Free Grade 3 Introducing Surds Lessons
Free Grade 3 lessons for Introducing Surds: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing surds
Identify introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing surds
Explain introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing surds
Calculate introducing surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing surds
Compare introducing surds 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 Surds 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 8:8.[1]
- 2.Simplify the ratio 30:50.[1]
- 3.Simplify the ratio 24:18.[1]
- 4.Simplify the ratio 60:36.[1]
- 5.Share 45 in the ratio 2:3.[2]
- 6.Share 42 in the ratio 1:6.[2]
- 7.Share 50 in the ratio 5:5.[2]
- 8.Share 132 in the ratio 5:6.[2]
- 9.Share 8 in the ratio 3:1.[3]
- 10.Share 48 in the ratio 1:7.[3]
- 11.Share 63 in the ratio 2:5.[3]
- 12.Share 60 in the ratio 5:5.[3]
Show answers and working
1. 1:1
HCF of 8 and 8 is 8. Divide both parts by it: 1:1.
2. 3:5
HCF of 30 and 50 is 10. Divide both parts by it: 3:5.
3. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
4. 5:3
HCF of 60 and 36 is 12. Divide both parts by it: 5:3.
5. 18 and 27
Total parts: 2 + 3 = 5. One part: 45 ÷ 5 = 9. 2 × 9 = 18, 3 × 9 = 27.
6. 6 and 36
Total parts: 1 + 6 = 7. One part: 42 ÷ 7 = 6. 1 × 6 = 6, 6 × 6 = 36.
7. 25 and 25
Total parts: 5 + 5 = 10. One part: 50 ÷ 10 = 5. 5 × 5 = 25, 5 × 5 = 25.
8. 60 and 72
Total parts: 5 + 6 = 11. One part: 132 ÷ 11 = 12. 5 × 12 = 60, 6 × 12 = 72.
9. 6 and 2
Total parts: 3 + 1 = 4. One part: 8 ÷ 4 = 2. 3 × 2 = 6, 1 × 2 = 2.
10. 6 and 42
Total parts: 1 + 7 = 8. One part: 48 ÷ 8 = 6. 1 × 6 = 6, 7 × 6 = 42.
11. 18 and 45
Total parts: 2 + 5 = 7. One part: 63 ÷ 7 = 9. 2 × 9 = 18, 5 × 9 = 45.
12. 30 and 30
Total parts: 5 + 5 = 10. One part: 60 ÷ 10 = 6. 5 × 6 = 30, 5 × 6 = 30.
Worked examples
Simplify the ratio 8:32.
- HCF of 8 and 32 is 8.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 48 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 48 ÷ 8 = 6.
- 2 × 6 = 12, 6 × 6 = 36.
- Answer: 12 and 36
Share 50 in the ratio 4:6.
- Total parts: 4 + 6 = 10.
- One part: 50 ÷ 10 = 5.
- 4 × 5 = 20, 6 × 5 = 30.
- Answer: 20 and 30
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 Surds
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Learn — Meet the idea.
Practice — Build fluency.
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Frequently asked
- Is this Grade 3 Introducing Surds 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 Rational Numbers. 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 Surds?
- Move on to Working with Surds, Surds in Context, Simplifying Surds, Pi as an Irrational, which build directly on this idea.
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