Free Grade 3 Irrational Numbers Lesson Plans
Free Grade 3 lesson plans for Irrational Numbers: 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
Stretch
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain irrational numbers
Explain irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate irrational numbers
Calculate irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare irrational numbers
Compare irrational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify irrational numbers
Justify irrational numbers 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 Irrational Numbers 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 12:16.[1]
- 2.Simplify the ratio 8:8.[1]
- 3.Simplify the ratio 16:8.[1]
- 4.Simplify the ratio 24:24.[1]
- 5.Share 18 in the ratio 4:5.[2]
- 6.Share 45 in the ratio 4:1.[2]
- 7.Share 24 in the ratio 5:1.[2]
- 8.Share 20 in the ratio 2:3.[2]
- 9.Share 28 in the ratio 2:2.[3]
- 10.Share 99 in the ratio 4:7.[3]
- 11.Share 84 in the ratio 5:2.[3]
- 12.Share 30 in the ratio 5:1.[3]
Show answers and working
1. 3:4
HCF of 12 and 16 is 4. Divide both parts by it: 3:4.
2. 1:1
HCF of 8 and 8 is 8. Divide both parts by it: 1:1.
3. 2:1
HCF of 16 and 8 is 8. Divide both parts by it: 2:1.
4. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
5. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
6. 36 and 9
Total parts: 4 + 1 = 5. One part: 45 ÷ 5 = 9. 4 × 9 = 36, 1 × 9 = 9.
7. 20 and 4
Total parts: 5 + 1 = 6. One part: 24 ÷ 6 = 4. 5 × 4 = 20, 1 × 4 = 4.
8. 8 and 12
Total parts: 2 + 3 = 5. One part: 20 ÷ 5 = 4. 2 × 4 = 8, 3 × 4 = 12.
9. 14 and 14
Total parts: 2 + 2 = 4. One part: 28 ÷ 4 = 7. 2 × 7 = 14, 2 × 7 = 14.
10. 36 and 63
Total parts: 4 + 7 = 11. One part: 99 ÷ 11 = 9. 4 × 9 = 36, 7 × 9 = 63.
11. 60 and 24
Total parts: 5 + 2 = 7. One part: 84 ÷ 7 = 12. 5 × 12 = 60, 2 × 12 = 24.
12. 25 and 5
Total parts: 5 + 1 = 6. One part: 30 ÷ 6 = 5. 5 × 5 = 25, 1 × 5 = 5.
Worked examples
Simplify the ratio 8:16.
- HCF of 8 and 16 is 8.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 40 in the ratio 2:3.
- Total parts: 2 + 3 = 5.
- One part: 40 ÷ 5 = 8.
- 2 × 8 = 16, 3 × 8 = 24.
- Answer: 16 and 24
Share 48 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 48 ÷ 8 = 6.
- 5 × 6 = 30, 3 × 6 = 18.
- Answer: 30 and 18
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 Irrational Numbers 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, Percentages. 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 Irrational Numbers?
- Move on to Real Numbers, Complex Numbers, Ratio, Proportion, which build directly on this idea.
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