Free Grade 3 Working with Pi as an Irrational Lesson Plans
Free Grade 3 lesson plans 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
35 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 20:16.[1]
- 2.Simplify the ratio 30:24.[1]
- 3.Simplify the ratio 8:32.[1]
- 4.Simplify the ratio 18:18.[1]
- 5.Share 40 in the ratio 4:1.[2]
- 6.Share 24 in the ratio 1:5.[2]
- 7.Share 30 in the ratio 4:2.[2]
- 8.Share 90 in the ratio 3:6.[2]
- 9.Share 66 in the ratio 1:5.[3]
- 10.Share 32 in the ratio 2:2.[3]
- 11.Share 8 in the ratio 2:2.[3]
- 12.Share 42 in the ratio 4:2.[3]
Show answers and working
1. 5:4
HCF of 20 and 16 is 4. Divide both parts by it: 5:4.
2. 5:4
HCF of 30 and 24 is 6. Divide both parts by it: 5:4.
3. 1:4
HCF of 8 and 32 is 8. Divide both parts by it: 1:4.
4. 1:1
HCF of 18 and 18 is 18. Divide both parts by it: 1:1.
5. 32 and 8
Total parts: 4 + 1 = 5. One part: 40 ÷ 5 = 8. 4 × 8 = 32, 1 × 8 = 8.
6. 4 and 20
Total parts: 1 + 5 = 6. One part: 24 ÷ 6 = 4. 1 × 4 = 4, 5 × 4 = 20.
7. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
8. 30 and 60
Total parts: 3 + 6 = 9. One part: 90 ÷ 9 = 10. 3 × 10 = 30, 6 × 10 = 60.
9. 11 and 55
Total parts: 1 + 5 = 6. One part: 66 ÷ 6 = 11. 1 × 11 = 11, 5 × 11 = 55.
10. 16 and 16
Total parts: 2 + 2 = 4. One part: 32 ÷ 4 = 8. 2 × 8 = 16, 2 × 8 = 16.
11. 4 and 4
Total parts: 2 + 2 = 4. One part: 8 ÷ 4 = 2. 2 × 2 = 4, 2 × 2 = 4.
12. 28 and 14
Total parts: 4 + 2 = 6. One part: 42 ÷ 6 = 7. 4 × 7 = 28, 2 × 7 = 14.
Worked examples
Simplify the ratio 40:50.
- HCF of 40 and 50 is 10.
- Divide both parts by it: 4:5.
- Answer: 4:5
Share 44 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 44 ÷ 4 = 11.
- 3 × 11 = 33, 1 × 11 = 11.
- Answer: 33 and 11
Share 56 in the ratio 2:6.
- Total parts: 2 + 6 = 8.
- One part: 56 ÷ 8 = 7.
- 2 × 7 = 14, 6 × 7 = 42.
- Answer: 14 and 42
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 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 Introducing Pi as an Irrational, Simplifying Surds. 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 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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