Free Grade 3 Introducing Cosine Ratio Flashcards
Free Grade 3 flashcards 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
Higher
20 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 6:24.[1]
- 2.Simplify the ratio 10:20.[1]
- 3.Simplify the ratio 24:12.[1]
- 4.Simplify the ratio 6:6.[1]
- 5.Share 21 in the ratio 2:5.[2]
- 6.Share 42 in the ratio 4:2.[2]
- 7.Share 12 in the ratio 3:3.[2]
- 8.Share 63 in the ratio 2:5.[2]
- 9.Share 56 in the ratio 1:7.[3]
- 10.Share 108 in the ratio 5:7.[3]
- 11.Share 77 in the ratio 4:7.[3]
- 12.Share 44 in the ratio 5:6.[3]
Show answers and working
1. 1:4
HCF of 6 and 24 is 6. Divide both parts by it: 1:4.
2. 1:2
HCF of 10 and 20 is 10. Divide both parts by it: 1:2.
3. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
4. 1:1
HCF of 6 and 6 is 6. Divide both parts by it: 1:1.
5. 6 and 15
Total parts: 2 + 5 = 7. One part: 21 ÷ 7 = 3. 2 × 3 = 6, 5 × 3 = 15.
6. 28 and 14
Total parts: 4 + 2 = 6. One part: 42 ÷ 6 = 7. 4 × 7 = 28, 2 × 7 = 14.
7. 6 and 6
Total parts: 3 + 3 = 6. One part: 12 ÷ 6 = 2. 3 × 2 = 6, 3 × 2 = 6.
8. 18 and 45
Total parts: 2 + 5 = 7. One part: 63 ÷ 7 = 9. 2 × 9 = 18, 5 × 9 = 45.
9. 7 and 49
Total parts: 1 + 7 = 8. One part: 56 ÷ 8 = 7. 1 × 7 = 7, 7 × 7 = 49.
10. 45 and 63
Total parts: 5 + 7 = 12. One part: 108 ÷ 12 = 9. 5 × 9 = 45, 7 × 9 = 63.
11. 28 and 49
Total parts: 4 + 7 = 11. One part: 77 ÷ 11 = 7. 4 × 7 = 28, 7 × 7 = 49.
12. 20 and 24
Total parts: 5 + 6 = 11. One part: 44 ÷ 11 = 4. 5 × 4 = 20, 6 × 4 = 24.
Worked examples
Simplify the ratio 48:36.
- HCF of 48 and 36 is 12.
- Divide both parts by it: 4:3.
- Answer: 4:3
Share 72 in the ratio 4:5.
- Total parts: 4 + 5 = 9.
- One part: 72 ÷ 9 = 8.
- 4 × 8 = 32, 5 × 8 = 40.
- Answer: 32 and 40
Share 88 in the ratio 4:7.
- Total parts: 4 + 7 = 11.
- One part: 88 ÷ 11 = 8.
- 4 × 8 = 32, 7 × 8 = 56.
- Answer: 32 and 56
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.
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Frequently asked
- Is this Grade 3 Introducing Cosine Ratio flashcards really free?
- Yes. Every flashcards 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 flashcards 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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