Free Grade 3 Working with Pi as an Irrational Lessons
Free Grade 3 lessons for Working with 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
Foundation
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with pi as an irrational
Identify working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with pi as an irrational
Explain working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with pi as an irrational
Calculate working with pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with pi as an irrational
Compare working with 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 Working with 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 8:16.[1]
- 2.Simplify the ratio 40:16.[1]
- 3.Simplify the ratio 30:24.[1]
- 4.Simplify the ratio 30:6.[1]
- 5.Share 30 in the ratio 3:2.[2]
- 6.Share 32 in the ratio 1:3.[2]
- 7.Share 30 in the ratio 1:5.[2]
- 8.Share 24 in the ratio 2:4.[2]
- 9.Share 99 in the ratio 4:5.[3]
- 10.Share 42 in the ratio 2:4.[3]
- 11.Share 54 in the ratio 2:4.[3]
- 12.Share 12 in the ratio 4:2.[3]
Show answers and working
1. 1:2
HCF of 8 and 16 is 8. Divide both parts by it: 1:2.
2. 5:2
HCF of 40 and 16 is 8. Divide both parts by it: 5:2.
3. 5:4
HCF of 30 and 24 is 6. Divide both parts by it: 5:4.
4. 5:1
HCF of 30 and 6 is 6. Divide both parts by it: 5:1.
5. 18 and 12
Total parts: 3 + 2 = 5. One part: 30 ÷ 5 = 6. 3 × 6 = 18, 2 × 6 = 12.
6. 8 and 24
Total parts: 1 + 3 = 4. One part: 32 ÷ 4 = 8. 1 × 8 = 8, 3 × 8 = 24.
7. 5 and 25
Total parts: 1 + 5 = 6. One part: 30 ÷ 6 = 5. 1 × 5 = 5, 5 × 5 = 25.
8. 8 and 16
Total parts: 2 + 4 = 6. One part: 24 ÷ 6 = 4. 2 × 4 = 8, 4 × 4 = 16.
9. 44 and 55
Total parts: 4 + 5 = 9. One part: 99 ÷ 9 = 11. 4 × 11 = 44, 5 × 11 = 55.
10. 14 and 28
Total parts: 2 + 4 = 6. One part: 42 ÷ 6 = 7. 2 × 7 = 14, 4 × 7 = 28.
11. 18 and 36
Total parts: 2 + 4 = 6. One part: 54 ÷ 6 = 9. 2 × 9 = 18, 4 × 9 = 36.
12. 8 and 4
Total parts: 4 + 2 = 6. One part: 12 ÷ 6 = 2. 4 × 2 = 8, 2 × 2 = 4.
Worked examples
Simplify the ratio 60:60.
- HCF of 60 and 60 is 60.
- Divide both parts by it: 1:1.
- Answer: 1:1
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 66 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 66 ÷ 6 = 11.
- 1 × 11 = 11, 5 × 11 = 55.
- Answer: 11 and 55
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 Working with 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 Introducing Pi as an Irrational, 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 Working with Pi as an Irrational?
- Move on to Pi as an Irrational in Context, Surds, Simplifying Surds, which build directly on this idea.
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