Free Grade 3 Working with Simplifying Surds Lessons
Free Grade 3 lessons for Working with Simplifying 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with simplifying surds
Identify working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with simplifying surds
Explain working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with simplifying surds
Calculate working with simplifying surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with simplifying surds
Compare working with simplifying 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 Working with Simplifying 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 8:16.[1]
- 2.Simplify the ratio 24:12.[1]
- 3.Simplify the ratio 12:12.[1]
- 4.Simplify the ratio 12:24.[1]
- 5.Share 63 in the ratio 1:6.[2]
- 6.Share 8 in the ratio 2:2.[2]
- 7.Share 84 in the ratio 4:3.[2]
- 8.Share 45 in the ratio 1:4.[2]
- 9.Share 45 in the ratio 3:2.[3]
- 10.Share 72 in the ratio 5:4.[3]
- 11.Share 90 in the ratio 5:5.[3]
- 12.Share 45 in the ratio 3:6.[3]
Show answers and working
1. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
2. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
3. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
4. 1:2
HCF of 12 and 24 is 12. Divide both parts by it: 1:2.
5. 9 and 54
Total parts: 1 + 6 = 7. One part: 63 ÷ 7 = 9. 1 × 9 = 9, 6 × 9 = 54.
6. 4 and 4
Total parts: 2 + 2 = 4. One part: 8 ÷ 4 = 2. 2 × 2 = 4, 2 × 2 = 4.
7. 48 and 36
Total parts: 4 + 3 = 7. One part: 84 ÷ 7 = 12. 4 × 12 = 48, 3 × 12 = 36.
8. 9 and 36
Total parts: 1 + 4 = 5. One part: 45 ÷ 5 = 9. 1 × 9 = 9, 4 × 9 = 36.
9. 27 and 18
Total parts: 3 + 2 = 5. One part: 45 ÷ 5 = 9. 3 × 9 = 27, 2 × 9 = 18.
10. 40 and 32
Total parts: 5 + 4 = 9. One part: 72 ÷ 9 = 8. 5 × 8 = 40, 4 × 8 = 32.
11. 45 and 45
Total parts: 5 + 5 = 10. One part: 90 ÷ 10 = 9. 5 × 9 = 45, 5 × 9 = 45.
12. 15 and 30
Total parts: 3 + 6 = 9. One part: 45 ÷ 9 = 5. 3 × 5 = 15, 6 × 5 = 30.
Worked examples
Simplify the ratio 10:40.
- HCF of 10 and 40 is 10.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 24 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 24 ÷ 4 = 6.
- 3 × 6 = 18, 1 × 6 = 6.
- Answer: 18 and 6
Share 56 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 56 ÷ 8 = 7.
- 5 × 7 = 35, 3 × 7 = 21.
- Answer: 35 and 21
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 Working with Simplifying 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 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 Working with Simplifying Surds?
- Move on to Simplifying Surds in Context, Surds, Pi as an Irrational, which build directly on this idea.
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