Free Grade 3 Working with Surds Lesson Plans
Free Grade 3 lesson plans for Working with 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 working with surds
Identify working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with surds
Explain working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with surds
Calculate working with surds accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with surds
Compare working with 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 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 24:18.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 8:40.[1]
- 4.Simplify the ratio 8:12.[1]
- 5.Share 56 in the ratio 3:5.[2]
- 6.Share 27 in the ratio 5:4.[2]
- 7.Share 42 in the ratio 2:5.[2]
- 8.Share 48 in the ratio 4:4.[2]
- 9.Share 100 in the ratio 4:6.[3]
- 10.Share 84 in the ratio 4:3.[3]
- 11.Share 40 in the ratio 1:7.[3]
- 12.Share 10 in the ratio 2:3.[3]
Show answers and working
1. 4:3
HCF of 24 and 18 is 6. Divide both parts by it: 4:3.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 1:5
HCF of 8 and 40 is 8. Divide both parts by it: 1:5.
4. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
5. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
6. 15 and 12
Total parts: 5 + 4 = 9. One part: 27 ÷ 9 = 3. 5 × 3 = 15, 4 × 3 = 12.
7. 12 and 30
Total parts: 2 + 5 = 7. One part: 42 ÷ 7 = 6. 2 × 6 = 12, 5 × 6 = 30.
8. 24 and 24
Total parts: 4 + 4 = 8. One part: 48 ÷ 8 = 6. 4 × 6 = 24, 4 × 6 = 24.
9. 40 and 60
Total parts: 4 + 6 = 10. One part: 100 ÷ 10 = 10. 4 × 10 = 40, 6 × 10 = 60.
10. 48 and 36
Total parts: 4 + 3 = 7. One part: 84 ÷ 7 = 12. 4 × 12 = 48, 3 × 12 = 36.
11. 5 and 35
Total parts: 1 + 7 = 8. One part: 40 ÷ 8 = 5. 1 × 5 = 5, 7 × 5 = 35.
12. 4 and 6
Total parts: 2 + 3 = 5. One part: 10 ÷ 5 = 2. 2 × 2 = 4, 3 × 2 = 6.
Worked examples
Simplify the ratio 18:18.
- HCF of 18 and 18 is 18.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 55 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 55 ÷ 5 = 11.
- 3 × 11 = 33, 2 × 11 = 22.
- Answer: 33 and 22
Share 81 in the ratio 4:5.
- Total parts: 4 + 5 = 9.
- One part: 81 ÷ 9 = 9.
- 4 × 9 = 36, 5 × 9 = 45.
- Answer: 36 and 45
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 Working with Surds
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Frequently asked
- Is this Grade 3 Working with Surds lesson plan really free?
- Yes. Every lesson plans 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 Surds, Rational Numbers. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Surds?
- Move on to Surds in Context, Simplifying Surds, Pi as an Irrational, which build directly on this idea.
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