Free Grade 3 Introducing Pi as an Irrational Lessons
Free Grade 3 lessons for Introducing Pi as an Irrational: 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing pi as an irrational
Identify introducing pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing pi as an irrational
Explain introducing pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing pi as an irrational
Calculate introducing pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing pi as an irrational
Compare introducing pi as an irrational 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 Pi as an Irrational 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 10:20.[1]
- 2.Simplify the ratio 24:60.[1]
- 3.Simplify the ratio 30:18.[1]
- 4.Simplify the ratio 8:8.[1]
- 5.Share 50 in the ratio 4:6.[2]
- 6.Share 30 in the ratio 4:2.[2]
- 7.Share 30 in the ratio 4:1.[2]
- 8.Share 16 in the ratio 1:3.[2]
- 9.Share 24 in the ratio 2:6.[3]
- 10.Share 54 in the ratio 3:3.[3]
- 11.Share 18 in the ratio 4:2.[3]
- 12.Share 24 in the ratio 3:1.[3]
Show answers and working
1. 1:2
HCF of 10 and 20 is 10. Divide both parts by it: 1:2.
2. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
3. 5:3
HCF of 30 and 18 is 6. Divide both parts by it: 5:3.
4. 1:1
HCF of 8 and 8 is 8. Divide both parts by it: 1:1.
5. 20 and 30
Total parts: 4 + 6 = 10. One part: 50 ÷ 10 = 5. 4 × 5 = 20, 6 × 5 = 30.
6. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
7. 24 and 6
Total parts: 4 + 1 = 5. One part: 30 ÷ 5 = 6. 4 × 6 = 24, 1 × 6 = 6.
8. 4 and 12
Total parts: 1 + 3 = 4. One part: 16 ÷ 4 = 4. 1 × 4 = 4, 3 × 4 = 12.
9. 6 and 18
Total parts: 2 + 6 = 8. One part: 24 ÷ 8 = 3. 2 × 3 = 6, 6 × 3 = 18.
10. 27 and 27
Total parts: 3 + 3 = 6. One part: 54 ÷ 6 = 9. 3 × 9 = 27, 3 × 9 = 27.
11. 12 and 6
Total parts: 4 + 2 = 6. One part: 18 ÷ 6 = 3. 4 × 3 = 12, 2 × 3 = 6.
12. 18 and 6
Total parts: 3 + 1 = 4. One part: 24 ÷ 4 = 6. 3 × 6 = 18, 1 × 6 = 6.
Worked examples
Simplify the ratio 40:32.
- HCF of 40 and 32 is 8.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 12 in the ratio 1:1.
- Total parts: 1 + 1 = 2.
- One part: 12 ÷ 2 = 6.
- 1 × 6 = 6, 1 × 6 = 6.
- Answer: 6 and 6
Share 63 in the ratio 2:7.
- Total parts: 2 + 7 = 9.
- One part: 63 ÷ 9 = 7.
- 2 × 7 = 14, 7 × 7 = 49.
- Answer: 14 and 49
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 Pi as an Irrational 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 Simplifying 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 Introducing Pi as an Irrational?
- Move on to Working with Pi as an Irrational, Pi as an Irrational in Context, Surds, Simplifying Surds, which build directly on this idea.
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