Free Grade 3 Introducing Cosine Ratio Lessons
Free Grade 3 lessons for Introducing Cosine 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
Core
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing cosine ratio
Explain introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing cosine ratio
Calculate introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing cosine ratio
Compare introducing cosine ratio accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing cosine ratio
Justify introducing cosine 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 Cosine 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 8:12.[1]
- 2.Simplify the ratio 12:60.[1]
- 3.Simplify the ratio 24:40.[1]
- 4.Simplify the ratio 40:10.[1]
- 5.Share 30 in the ratio 4:6.[2]
- 6.Share 45 in the ratio 1:4.[2]
- 7.Share 40 in the ratio 3:5.[2]
- 8.Share 88 in the ratio 5:3.[2]
- 9.Share 20 in the ratio 1:3.[3]
- 10.Share 54 in the ratio 1:5.[3]
- 11.Share 32 in the ratio 3:1.[3]
- 12.Share 56 in the ratio 4:4.[3]
Show answers and working
1. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
2. 1:5
HCF of 12 and 60 is 12. Divide both parts by it: 1:5.
3. 3:5
HCF of 24 and 40 is 8. Divide both parts by it: 3:5.
4. 4:1
HCF of 40 and 10 is 10. Divide both parts by it: 4:1.
5. 12 and 18
Total parts: 4 + 6 = 10. One part: 30 ÷ 10 = 3. 4 × 3 = 12, 6 × 3 = 18.
6. 9 and 36
Total parts: 1 + 4 = 5. One part: 45 ÷ 5 = 9. 1 × 9 = 9, 4 × 9 = 36.
7. 15 and 25
Total parts: 3 + 5 = 8. One part: 40 ÷ 8 = 5. 3 × 5 = 15, 5 × 5 = 25.
8. 55 and 33
Total parts: 5 + 3 = 8. One part: 88 ÷ 8 = 11. 5 × 11 = 55, 3 × 11 = 33.
9. 5 and 15
Total parts: 1 + 3 = 4. One part: 20 ÷ 4 = 5. 1 × 5 = 5, 3 × 5 = 15.
10. 9 and 45
Total parts: 1 + 5 = 6. One part: 54 ÷ 6 = 9. 1 × 9 = 9, 5 × 9 = 45.
11. 24 and 8
Total parts: 3 + 1 = 4. One part: 32 ÷ 4 = 8. 3 × 8 = 24, 1 × 8 = 8.
12. 28 and 28
Total parts: 4 + 4 = 8. One part: 56 ÷ 8 = 7. 4 × 7 = 28, 4 × 7 = 28.
Worked examples
Simplify the ratio 20:4.
- HCF of 20 and 4 is 4.
- Divide both parts by it: 5:1.
- Answer: 5:1
Share 40 in the ratio 2:3.
- Total parts: 2 + 3 = 5.
- One part: 40 ÷ 5 = 8.
- 2 × 8 = 16, 3 × 8 = 24.
- Answer: 16 and 24
Share 12 in the ratio 1:1.
- Total parts: 1 + 1 = 2.
- One part: 12 ÷ 2 = 6.
- 1 × 6 = 6, 1 × 6 = 6.
- Answer: 6 and 6
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 Cosine Ratio
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Frequently asked
- Is this Grade 3 Introducing Cosine 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 Sine 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 Cosine Ratio?
- Move on to Working with Cosine Ratio, Cosine Ratio in Context, Sine Ratio, Tangent Ratio, which build directly on this idea.
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