Free Grade 3 Pi as an Irrational Lesson Plans
Free Grade 3 lesson plans for 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify pi as an irrational
Identify pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain pi as an irrational
Explain pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate pi as an irrational
Calculate pi as an irrational accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare pi as an irrational
Compare 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 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 24:30.[1]
- 2.Simplify the ratio 40:8.[1]
- 3.Simplify the ratio 20:10.[1]
- 4.Simplify the ratio 36:36.[1]
- 5.Share 60 in the ratio 1:5.[2]
- 6.Share 80 in the ratio 5:5.[2]
- 7.Share 12 in the ratio 5:1.[2]
- 8.Share 90 in the ratio 4:6.[2]
- 9.Share 35 in the ratio 3:2.[3]
- 10.Share 36 in the ratio 3:3.[3]
- 11.Share 63 in the ratio 1:6.[3]
- 12.Share 4 in the ratio 1:1.[3]
Show answers and working
1. 4:5
HCF of 24 and 30 is 6. Divide both parts by it: 4:5.
2. 5:1
HCF of 40 and 8 is 8. Divide both parts by it: 5:1.
3. 2:1
HCF of 20 and 10 is 10. Divide both parts by it: 2:1.
4. 1:1
HCF of 36 and 36 is 36. Divide both parts by it: 1:1.
5. 10 and 50
Total parts: 1 + 5 = 6. One part: 60 ÷ 6 = 10. 1 × 10 = 10, 5 × 10 = 50.
6. 40 and 40
Total parts: 5 + 5 = 10. One part: 80 ÷ 10 = 8. 5 × 8 = 40, 5 × 8 = 40.
7. 10 and 2
Total parts: 5 + 1 = 6. One part: 12 ÷ 6 = 2. 5 × 2 = 10, 1 × 2 = 2.
8. 36 and 54
Total parts: 4 + 6 = 10. One part: 90 ÷ 10 = 9. 4 × 9 = 36, 6 × 9 = 54.
9. 21 and 14
Total parts: 3 + 2 = 5. One part: 35 ÷ 5 = 7. 3 × 7 = 21, 2 × 7 = 14.
10. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
11. 9 and 54
Total parts: 1 + 6 = 7. One part: 63 ÷ 7 = 9. 1 × 9 = 9, 6 × 9 = 54.
12. 2 and 2
Total parts: 1 + 1 = 2. One part: 4 ÷ 2 = 2. 1 × 2 = 2, 1 × 2 = 2.
Worked examples
Simplify the ratio 50:50.
- HCF of 50 and 50 is 50.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 40 in the ratio 4:4.
- Total parts: 4 + 4 = 8.
- One part: 40 ÷ 8 = 5.
- 4 × 5 = 20, 4 × 5 = 20.
- Answer: 20 and 20
Share 72 in the ratio 3:5.
- Total parts: 3 + 5 = 8.
- One part: 72 ÷ 8 = 9.
- 3 × 9 = 27, 5 × 9 = 45.
- Answer: 27 and 45
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.
Every free resource for Pi as an Irrational
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 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 Simplifying Surds, Surds, Rational Numbers. 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 Pi as an Irrational?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
Related resources
Stuck on Pi as an Irrational? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor