Free Grade 3 Symmetry Lessons
Free Grade 3 lessons for Symmetry: 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 symmetry
Explain symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate symmetry
Calculate symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare symmetry
Compare symmetry accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify symmetry
Justify symmetry 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 Symmetry 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 3 cm. Find its perimeter and area.[1]
- 2.A rectangle is 7 cm by 11 cm. Find its perimeter and area.[1]
- 3.A rectangle is 5 cm by 8 cm. Find its perimeter and area.[1]
- 4.A rectangle is 13 cm by 14 cm. Find its perimeter and area.[1]
- 5.A triangle has base 28 cm and height 13 cm. Find its area.[2]
- 6.A triangle has base 26 cm and height 15 cm. Find its area.[2]
- 7.A triangle has base 6 cm and height 2 cm. Find its area.[2]
- 8.A triangle has base 8 cm and height 10 cm. Find its area.[2]
- 9.Find the area and circumference of a circle with radius 9 cm (to 1 d.p.).[3]
- 10.Find the area and circumference of a circle with radius 11 cm (to 1 d.p.).[3]
- 11.Find the area and circumference of a circle with radius 6 cm (to 1 d.p.).[3]
- 12.Find the area and circumference of a circle with radius 4 cm (to 1 d.p.).[3]
Show answers and working
1. Perimeter 22 cm, area 24 cm²
Perimeter = 8 + 3 + 8 + 3 = 22 cm. Area = 8 × 3 = 24 cm².
2. Perimeter 36 cm, area 77 cm²
Perimeter = 7 + 11 + 7 + 11 = 36 cm. Area = 7 × 11 = 77 cm².
3. Perimeter 26 cm, area 40 cm²
Perimeter = 5 + 8 + 5 + 8 = 26 cm. Area = 5 × 8 = 40 cm².
4. Perimeter 54 cm, area 182 cm²
Perimeter = 13 + 14 + 13 + 14 = 54 cm. Area = 13 × 14 = 182 cm².
5. 182 cm²
Area = ½ × base × height. ½ × 28 × 13 = 182 cm².
6. 195 cm²
Area = ½ × base × height. ½ × 26 × 15 = 195 cm².
7. 6 cm²
Area = ½ × base × height. ½ × 6 × 2 = 6 cm².
8. 40 cm²
Area = ½ × base × height. ½ × 8 × 10 = 40 cm².
9. Area 254.5 cm², circumference 56.5 cm
Area = πr² = π × 9² = 254.5 cm². Circumference = 2πr = 2 × π × 9 = 56.5 cm.
10. Area 380.1 cm², circumference 69.1 cm
Area = πr² = π × 11² = 380.1 cm². Circumference = 2πr = 2 × π × 11 = 69.1 cm.
11. Area 113.1 cm², circumference 37.7 cm
Area = πr² = π × 6² = 113.1 cm². Circumference = 2πr = 2 × π × 6 = 37.7 cm.
12. Area 50.3 cm², circumference 25.1 cm
Area = πr² = π × 4² = 50.3 cm². Circumference = 2πr = 2 × π × 4 = 25.1 cm.
Worked examples
A rectangle is 14 cm by 7 cm. Find its perimeter and area.
- Perimeter = 14 + 7 + 14 + 7 = 42 cm.
- Area = 14 × 7 = 98 cm².
- Answer: Perimeter 42 cm, area 98 cm²
A triangle has base 12 cm and height 3 cm. Find its area.
- Area = ½ × base × height.
- ½ × 12 × 3 = 18 cm².
- Answer: 18 cm²
Find the area and circumference of a circle with radius 7 cm (to 1 d.p.).
- Area = πr² = π × 7² = 153.9 cm².
- Circumference = 2πr = 2 × π × 7 = 44 cm.
- Answer: Area 153.9 cm², circumference 44 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 Symmetry
One concept, one ecosystem — all of it free.
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The entities below this one, each with the same complete free resource set.
Sibling concepts
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Lateral links, including across subjects.
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Symmetry 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 Polygons, Circles, Angles. 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 Symmetry?
- Move on to Angles, Perimeter and Area, 3D Shapes, Transformations, which build directly on this idea.
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