Free Grade 3 Introducing Tangent Ratio Lessons
Free Grade 3 lessons for Introducing Tangent Ratio: 12 real questions with a full answer key and worked solutions. A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
Free
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing tangent ratio
Explain introducing tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing tangent ratio
Calculate introducing tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing tangent ratio
Compare introducing tangent ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing tangent ratio
Justify introducing tangent ratio 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 Introducing Tangent Ratio works
A ratio compares parts of a whole. To share in a ratio, add the parts, find one part, then multiply.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.Simplify the ratio 60:12.[1]
- 2.Simplify the ratio 20:12.[1]
- 3.Simplify the ratio 6:24.[1]
- 4.Simplify the ratio 8:4.[1]
- 5.Share 96 in the ratio 2:6.[2]
- 6.Share 20 in the ratio 3:2.[2]
- 7.Share 9 in the ratio 1:2.[2]
- 8.Share 81 in the ratio 5:4.[2]
- 9.Share 72 in the ratio 5:3.[3]
- 10.Share 16 in the ratio 2:2.[3]
- 11.Share 33 in the ratio 2:1.[3]
- 12.Share 70 in the ratio 1:6.[3]
Show answers and working
1. 5:1
HCF of 60 and 12 is 12. Divide both parts by it: 5:1.
2. 5:3
HCF of 20 and 12 is 4. Divide both parts by it: 5:3.
3. 1:4
HCF of 6 and 24 is 6. Divide both parts by it: 1:4.
4. 2:1
HCF of 8 and 4 is 4. Divide both parts by it: 2:1.
5. 24 and 72
Total parts: 2 + 6 = 8. One part: 96 ÷ 8 = 12. 2 × 12 = 24, 6 × 12 = 72.
6. 12 and 8
Total parts: 3 + 2 = 5. One part: 20 ÷ 5 = 4. 3 × 4 = 12, 2 × 4 = 8.
7. 3 and 6
Total parts: 1 + 2 = 3. One part: 9 ÷ 3 = 3. 1 × 3 = 3, 2 × 3 = 6.
8. 45 and 36
Total parts: 5 + 4 = 9. One part: 81 ÷ 9 = 9. 5 × 9 = 45, 4 × 9 = 36.
9. 45 and 27
Total parts: 5 + 3 = 8. One part: 72 ÷ 8 = 9. 5 × 9 = 45, 3 × 9 = 27.
10. 8 and 8
Total parts: 2 + 2 = 4. One part: 16 ÷ 4 = 4. 2 × 4 = 8, 2 × 4 = 8.
11. 22 and 11
Total parts: 2 + 1 = 3. One part: 33 ÷ 3 = 11. 2 × 11 = 22, 1 × 11 = 11.
12. 10 and 60
Total parts: 1 + 6 = 7. One part: 70 ÷ 7 = 10. 1 × 10 = 10, 6 × 10 = 60.
Worked examples
Simplify the ratio 20:30.
- HCF of 20 and 30 is 10.
- Divide both parts by it: 2:3.
- Answer: 2:3
Share 18 in the ratio 1:2.
- Total parts: 1 + 2 = 3.
- One part: 18 ÷ 3 = 6.
- 1 × 6 = 6, 2 × 6 = 12.
- Answer: 6 and 12
Share 81 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 81 ÷ 9 = 9.
- 3 × 9 = 27, 6 × 9 = 54.
- Answer: 27 and 54
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Divides the total by the ratio numbers directly.
Correction: Add the parts first to find what one part is worth.
Writes the ratio in the wrong order.
Correction: Keep the order the question uses.
Teacher tips
- · Use bar models with equal-sized boxes for each part.
Parent tips
- · Make squash in a 1:4 ratio.
Real-life applications
- · Mixing paint or squash, scaling recipes.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Introducing Tangent Ratio
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Frequently asked
- Is this Grade 3 Introducing Tangent Ratio 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 Cosine Ratio. 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 Introducing Tangent Ratio?
- Move on to Working with Tangent Ratio, Tangent Ratio in Context, Sine Ratio, Cosine Ratio, which build directly on this idea.
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