Free Grade 3 Working with Circles Lessons
Free Grade 3 lessons for Working with Circles: 12 real questions with a full answer key and worked solutions. Perimeter is the distance around a shape; area is the space inside. Rectangle area = length × width; triangle = ½ × base × height; circle = πr².
Free
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with circles
Explain working with circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with circles
Calculate working with circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with circles
Compare working with circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with circles
Justify working with circles accurately in a familiar context.
Assessed by: Exit ticket of four short items
Prerequisites
Close these gaps first — each has its own free lesson, worksheet and quiz.
How Working with Circles works
Perimeter is the distance around a shape; area is the space inside. Rectangle area = length × width; triangle = ½ × base × height; circle = πr².
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.A rectangle is 8 cm by 15 cm. Find its perimeter and area.[1]
- 2.A rectangle is 14 cm by 8 cm. Find its perimeter and area.[1]
- 3.A rectangle is 3 cm by 9 cm. Find its perimeter and area.[1]
- 4.A rectangle is 2 cm by 6 cm. Find its perimeter and area.[1]
- 5.A triangle has base 22 cm and height 3 cm. Find its area.[2]
- 6.A triangle has base 22 cm and height 6 cm. Find its area.[2]
- 7.A triangle has base 28 cm and height 13 cm. Find its area.[2]
- 8.A triangle has base 16 cm and height 8 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 4 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 7 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 3 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 8 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 46 cm, area 120 cm²
Perimeter = 8 + 15 + 8 + 15 = 46 cm. Area = 8 × 15 = 120 cm².
2. Perimeter 44 cm, area 112 cm²
Perimeter = 14 + 8 + 14 + 8 = 44 cm. Area = 14 × 8 = 112 cm².
3. Perimeter 24 cm, area 27 cm²
Perimeter = 3 + 9 + 3 + 9 = 24 cm. Area = 3 × 9 = 27 cm².
4. Perimeter 16 cm, area 12 cm²
Perimeter = 2 + 6 + 2 + 6 = 16 cm. Area = 2 × 6 = 12 cm².
5. 33 cm²
Area = ½ × base × height. ½ × 22 × 3 = 33 cm².
6. 66 cm²
Area = ½ × base × height. ½ × 22 × 6 = 66 cm².
7. 182 cm²
Area = ½ × base × height. ½ × 28 × 13 = 182 cm².
8. 64 cm²
Area = ½ × base × height. ½ × 16 × 8 = 64 cm².
9. Area 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
10. Area 153.9 cm², circumference 44 cm
Area = πr² = π × 7² = 153.9 cm². Circumference = 2πr = 2 × π × 7 = 44 cm.
11. Area 28.3 cm², circumference 18.8 cm
Area = πr² = π × 3² = 28.3 cm². Circumference = 2πr = 2 × π × 3 = 18.8 cm.
12. Area 201.1 cm², circumference 50.3 cm
Area = πr² = π × 8² = 201.1 cm². Circumference = 2πr = 2 × π × 8 = 50.3 cm.
Worked examples
A rectangle is 15 cm by 13 cm. Find its perimeter and area.
- Perimeter = 15 + 13 + 15 + 13 = 56 cm.
- Area = 15 × 13 = 195 cm².
- Answer: Perimeter 56 cm, area 195 cm²
A triangle has base 28 cm and height 15 cm. Find its area.
- Area = ½ × base × height.
- ½ × 28 × 15 = 210 cm².
- Answer: 210 cm²
Find the area and circumference of a circle with radius 6 cm (to 1 d.p.).
- Area = πr² = π × 6² = 113.1 cm².
- Circumference = 2πr = 2 × π × 6 = 37.7 cm.
- Answer: Area 113.1 cm², circumference 37.7 cm
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up area and perimeter.
Correction: Perimeter is a fence (around), area is grass (inside).
Uses the slanted side as the height of a triangle.
Correction: Height must be at right angles to the base.
Teacher tips
- · Draw shapes on squared paper and count squares first.
Parent tips
- · Measure a room and work out how much carpet you'd need.
Real-life applications
- · Carpeting a room, fencing a garden.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Circles
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Learn — Meet the idea.
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Frequently asked
- Is this Grade 3 Working with Circles lesson really free?
- Yes. Every lessons on FreeMathWorksheet is free to use, print and share — no account, no paywall and no watermark.
- What should a learner already know before this?
- Start with Introducing Circles, Quadrilaterals. Each one has its own free lesson, worksheet and quiz.
- How is the lesson sequenced?
- Recognition first, then understanding, application, reasoning and finally mastery — the same ladder used across every free resource on the platform.
- What comes next after Working with Circles?
- Move on to Circles in Context, Triangles, Quadrilaterals, Polygons, which build directly on this idea.
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