Free Grade 3 Pi as an Irrational in Context Worksheets
Free Grade 3 worksheets for Pi as an Irrational in Context: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain pi as an irrational in context
Explain pi as an irrational in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate pi as an irrational in context
Calculate pi as an irrational in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare pi as an irrational in context
Compare pi as an irrational in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify pi as an irrational in context
Justify pi as an irrational in context 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 Pi as an Irrational in Context 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 8:40.[1]
- 2.Simplify the ratio 24:6.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 4:4.[1]
- 5.Share 12 in the ratio 5:1.[2]
- 6.Share 72 in the ratio 4:5.[2]
- 7.Share 20 in the ratio 3:1.[2]
- 8.Share 56 in the ratio 2:6.[2]
- 9.Share 40 in the ratio 4:6.[3]
- 10.Share 110 in the ratio 4:6.[3]
- 11.Share 35 in the ratio 2:5.[3]
- 12.Share 60 in the ratio 1:4.[3]
Show answers and working
1. 1:5
HCF of 8 and 40 is 8. Divide both parts by it: 1:5.
2. 4:1
HCF of 24 and 6 is 6. Divide both parts by it: 4:1.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 1:1
HCF of 4 and 4 is 4. Divide both parts by it: 1:1.
5. 10 and 2
Total parts: 5 + 1 = 6. One part: 12 ÷ 6 = 2. 5 × 2 = 10, 1 × 2 = 2.
6. 32 and 40
Total parts: 4 + 5 = 9. One part: 72 ÷ 9 = 8. 4 × 8 = 32, 5 × 8 = 40.
7. 15 and 5
Total parts: 3 + 1 = 4. One part: 20 ÷ 4 = 5. 3 × 5 = 15, 1 × 5 = 5.
8. 14 and 42
Total parts: 2 + 6 = 8. One part: 56 ÷ 8 = 7. 2 × 7 = 14, 6 × 7 = 42.
9. 16 and 24
Total parts: 4 + 6 = 10. One part: 40 ÷ 10 = 4. 4 × 4 = 16, 6 × 4 = 24.
10. 44 and 66
Total parts: 4 + 6 = 10. One part: 110 ÷ 10 = 11. 4 × 11 = 44, 6 × 11 = 66.
11. 10 and 25
Total parts: 2 + 5 = 7. One part: 35 ÷ 7 = 5. 2 × 5 = 10, 5 × 5 = 25.
12. 12 and 48
Total parts: 1 + 4 = 5. One part: 60 ÷ 5 = 12. 1 × 12 = 12, 4 × 12 = 48.
Worked examples
Simplify the ratio 36:48.
- HCF of 36 and 48 is 12.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 72 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 72 ÷ 6 = 12.
- 5 × 12 = 60, 1 × 12 = 12.
- Answer: 60 and 12
Share 42 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 42 ÷ 7 = 6.
- 3 × 6 = 18, 4 × 6 = 24.
- Answer: 18 and 24
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 Pi as an Irrational in Context worksheet really free?
- Yes. Every worksheets 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 Working with Pi as an Irrational, Introducing Pi as an Irrational, Simplifying Surds. Each one has its own free lesson, worksheet and quiz.
- How is the worksheet 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 Pi as an Irrational in Context?
- Move on to Surds, Simplifying Surds, which build directly on this idea.
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