Free Grade 3 Surds Lesson Plans
Free Grade 3 lesson plans 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
Core
15 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 24:30.[1]
- 2.Simplify the ratio 8:16.[1]
- 3.Simplify the ratio 32:40.[1]
- 4.Simplify the ratio 12:8.[1]
- 5.Share 4 in the ratio 1:1.[2]
- 6.Share 21 in the ratio 1:2.[2]
- 7.Share 63 in the ratio 3:6.[2]
- 8.Share 18 in the ratio 4:5.[2]
- 9.Share 45 in the ratio 4:1.[3]
- 10.Share 40 in the ratio 1:7.[3]
- 11.Share 63 in the ratio 5:4.[3]
- 12.Share 55 in the ratio 4:1.[3]
Show answers and working
1. 4:5
HCF of 24 and 30 is 6. Divide both parts by it: 4:5.
2. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
3. 4:5
HCF of 32 and 40 is 8. Divide both parts by it: 4:5.
4. 3:2
HCF of 12 and 8 is 4. Divide both parts by it: 3:2.
5. 2 and 2
Total parts: 1 + 1 = 2. One part: 4 ÷ 2 = 2. 1 × 2 = 2, 1 × 2 = 2.
6. 7 and 14
Total parts: 1 + 2 = 3. One part: 21 ÷ 3 = 7. 1 × 7 = 7, 2 × 7 = 14.
7. 21 and 42
Total parts: 3 + 6 = 9. One part: 63 ÷ 9 = 7. 3 × 7 = 21, 6 × 7 = 42.
8. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
9. 36 and 9
Total parts: 4 + 1 = 5. One part: 45 ÷ 5 = 9. 4 × 9 = 36, 1 × 9 = 9.
10. 5 and 35
Total parts: 1 + 7 = 8. One part: 40 ÷ 8 = 5. 1 × 5 = 5, 7 × 5 = 35.
11. 35 and 28
Total parts: 5 + 4 = 9. One part: 63 ÷ 9 = 7. 5 × 7 = 35, 4 × 7 = 28.
12. 44 and 11
Total parts: 4 + 1 = 5. One part: 55 ÷ 5 = 11. 4 × 11 = 44, 1 × 11 = 11.
Worked examples
Simplify the ratio 48:60.
- HCF of 48 and 60 is 12.
- Divide both parts by it: 4:5.
- Answer: 4:5
Share 27 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 27 ÷ 3 = 9.
- 2 × 9 = 18, 1 × 9 = 9.
- Answer: 18 and 9
Share 12 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 12 ÷ 6 = 2.
- 5 × 2 = 10, 1 × 2 = 2.
- Answer: 10 and 2
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
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
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 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 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 Surds?
- Move on to Simplifying Surds, Pi as an Irrational, Whole Numbers, Counting, which build directly on this idea.
Related resources
Stuck on Surds? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor