Free Grade 3 Working with Pi as an Irrational Flashcards
Free Grade 3 flashcards 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
Core
30 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 12:8.[1]
- 2.Simplify the ratio 40:24.[1]
- 3.Simplify the ratio 12:36.[1]
- 4.Simplify the ratio 16:4.[1]
- 5.Share 56 in the ratio 4:4.[2]
- 6.Share 60 in the ratio 1:5.[2]
- 7.Share 48 in the ratio 2:4.[2]
- 8.Share 24 in the ratio 2:6.[2]
- 9.Share 12 in the ratio 1:5.[3]
- 10.Share 96 in the ratio 2:6.[3]
- 11.Share 30 in the ratio 1:2.[3]
- 12.Share 30 in the ratio 4:2.[3]
Show answers and working
1. 3:2
HCF of 12 and 8 is 4. Divide both parts by it: 3:2.
2. 5:3
HCF of 40 and 24 is 8. Divide both parts by it: 5:3.
3. 1:3
HCF of 12 and 36 is 12. Divide both parts by it: 1:3.
4. 4:1
HCF of 16 and 4 is 4. Divide both parts by it: 4:1.
5. 28 and 28
Total parts: 4 + 4 = 8. One part: 56 ÷ 8 = 7. 4 × 7 = 28, 4 × 7 = 28.
6. 10 and 50
Total parts: 1 + 5 = 6. One part: 60 ÷ 6 = 10. 1 × 10 = 10, 5 × 10 = 50.
7. 16 and 32
Total parts: 2 + 4 = 6. One part: 48 ÷ 6 = 8. 2 × 8 = 16, 4 × 8 = 32.
8. 6 and 18
Total parts: 2 + 6 = 8. One part: 24 ÷ 8 = 3. 2 × 3 = 6, 6 × 3 = 18.
9. 2 and 10
Total parts: 1 + 5 = 6. One part: 12 ÷ 6 = 2. 1 × 2 = 2, 5 × 2 = 10.
10. 24 and 72
Total parts: 2 + 6 = 8. One part: 96 ÷ 8 = 12. 2 × 12 = 24, 6 × 12 = 72.
11. 10 and 20
Total parts: 1 + 2 = 3. One part: 30 ÷ 3 = 10. 1 × 10 = 10, 2 × 10 = 20.
12. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
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 63 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 63 ÷ 9 = 7.
- 5 × 7 = 35, 4 × 7 = 28.
- Answer: 35 and 28
Share 99 in the ratio 4:5.
- Total parts: 4 + 5 = 9.
- One part: 99 ÷ 9 = 11.
- 4 × 11 = 44, 5 × 11 = 55.
- Answer: 44 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 flashcards really free?
- Yes. Every flashcards 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 flashcards 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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