Free Grade 3 Introducing Surds Essentials Lessons
Free Grade 3 lessons for Introducing Surds Essentials: 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 introducing surds essentials
Explain introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing surds essentials
Calculate introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing surds essentials
Compare introducing surds essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing surds essentials
Justify introducing surds essentials 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 Essentials 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 6:30.[1]
- 2.Simplify the ratio 12:24.[1]
- 3.Simplify the ratio 40:20.[1]
- 4.Simplify the ratio 12:12.[1]
- 5.Share 72 in the ratio 1:5.[2]
- 6.Share 44 in the ratio 1:3.[2]
- 7.Share 15 in the ratio 2:1.[2]
- 8.Share 90 in the ratio 3:6.[2]
- 9.Share 36 in the ratio 5:4.[3]
- 10.Share 36 in the ratio 2:1.[3]
- 11.Share 72 in the ratio 3:6.[3]
- 12.Share 56 in the ratio 4:4.[3]
Show answers and working
1. 1:5
HCF of 6 and 30 is 6. Divide both parts by it: 1:5.
2. 1:2
HCF of 12 and 24 is 12. Divide both parts by it: 1:2.
3. 2:1
HCF of 40 and 20 is 20. Divide both parts by it: 2:1.
4. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
5. 12 and 60
Total parts: 1 + 5 = 6. One part: 72 ÷ 6 = 12. 1 × 12 = 12, 5 × 12 = 60.
6. 11 and 33
Total parts: 1 + 3 = 4. One part: 44 ÷ 4 = 11. 1 × 11 = 11, 3 × 11 = 33.
7. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
8. 30 and 60
Total parts: 3 + 6 = 9. One part: 90 ÷ 9 = 10. 3 × 10 = 30, 6 × 10 = 60.
9. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
10. 24 and 12
Total parts: 2 + 1 = 3. One part: 36 ÷ 3 = 12. 2 × 12 = 24, 1 × 12 = 12.
11. 24 and 48
Total parts: 3 + 6 = 9. One part: 72 ÷ 9 = 8. 3 × 8 = 24, 6 × 8 = 48.
12. 28 and 28
Total parts: 4 + 4 = 8. One part: 56 ÷ 8 = 7. 4 × 7 = 28, 4 × 7 = 28.
Worked examples
Simplify the ratio 8:20.
- HCF of 8 and 20 is 4.
- Divide both parts by it: 2:5.
- Answer: 2:5
Share 40 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 40 ÷ 8 = 5.
- 2 × 5 = 10, 6 × 5 = 30.
- Answer: 10 and 30
Share 121 in the ratio 5:6.
- Total parts: 5 + 6 = 11.
- One part: 121 ÷ 11 = 11.
- 5 × 11 = 55, 6 × 11 = 66.
- Answer: 55 and 66
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 Introducing Surds Essentials 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 Essentials?
- Move on to Introducing Surds Techniques, Introducing Surds Word Problems, Introducing Surds Common Errors, Working with Surds, which build directly on this idea.
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