Year 10 - Maths
Problem solving with advanced similarity knowledge
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/object is very useful.
- Being able to scale the perimeter/area/volume can reduce the number of calculations.
- This knowledge of similarity can be extended to include surface area.
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.
- Volume: The amount of space occupied by a closed 3D shape.
Common Mistakes To Avoid
- "One shape has an area that is 21% larger than another shape. I can't find the area scale factor between the shapes, since I don't know the actual area of either shape."
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/object is very useful. Being able to scale the perimeter/area/volume 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: "One shape has an area that is 21% larger than another shape. I can't find the area scale factor between the shapes, since I don't know the actual area of either shape.". Correction: It is possible to find scale factors, even if only a percentage that describes their areas is given. One shape will have an area of 100%, so the other shape will have an area 21% larger, at 121%. The scale factor is 1.21 because 100% × 1.21 = 121%.
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 similarity 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
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