Ordering: Error Analysis & Misconceptions
Mathematics
GCSE Foundation
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on understanding and correcting misconceptions related to ordering numbers to the billions. Designed to develop procedural skills, reasoning, and real-world application for GCSE Foundation students.
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Ordering: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Foundation
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Untitled Worksheet
Grade GCSE Foundation
A
Fluency & Practice
Answer all questions carefully. Show your working in the grid spaces provided where necessary.
1.
Arrange the following numbers in ascending order: 3,245,678, 3,456,789, 3,278,901.
[2 marks]2.
Order these numbers from largest to smallest: 12,345,678; 12,345,679; 12,345,677.
[2 marks]3.
List the numbers 7,654,321 and 7,654,312 in order from smallest to largest.
[2 marks]4.
Arrange the following numbers in descending order: 5,678,901, 5,689,012, 5,678,905.
[2 marks]B
Problem Solving & Reasoning
Answer the questions thoughtfully, explaining your reasoning clearly.
1.
Two numbers differ by 1,234,567. If one is 4,567,890, what is the other? Explain how you determine your answer.
[4 marks]2.
A customer has a bank balance of 7,890,123. They spend 2,345,678. What is the new balance? Show your working.
[3 marks]3.
A data set includes the numbers 1,234,567; 1,234,568; 1,234,569. Identify the order from smallest to largest and justify your choice.
[4 marks]C
Real-world Applications
Read the scenarios carefully and answer the questions based on practical contexts.
1.
A company's revenue for four years was: 1,234,567, 2,345,678, 1,987,654, and 2,123,456. Arrange these figures from highest to lowest to determine the best year.
[3 marks]2.
A car's odometer shows 9,876,543 miles. After a long trip, it shows 10,123,456 miles. How many miles were traveled? Explain your reasoning.
[3 marks]D
Challenge & Extension
Attempt these challenging questions to extend your understanding.
1.
Construct two six-digit numbers where the first is greater than the second, but the hundreds digit in both is the same. Explain your construction process.
[4 marks]2.
Determine the correct order when comparing 9,876,543 and 9,876,534, and justify your answer.
[2 marks]E
Mixed Review & Error Analysis
Identify the mistakes in the following questions and correct them.
1.
Incorrectly ordered: 3,456,789; 3,456,700; 3,456,780. Find the mistake and correct the order.
[3 marks]2.
A student claims 12,345,678 is less than 12,345,678. Identify the error and explain how to properly compare these numbers.
[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