Year 8 - Maths
Multiplicative relationships in circles
Perimeter, area and volume
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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 extend their knowledge of shapes by exploring the properties of circles and composite shapes before developing understanding of 3-D shapes including surface area and volume.
Lesson Summary
You will learn to recognise that there is a constant multiplicative relationship (π) between the diameter and circumference of a circle.
Key Notes
- There is a multiplicative relationship between the radius and diameter of a circle.
- The ratio between the diameter and circumference of a circle is always the same.
- That ratio is called π and it is an irrational number.
- The formula for the circumference of a circle is C = πd.
- Using the definition of the diameter you can also write this as C = 2πr.
Vocabulary To Learn
- Diameter: The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre.
- Radius: The radius of a circle is any line segment that joins the centre of a circle to its edge.
- Circumference: The circumference of a circle is the perimeter of the circle.
Common Mistakes To Avoid
- Pupils may think that the π symbol represents a variable, similar to letters such as r and d.
3 Quick Questions (With Answers)
1. Solve this in steps: explain the method from this lesson and why each step matters.
There is a multiplicative relationship between the radius and diameter of a circle. The ratio between the diameter and circumference of a circle is always the same.
2. Use this key word in a maths sentence and explain it clearly. 'Diameter'
The diameter of a circle is any line segment that starts and ends on the edge of the circle and passes through the centre. Use this word when showing your method, then check your final answer is reasonable.
3. Spot and fix this common maths mistake.
Mistake: Pupils may think that the π symbol represents a variable, similar to letters such as r and d. Correction: Reiterate the difference between variables and constants. Explain that while the radius may differ between circles, π is always the same.
More Lessons In This Unit
- Area of a circle Study Guide
- Area of composite shapes Study Guide
- Checking understanding of area Study Guide
- Checking understanding of perimeter Study Guide
- Circumference of a circle Study Guide
- Finding a length in composite shapes Study Guide
- Perimeter of composite shapes Study Guide
- Problem solving with perimeter, area and volume Study Guide
- Properties of prisms Study Guide
- Surface area of cuboids Study Guide
- Surface area of cylinders Study Guide
- Surface area of prisms Study Guide
- Using the formula for the area of a circle Study Guide
- Volume of cylinders Study Guide
- Volume of prisms Study Guide
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