1.8) and divisor (0.6) by 10 to eliminate the decimals, we get "18 ÷ 6".
   • Write this transformation on the board and solve: 18 ÷ 6 = 3.
   • Emphasise that shifting the decimal point doesn’t change the original problem — we are simply simplifying to make it easier to solve!

3. Group Example:

   • Work through another example together: 3.78 ÷ 1.2. Guide students step-by-step:
     a) Multiply both by 10 → 37.8 ÷ 12.
     b) Perform the division → 3.15.
     c) Write the final answer and explain each stage.

4. Reflection Question: Why does this method work? Ask students to turn to their partner and share ideas before discussing as a class.

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3. Group Practice Rotations (25 minutes)

Objective: Practise skills through collaborative group work while applying the taught strategy.

• Structure: Divide the class of 27 students into groups of 3 (9 groups total). Each group rotates between three collaborative challenge stations:

Station 1: Skill Drill

• Solve 6 progressively harder division problems, e.g.:

  1. 4.5 ÷ 0.9
  2. 7.56 ÷ 1.2
  3. 0.72 ÷ 0.6
  4. 15.48 ÷ 0.3
  5. 0.009 ÷ 0.03
  6. 56.763 ÷ 27.

• Students use whiteboards to record their work step-by-step, showing how they simplified each problem.

• Quick teacher check: float between groups to observe and clarify misunderstandings.

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Station 2: Real-World Problems

• Apply decimal division to solve realistic scenarios. Example problems:

  1. If a car travels 245.76 miles using 14.4 gallons of fuel, what is the mileage per gallon?
  2. A recipe requires 0.36 kg of sugar for 3 cakes. How much sugar is needed for 1 cake?

• Encourage discussion within groups to decide how to approach each problem.

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Station 3: Creative Task

• Design a "tricky decimal division" problem for another group to solve.

• Encourage creativity within groups — they should focus on making the problem realistic but challenging. Once solved, groups can swap problems and test each other.

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4. Plenary and Reflection (10 minutes)

Objective: Summarise learning and reinforce progress from the unit.

1. Recap Key Learning: On the board, write:

   • Step 1: Eliminate decimals by multiplying both numbers by 10, 100, etc.
   • Step 2: Perform the division as usual.
   • Step 3: Interpret the result in context.

   Ask students to repeat this out loud together and share which step they find easiest/trickiest.

2. Whole-Class Reflection:

   • Prompts for discussion:

     1. "How has your confidence with decimal division improved throughout this unit?"
     2. "What is one strategy you will use when dividing decimals going forward?"

   • Use “cold call” questioning to involve as many different students as possible in the discussion.

3. Exit Ticket:
   Write a problem on the board (e.g., 13.2 ÷ 0.4). Students solve it independently in their books before leaving class.

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Homework

• Differentiated practice sheet with 10 problems, ranging from straightforward calculations to worded problems involving decimal division.
• Extension challenge: Create a real-life problem involving dividing decimals for a family member to solve.

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Resources Needed

1. Whiteboards and markers for group activities.
2. Maths exercise books.
3. Challenge cards for Station Rotations (pre-prepared by the teacher).
4. Timing tool (visible stopwatch or timer for the board).

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Assessment and Differentiation

• Assessment of Learning:

  • Formative assessment through observation during rotations and plenary discussions.
  • Exit ticket checked for accuracy and method.

• Differentiation Strategies:

  • Peer support in group rotations.
  • Stretch tasks for higher-ability students, e.g., solving problems involving division of four-decimal-place numbers or creating word problems with larger numbers.
  • Teacher scaffolding with small group support, focusing on pupils requiring extra guidance.

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Teacher’s Reflection Prompt

• Was the collaborative element of the lesson engaging and effective?
• Did students demonstrate fluency and confidence when working on real-world decimal problems?
• How well did the overall unit prepare students for future use of decimals in GCSE problem-solving scenarios?