Mastering Short Division

Learning Objectives (LO):

To use short division

Success Criteria:

By the end of the lesson, students will:

1. Understand how to set up short division calculations correctly.
2. Accurately divide using the short division method, including when remainders occur.
3. Begin to interpret remainders in context within word problems.

Key Vocabulary:

• Division
• Dividend
• Divisor
• Remainder
• Quotient
• Bus stop method

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Curriculum Area and Level:

National Curriculum – Year 5 KS2

• Programme of Study: Solve problems involving all four operations, including understanding the meaning of remainders and interpreting solutions in context using efficient methods.
• Focus Skill: Use formal written methods, including short division, with whole numbers within the range of numbers they can multiply and divide mentally.

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Lesson Overview:

Lesson Duration: 40 minutes
Class Context: 18 Year 5 students of middle to low ability.

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Lesson Structure

Starter Activity (5 Minutes)

Objective: Activate prior knowledge of division facts.

• Activity: Quick-fire division warm-up (written on the board or displayed on a presentation):
  • Divide mentally: 20 ÷ 4, 36 ÷ 6, 48 ÷ 8.
  • Focus on practising division facts for multiplication tables up to 12.
• Ask: "What is division? Can anyone explain in their own words?"
• Emphasise division as splitting or grouping.

Challenge Qs for discussion:

• "What happens if we cannot group the number equally?"
• Introduce the term remainder briefly to set the scene for the lesson.

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Main Lesson

Model 1: Basic 2-digit ÷ 1-digit (No Remainders) (10 Minutes)

E.g. 48 ÷ 4 = 12

1. Draw and label a "bus stop" division structure. Write 48 under the bus stop and 4 outside.
2. Explain step-by-step how the 4 fits into each digit:
   Ask:
   • "How many 4s fit into 4?" (Answer: 1)
   • "How many 4s fit into 8?" (Answer: 2).
3. Write the digits of the quotient above the bus stop and recap that the solution is 12.

Student involvement: Work through:

• 64 ÷ 8
• 72 ÷ 6
• 56 ÷ 7.

Teacher Questions:

• "Why do you think this method is called the bus stop method?"
• "Why is the divisor written outside the bus stop?"

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Model 2: 3-digit ÷ 1-digit (With Remainders) (10 Minutes)

E.g. 352 ÷ 3 = 117 remainder 1

1. Set up 352 ÷ 3 in the bus stop structure on the board.
2. Work through step-by-step:
   • 3 goes into 3 (hundreds place) 1 time. Write 1 on top.
   • 3 goes into 5 (tens place) 1 time, remainder 2.
   • Carry the remainder 2 over to make 22 in the units place.
   • 3 goes into 22 (units place) 7 times, remainder 1.
3. Write answer as: 117 remainder 1.
   Emphasise the carrying process. Use concrete examples like bundles of straws or counters for those struggling.

Student involvement: Solve together:

• 231 ÷ 2
• 462 ÷ 5.

Teacher Questions:

• "What do we do if the number isn’t in the times table of the divisor?"
• "What do we call the leftover value?"

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Model 3: Interpreting Word Problems Using Remainders (10 Minutes)

E.g. A farmer has 455 apples and puts them into bags of 6. How many full bags can he make, and how many apples will he have left over?

1. Solve the division: 455 ÷ 6 = 75 remainder 5.
2. Discuss what the remainder means:
   • 75 full bags of apples.
   • 5 apples left over that don't fully go into a bag.
3. Use context to explain why the whole number part of the division and the remainder both matter in these scenarios.

Student involvement: Scaffolded activity:

• Lisa buys 281 pencils and puts them in boxes of 9.
  • How many full boxes? How many are left?
• A builder has 348 bricks and uses them to make walls of 15 bricks. How many walls? How many bricks are left?

Teacher Questions:

• "Why is it important to understand what the remainder means in real life?"
• "If we wanted no remainder left, what could we do in this situation?"

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Plenary and Recap (5 Minutes)

• Quick true/false quiz (display or verbally present):

  • “Short division can only be used for 2-digit numbers.” (False)
  • “The number outside the bus stop is called the divisor.” (True)
  • “You always have a remainder in short division.” (False).

• Discussion: Ask students which part of short division they found easiest and which was trickiest. Encourage reflection.

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Differentiation:

• Lower Ability: Provide practical resources like counters or place value grids for remainder problems.
• Middle Ability: Focus on understanding the carrying process in 3-digit problems with a remainder.

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Assessment Checkpoints:

By the end of the lesson:

• Can students set up the bus stop correctly?
• Do students calculate accurately, accounting for remainders?
• Can students interpret what remainders mean in real-world scenarios?

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Resources Required:

• Whiteboard and marker.
• Division problem cards for examples (pre-prepared).
• Counters or blocks for lower-ability students.

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This creative and scaffolded approach is designed to make short division accessible, enjoyable, and meaningful for all Year 5 learners!