Dividing by Decimals

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Overview

Lesson Title: Dividing Whole Numbers by Decimals
Unit Title: Decimals in Division (Lesson 3 of 5)
Year Group: Year 7
Time Allocation: 60 minutes
Class Size: 27 students
UK Curriculum Reference: Key Stage 3 Mathematics - Number, specifically performing calculations with decimals and interpreting the result in context.

Learning Objectives

By the end of this lesson, students will be able to:

1. Understand how to convert divisions involving decimals into simpler calculations by multiplying both the divisor and dividend by powers of ten.
2. Accurately divide whole numbers by decimals and interpret the results.
3. Apply these techniques to solve real-world problems involving decimal division.

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Lesson Structure

1. Starter Activity (10 Minutes)

Objective: Recap understanding of decimals and set the stage for dividing by decimals.

1. Quick Brain Teaser (5 minutes): Write the following question on the board:
   Why is dividing by 0.5 the same as multiplying by 2? Does this work for all decimals? Discuss briefly and allow students to voice ideas.
   Example discussion answer: Converting 0.5 to 5/10 shows it’s half of 1, so twice of any number fits back to 1 of it.

2. Mini Review (5 minutes): Revisit key prior knowledge from Lesson 2 (Dividing Decimals by Whole Numbers). Use these examples to warm up students:

   • 24 ÷ 6
   • 12 ÷ 0.5 (hint at the need to convert)

Ask students to attempt these questions on their mini whiteboards as you circulate to check engagement.

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2. Main Teaching (15 Minutes)

Objective: Teach how to divide whole numbers by decimals using transformations.

1. Key Concept Introduction (5 minutes): Using clear mathematical language, explain:

   • A division problem like 24 ÷ 0.4 can feel tricky because the divisor (0.4) is a decimal.
   • Simplify by multiplying both the dividend (24) and the divisor (0.4) by 10 to create a simpler equivalent problem: 240 ÷ 4.
   • Now, solve this as a whole-number division to get the result.
     Draw this process on the board with the equation:

   24 ÷ 0.4  
   = (24 x 10) ÷ (0.4 x 10)  
   = 240 ÷ 4  
   = 60  
   

2. Teacher-Guided Example (5 minutes): Work through additional examples with the class:

   • Example 1: 36 ÷ 0.3
   • Example 2: 45 ÷ 0.15 (introduce multiplying by 100 to deal with two decimal places).

3. Key Steps Anchor Chart (5 minutes): Create a steps-based problem-solving chart on the board:

   • Identify the divisor (the number you're dividing by).
   • Multiply both the divisor and dividend by the same power of 10 to remove the decimal in the divisor.
   • Perform the division as a whole-number operation.
   • Interpret the result.

Ask students to copy this into their notebooks and underline key terms.

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3. Classroom Activity: Paired Practice (20 Minutes)

Objective: Build student confidence through collaborative problem-solving.

1. Partner Tasks (15 minutes):
   Split students into pairs and distribute a worksheet with the following questions:

   • Calculate:
     1. 56 ÷ 0.7
     2. 81 ÷ 0.9
     3. 12 ÷ 0.25
     4. 48 ÷ 0.06
     5. Challenge Extension: If x ÷ 0.04 = 125, find x.

   Encourage pairs to follow the steps learned earlier and show all their workings clearly. Teachers circulate and provide scaffolding to students who need additional support.

   Differentiation:

   • Fast finishers tackle bonus word problems:
     A car travels 36 miles on 0.8 gallons of petrol. How far can it go on 1 gallon?
   • Students needing more guidance start with simpler divisions, e.g. 20 ÷ 0.5.

2. Interactive Peer Review (5 minutes): Ask students to swap their worksheets with another pair and mark them using the answer key provided on the board. Discuss where most common errors occurred (e.g., forgetting to scale both numbers by the same factor).

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4. Plenary (10 Minutes)

Objective: Solidify today's learning and connect it to real-life applications.

1. ‘Think-Pair-Share’ Discussion (5 minutes):
   Pose an open-ended question to the class:
   "Why do you think being able to divide by decimals is important in real life? Can you brainstorm examples?"

   • Examples might include grocery prices, fuel efficiency, or recipe scaling.

2. Exit Ticket (5 minutes):
   Distribute a slip of paper to each student with one unique problem like:

   • 72 ÷ 0.8
   • 50 ÷ 0.25

Ask students to solve it and write down the three-step method they used on the back of the ticket. Collect these as they leave the classroom to assess understanding.

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Resources and Materials Needed

• Whiteboard and markers
• Mini whiteboards and pens for students
• Pre-prepared Anchor Chart for “Key Steps”
• Partner Worksheet with practice problems
• Exit Tickets

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Homework Assignment

For homework, ask students to complete 6 questions in their maths workbooks, similar to those covered in class. Include a word problem encouraging real-world application:
"A worker earns £12.75 an hour and works for 0.8 hours. How much do they earn for that period?"

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Assessment Opportunities

• Formative: Observe responses during the starter activity and circulate during paired practice to gauge understanding.
• Summative: Exit tickets provide insight into individual mastery of the lesson’s method.

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Reflection and Next Steps

Encourage students to reflect on their learning by writing down one question they still have about dividing by decimals. Start Lesson 4 by addressing the most common concerns.