Pattern Recognition: Error Analysis & Misconceptions
Mathematics
Grade 6
13 questions
~26 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on pattern recognition in geometric sequences, emphasizing error analysis and addressing common misconceptions for Grade 6 students.
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Pattern Recognition: Error Analysis & Misconceptions
Subject: MathematicsGrade: Grade 6
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Untitled Worksheet
Grade Grade 6
A
Introduction
Review the key concept: In a geometric sequence, each term is found by multiplying the previous term by a common ratio. The general formula is a_n = a_1 * r^(n-1).
B
Fluency & Practice
Answer the following questions to practice your understanding of geometric sequences.
1.
Find the 5th term of the sequence where the first term is 3 and the common ratio is 2.
[2 marks]2.
Calculate the common ratio if the first term is 5 and the third term is 20.
[2 marks]3.
Determine the 7th term of the sequence: 2, 6, 18, ...
[2 marks]4.
What is the first term if the 4th term is 32 and the common ratio is 2?
[2 marks]C
Problem Solving & Reasoning
Analyze the following situations and explain your reasoning.
1.
A sequence starts with 4, and each term is multiplied by 3 to get the next. What is the 6th term? Explain your steps.
[3 marks]2.
If a mistake is made by adding instead of multiplying to find each term in a geometric sequence, what pattern do you get? How does it differ from the correct sequence?
[3 marks]D
Real-world Applications
Solve these word problems based on real-life contexts.
1.
A bacteria culture doubles in size every hour. If it starts with 5 bacteria, how many bacteria are there after 4 hours?
[3 marks]2.
A savings account earns 5% interest compounded yearly. If you start with $100, how much will you have after 3 years? (Use the sequence formula).
[3 marks]E
Challenge & Extension
Attempt these advanced problems to extend your understanding.
1.
Given a geometric sequence where the 2nd term is 8 and the 4th term is 32, find the first term and the common ratio.
[4 marks]2.
Construct a sequence that starts with 3 and has a common ratio of 0.5. What is the 5th term? Show your work.
[3 marks]F
Mixed Review & Error Analysis
Review these common mistakes and answer the questions.
1.
A student calculates the 4th term of a sequence by multiplying the 2nd term by 4. Identify and explain the mistake.
[2 marks]2.
A sequence is given as 5, 10, 20, 40, ... but a student claims it is geometric with ratio 2. Is this correct? Why or why not?
[2 marks]3.
Correct the following incorrect sequence: 1, 3, 7, 15, ...
[2 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