Free Grade 3 Surds Lessons
Free Grade 3 lessons for 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
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain surds
Explain surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate surds
Calculate surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare surds
Compare surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify surds
Justify 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 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 16:16.[1]
- 2.Simplify the ratio 12:60.[1]
- 3.Simplify the ratio 20:50.[1]
- 4.Simplify the ratio 12:20.[1]
- 5.Share 60 in the ratio 1:5.[2]
- 6.Share 99 in the ratio 5:4.[2]
- 7.Share 24 in the ratio 5:3.[2]
- 8.Share 18 in the ratio 5:4.[2]
- 9.Share 110 in the ratio 5:6.[3]
- 10.Share 88 in the ratio 5:3.[3]
- 11.Share 36 in the ratio 5:4.[3]
- 12.Share 132 in the ratio 4:7.[3]
Show answers and working
1. 1:1
HCF of 16 and 16 is 16. Divide both parts by it: 1:1.
2. 1:5
HCF of 12 and 60 is 12. Divide both parts by it: 1:5.
3. 2:5
HCF of 20 and 50 is 10. Divide both parts by it: 2:5.
4. 3:5
HCF of 12 and 20 is 4. Divide both parts by it: 3:5.
5. 10 and 50
Total parts: 1 + 5 = 6. One part: 60 ÷ 6 = 10. 1 × 10 = 10, 5 × 10 = 50.
6. 55 and 44
Total parts: 5 + 4 = 9. One part: 99 ÷ 9 = 11. 5 × 11 = 55, 4 × 11 = 44.
7. 15 and 9
Total parts: 5 + 3 = 8. One part: 24 ÷ 8 = 3. 5 × 3 = 15, 3 × 3 = 9.
8. 10 and 8
Total parts: 5 + 4 = 9. One part: 18 ÷ 9 = 2. 5 × 2 = 10, 4 × 2 = 8.
9. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
10. 55 and 33
Total parts: 5 + 3 = 8. One part: 88 ÷ 8 = 11. 5 × 11 = 55, 3 × 11 = 33.
11. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
12. 48 and 84
Total parts: 4 + 7 = 11. One part: 132 ÷ 11 = 12. 4 × 12 = 48, 7 × 12 = 84.
Worked examples
Simplify the ratio 8:4.
- HCF of 8 and 4 is 4.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 63 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 63 ÷ 9 = 7.
- 3 × 7 = 21, 6 × 7 = 42.
- Answer: 21 and 42
Share 81 in the ratio 2:7.
- Total parts: 2 + 7 = 9.
- One part: 81 ÷ 9 = 9.
- 2 × 9 = 18, 7 × 9 = 63.
- Answer: 18 and 63
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 Surds
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Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 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 Surds?
- Move on to Simplifying Surds, Pi as an Irrational, Whole Numbers, Counting, which build directly on this idea.
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