Partitioning: Challenge & Extension
Mathematics
Year 9
14 questions
~28 mins
1 views0 downloads
About This Worksheet
A worksheet exploring advanced partitioning techniques within Place Value to Millions, designed to challenge Year 9 students.
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Partitioning: Challenge & Extension
Subject: MathematicsGrade: Year 9
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Untitled Worksheet
Grade Year 9
A
Fluency & Practice
Answer all questions. Use the grid to partition numbers as required.
1.
Partition 4,587,032 into hundreds of thousands, ten thousands, thousands, hundreds, tens, and units.
[3 marks]2.
Write 362,749 as a sum of its partitioned components.
[2 marks]3.
Partition 7,045,206 into its place value components.
[3 marks]4.
Express 1,234,567 as the sum of its parts.
[2 marks]B
Problem Solving & Reasoning
Solve the following multi-step problems and explain your reasoning.
1.
A supermarket has 2,583,416 items. If they are grouped into packets of 4,000 items each, how many full packets are needed? Show your working.
[4 marks]2.
A company orders 1,245,379 units of a product. They want to divide the total into equal groups of 10,000 units each. How many groups will there be? Explain your calculation.
[4 marks]C
Real-world Applications
Apply your partitioning skills to these real-world word problems.
1.
A library has 5,768,290 books. They are arranged into sections containing 50,000 books each. How many sections are formed? How many books are left ungrouped? Show all steps.
[4 marks]2.
A factory produces 9,456,781 items annually. If each shipment contains 250,000 items, how many shipments are needed per year? How many items are in the last shipment?
[4 marks]D
Challenge & Extension
Tackle these advanced problems involving partitioning.
1.
Construct a number greater than 3,000,000 that can be partitioned into exactly seven distinct parts, each divisible by 100,000. Provide the number and its partition.
[4 marks]2.
Find a number between 5,000,000 and 6,000,000 that, when partitioned, has all parts ending with zero and includes exactly five parts. Explain your reasoning.
[4 marks]E
Mixed Review
Answer these questions to review your understanding of partitioning.
1.
Partition 6,789,012 into hundreds of thousands, ten thousands, thousands, hundreds, tens, and units.
[3 marks]2.
Express 985,324 as a sum of its partitioned parts.
[2 marks]F
Error Analysis
Identify and correct the mistake in each of the following partitioning attempts.
1.
A student partitioned 2,345,678 as 2,000,000 + 300,000 + 40,000 + 5,000 + 600 + 70 + 8, but forgot to include the 3,000. Find and correct the mistake.
[3 marks]2.
A student wrote 1,234,567 as 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7, but made an error in the placement. Identify the mistake and correct it.
[3 marks]Quick Actions
What is Remix?
Create a new worksheet based on this one. Change the grade level, topic, number of questions, or difficulty - then generate a fresh version.
- • Change grade level (Grade 6 → Grade 7)
- • Swap topics (Harry Potter → Macbeth)
- • Add more questions (10 → 15)
- • Adjust difficulty
Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet