Free Grade 3 Working with Sine Graph Lessons
Free Grade 3 lessons for Working with Sine Graph: 12 real questions with a full answer key and worked solutions. Charts show data visually. In a pie chart, each category's angle is its fraction of the total multiplied by 360°.
Free
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with sine graph
Explain working with sine graph accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with sine graph
Calculate working with sine graph accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with sine graph
Compare working with sine graph accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with sine graph
Justify working with sine graph 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 Sine Graph works
Charts show data visually. In a pie chart, each category's angle is its fraction of the total multiplied by 360°.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.In a survey: Red 10, Blue 4, Green 9, Yellow 14. In a pie chart, what angle does Yellow get?[1]
- 2.In a survey: Red 2, Blue 8, Green 2, Yellow 9. In a pie chart, what angle does Red get?[1]
- 3.In a survey: Red 8, Blue 7, Green 6, Yellow 14. In a pie chart, what angle does Blue get?[1]
- 4.In a survey: Red 10, Blue 4, Green 2, Yellow 4. In a pie chart, what angle does Blue get?[1]
- 5.In a survey: Red 12, Blue 11, Green 5, Yellow 11. In a pie chart, what angle does Blue get?[2]
- 6.In a survey: Red 2, Blue 12, Green 12, Yellow 7. In a pie chart, what angle does Yellow get?[2]
- 7.In a survey: Red 7, Blue 7, Green 5, Yellow 15. In a pie chart, what angle does Red get?[2]
- 8.In a survey: Red 8, Blue 8, Green 3, Yellow 7. In a pie chart, what angle does Blue get?[2]
- 9.In a survey: Red 13, Blue 11, Green 3, Yellow 12. In a pie chart, what angle does Blue get?[3]
- 10.In a survey: Red 3, Blue 7, Green 10, Yellow 2. In a pie chart, what angle does Green get?[3]
- 11.In a survey: Red 11, Blue 14, Green 2, Yellow 8. In a pie chart, what angle does Green get?[3]
- 12.In a survey: Red 4, Blue 15, Green 7, Yellow 9. In a pie chart, what angle does Red get?[3]
Show answers and working
1. 136.2°
Total = 37. Yellow fraction = 14/37. 14/37 × 360° = 136.2°.
2. 34.3°
Total = 21. Red fraction = 2/21. 2/21 × 360° = 34.3°.
3. 72°
Total = 35. Blue fraction = 7/35. 7/35 × 360° = 72°.
4. 72°
Total = 20. Blue fraction = 4/20. 4/20 × 360° = 72°.
5. 101.5°
Total = 39. Blue fraction = 11/39. 11/39 × 360° = 101.5°.
6. 76.4°
Total = 33. Yellow fraction = 7/33. 7/33 × 360° = 76.4°.
7. 74.1°
Total = 34. Red fraction = 7/34. 7/34 × 360° = 74.1°.
8. 110.8°
Total = 26. Blue fraction = 8/26. 8/26 × 360° = 110.8°.
9. 101.5°
Total = 39. Blue fraction = 11/39. 11/39 × 360° = 101.5°.
10. 163.6°
Total = 22. Green fraction = 10/22. 10/22 × 360° = 163.6°.
11. 20.6°
Total = 35. Green fraction = 2/35. 2/35 × 360° = 20.6°.
12. 41.1°
Total = 35. Red fraction = 4/35. 4/35 × 360° = 41.1°.
Worked examples
In a survey: Red 7, Blue 13, Green 12, Yellow 11. In a pie chart, what angle does Blue get?
- Total = 43.
- Blue fraction = 13/43.
- 13/43 × 360° = 108.8°.
- Answer: 108.8°
In a survey: Red 7, Blue 9, Green 3, Yellow 5. In a pie chart, what angle does Yellow get?
- Total = 24.
- Yellow fraction = 5/24.
- 5/24 × 360° = 75°.
- Answer: 75°
In a survey: Red 11, Blue 2, Green 7, Yellow 6. In a pie chart, what angle does Blue get?
- Total = 26.
- Blue fraction = 2/26.
- 2/26 × 360° = 27.7°.
- Answer: 27.7°
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Uses 100 instead of 360 for pie-chart angles.
Correction: A full circle is 360°.
Forgets to find the total first.
Correction: Add all frequencies before working out fractions.
Teacher tips
- · Have pupils check that all angles add to 360°.
Parent tips
- · Look at charts in the news and ask what they show.
Real-life applications
- · News infographics, survey results.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Working with Sine Graph
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Frequently asked
- Is this Grade 3 Working with Sine Graph 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 Sine Graph, Non-right-angled Trigonometry. 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 Sine Graph?
- Move on to Sine Graph in Context, Cosine Graph, Tangent Graph, Trigonometric Identities, which build directly on this idea.
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