Free Grade 3 Simplifying Surds in Context Lessons
Free Grade 3 lessons for Simplifying Surds in Context: 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 simplifying surds in context
Explain simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate simplifying surds in context
Calculate simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare simplifying surds in context
Compare simplifying surds in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify simplifying surds in context
Justify simplifying surds in context 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 Simplifying Surds in Context 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 20:16.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 20:12.[1]
- 5.Share 30 in the ratio 4:6.[2]
- 6.Share 64 in the ratio 2:6.[2]
- 7.Share 36 in the ratio 3:3.[2]
- 8.Share 60 in the ratio 2:3.[2]
- 9.Share 25 in the ratio 4:1.[3]
- 10.Share 80 in the ratio 4:6.[3]
- 11.Share 33 in the ratio 2:1.[3]
- 12.Share 50 in the ratio 4:6.[3]
Show answers and working
1. 5:4
HCF of 20 and 16 is 4. Divide both parts by it: 5:4.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 5:3
HCF of 20 and 12 is 4. Divide both parts by it: 5:3.
5. 12 and 18
Total parts: 4 + 6 = 10. One part: 30 ÷ 10 = 3. 4 × 3 = 12, 6 × 3 = 18.
6. 16 and 48
Total parts: 2 + 6 = 8. One part: 64 ÷ 8 = 8. 2 × 8 = 16, 6 × 8 = 48.
7. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
8. 24 and 36
Total parts: 2 + 3 = 5. One part: 60 ÷ 5 = 12. 2 × 12 = 24, 3 × 12 = 36.
9. 20 and 5
Total parts: 4 + 1 = 5. One part: 25 ÷ 5 = 5. 4 × 5 = 20, 1 × 5 = 5.
10. 32 and 48
Total parts: 4 + 6 = 10. One part: 80 ÷ 10 = 8. 4 × 8 = 32, 6 × 8 = 48.
11. 22 and 11
Total parts: 2 + 1 = 3. One part: 33 ÷ 3 = 11. 2 × 11 = 22, 1 × 11 = 11.
12. 20 and 30
Total parts: 4 + 6 = 10. One part: 50 ÷ 10 = 5. 4 × 5 = 20, 6 × 5 = 30.
Worked examples
Simplify the ratio 50:50.
- HCF of 50 and 50 is 50.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 36 in the ratio 1:2.
- Total parts: 1 + 2 = 3.
- One part: 36 ÷ 3 = 12.
- 1 × 12 = 12, 2 × 12 = 24.
- Answer: 12 and 24
Share 56 in the ratio 5:2.
- Total parts: 5 + 2 = 7.
- One part: 56 ÷ 7 = 8.
- 5 × 8 = 40, 2 × 8 = 16.
- Answer: 40 and 16
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 Simplifying Surds in Context 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 Working with Simplifying Surds, Introducing Simplifying Surds, Surds. 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 Simplifying Surds in Context?
- Move on to Surds, Pi as an Irrational, which build directly on this idea.
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