Year 10 - Maths
Problem solving with similarity
Similarity
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This pupil-friendly study guide includes a unit summary, clear notes, common mistakes, and quick questions with answers.
Unit Summary
In this unit, pupils investigate the effect of an enlargement on the perimeter and area of a 2-D shape and the volume of a 3-D shape.
Lesson Summary
You will learn to use your knowledge of similarity to solve problems.
Key Notes
- A scaled version of a shape is very useful.
- Being able to scale the perimeter can reduce the number of calculations.
- Enlargement (transformations) and similar shapes are connected.
Vocabulary To Learn
- Similar: Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions.
- Invariant: A property of a shape is invariant if that property has not changed after the shape is transformed.
- Enlargement: Enlargement is a transformation that causes a change of size.
- Scale factor: A scale factor is the multiplier between similar shapes that describes how large one shape is compared to the other.
Common Mistakes To Avoid
- A ratio of 1 : 400 for a scale model of a car to a real car will have units of cm and metres, because a scale model is measured in cm and a real car is measured in metres.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
A scaled version of a shape is very useful. Being able to scale the perimeter can reduce the number of calculations.
2. Use this key word in a maths sentence and explain it clearly. 'Similar'
Two shapes are similar if the only difference between them is their size. Their side lengths are in the same proportions. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: A ratio of 1 : 400 for a scale model of a car to a real car will have units of cm and metres, because a scale model is measured in cm and a real car is measured in metres. Correction: Unless the scale explicitly includes different units of measure for each part, you must always use the same unit for each part of a ratio. So, 1 : 400 should be seen as 1 cm : 400 cm, not 400 metres, which is far too long for a car!
More Lessons In This Unit
- Checking and securing understanding of congruent triangles (ASA) Study Guide
- Checking and securing understanding of congruent triangles (RHS) Study Guide
- Checking and securing understanding of congruent triangles (SAS) Study Guide
- Checking and securing understanding of congruent triangles (SSS) Study Guide
- Checking and securing understanding of direct proportion in context Study Guide
- Problem solving with advanced similarity knowledge Study Guide
- The effect of enlargement on the area of a shape Study Guide
- The effect of enlargement on the perimeter of a shape Study Guide
- The effect of enlargement on the volume of a 3D shape Study Guide
- Using the scale factor for enlarging a volume Study Guide
- Using the scale factor for enlarging an area Study Guide
Browse all guides in the Year 10 Maths guide library.