Free Grade 3 Introducing Definite Integrals Lesson Plans
Free Grade 3 lesson plans for Introducing Definite Integrals: 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing definite integrals
Identify introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing definite integrals
Explain introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing definite integrals
Calculate introducing definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing definite integrals
Compare introducing definite integrals 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 Introducing Definite Integrals 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 32:24.[1]
- 2.Simplify the ratio 8:40.[1]
- 3.Simplify the ratio 50:10.[1]
- 4.Simplify the ratio 6:30.[1]
- 5.Share 18 in the ratio 2:1.[2]
- 6.Share 24 in the ratio 2:4.[2]
- 7.Share 70 in the ratio 1:6.[2]
- 8.Share 4 in the ratio 1:1.[2]
- 9.Share 10 in the ratio 2:3.[3]
- 10.Share 108 in the ratio 3:6.[3]
- 11.Share 16 in the ratio 1:1.[3]
- 12.Share 66 in the ratio 5:6.[3]
Show answers and working
1. 4:3
HCF of 32 and 24 is 8. Divide both parts by it: 4:3.
2. 1:5
HCF of 8 and 40 is 8. Divide both parts by it: 1:5.
3. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
4. 1:5
HCF of 6 and 30 is 6. Divide both parts by it: 1:5.
5. 12 and 6
Total parts: 2 + 1 = 3. One part: 18 ÷ 3 = 6. 2 × 6 = 12, 1 × 6 = 6.
6. 8 and 16
Total parts: 2 + 4 = 6. One part: 24 ÷ 6 = 4. 2 × 4 = 8, 4 × 4 = 16.
7. 10 and 60
Total parts: 1 + 6 = 7. One part: 70 ÷ 7 = 10. 1 × 10 = 10, 6 × 10 = 60.
8. 2 and 2
Total parts: 1 + 1 = 2. One part: 4 ÷ 2 = 2. 1 × 2 = 2, 1 × 2 = 2.
9. 4 and 6
Total parts: 2 + 3 = 5. One part: 10 ÷ 5 = 2. 2 × 2 = 4, 3 × 2 = 6.
10. 36 and 72
Total parts: 3 + 6 = 9. One part: 108 ÷ 9 = 12. 3 × 12 = 36, 6 × 12 = 72.
11. 8 and 8
Total parts: 1 + 1 = 2. One part: 16 ÷ 2 = 8. 1 × 8 = 8, 1 × 8 = 8.
12. 30 and 36
Total parts: 5 + 6 = 11. One part: 66 ÷ 11 = 6. 5 × 6 = 30, 6 × 6 = 36.
Worked examples
Simplify the ratio 12:24.
- HCF of 12 and 24 is 12.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 54 in the ratio 2:4.
- Total parts: 2 + 4 = 6.
- One part: 54 ÷ 6 = 9.
- 2 × 9 = 18, 4 × 9 = 36.
- Answer: 18 and 36
Share 99 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 99 ÷ 9 = 11.
- 5 × 11 = 55, 4 × 11 = 44.
- Answer: 55 and 44
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 Introducing Definite Integrals 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 Reverse Differentiation. 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 Introducing Definite Integrals?
- Move on to Working with Definite Integrals, Definite Integrals in Context, Reverse Differentiation, Area Under a Curve, which build directly on this idea.
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