Breaking Down: Error Analysis & Misconceptions
Mathematics
GCSE Higher
8 questions
~16 mins
1 views0 downloads
About This Worksheet
A worksheet focusing on breaking down complex shapes to find perimeters, highlighting common errors and misconceptions for GCSE Higher students.
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Breaking Down: Error Analysis & Misconceptions
Subject: MathematicsGrade: GCSE Higher
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Untitled Worksheet
Grade GCSE Higher
A
Introduction
Review the key concept: When breaking down complex shapes, perimeter is found by summing the lengths of all outer sides. Be cautious of overlapping sides or missing segments, which often cause errors.
B
Fluency & Practice
Answer the following questions to practice breaking down shapes and calculating perimeters.
1.
Calculate the perimeter of a shape formed by a rectangle of length 8 cm and width 3 cm, with a small rectangle of length 2 cm and width 1 cm removed from one corner. Break down the shape into simpler parts.
[3 marks]2.
A compound shape consists of a large square (side 10 cm) with a rectangular notch (3 cm by 4 cm) cut out from the top left corner. Using breaking down, find the perimeter.
[3 marks]3.
A shape combines a rectangle (6 cm by 4 cm) and a triangle (base 4 cm, height 3 cm) attached along one side. Break down and calculate the total perimeter.
[3 marks]C
Problem Solving & Reasoning
Solve these multi-step problems, explaining your reasoning and breaking down the shape into parts.
1.
A garden has a shape made by combining a rectangle (12 m by 8 m) and a semi-circle with a radius of 4 m attached along the longer side. Find the total perimeter of the garden, breaking down the shape into parts.
[4 marks]2.
A L-shaped room is formed by removing a smaller rectangle from a larger rectangle. The larger rectangle is 15 m by 10 m, and the cut-out rectangle is 5 m by 4 m. Break down the perimeter of the L-shape and find its total length.
[4 marks]D
Real-world Applications
Apply breaking down techniques to real-life scenarios involving perimeter calculations.
1.
A fence is to be built around a playground in the shape of an irregular polygon. The sides are 5 m, 7 m, 3 m, 8 m, and 6 m. Describe how to break down and find the total length of the fence.
[3 marks]E
Challenge & Extension
Attempt these more complex problems to extend your understanding.
1.
A composite shape consists of a rectangle (10 cm by 6 cm) with a smaller rectangle (3 cm by 4 cm) attached on top. The smaller rectangle overlaps the main rectangle by 1 cm. Break down the shape to find its perimeter, noting common mistakes students may make.
[4 marks]2.
A complex shape is formed by two rectangles of 8 cm by 5 cm and 6 cm by 4 cm, joined along a 4 cm side. Break down and calculate the perimeter, identifying potential errors.
[4 marks]Quick Actions
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Details
- Created
- 1/1/2026
- Updated
- 1/1/2026
- Type
- worksheet