Free Grade 3 Introducing Definite Integrals Lessons
Free Grade 3 lessons 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
20 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 40:20.[1]
- 2.Simplify the ratio 60:24.[1]
- 3.Simplify the ratio 12:8.[1]
- 4.Simplify the ratio 40:24.[1]
- 5.Share 63 in the ratio 3:6.[2]
- 6.Share 33 in the ratio 5:6.[2]
- 7.Share 108 in the ratio 3:6.[2]
- 8.Share 35 in the ratio 4:1.[2]
- 9.Share 18 in the ratio 2:4.[3]
- 10.Share 49 in the ratio 3:4.[3]
- 11.Share 50 in the ratio 4:1.[3]
- 12.Share 28 in the ratio 3:1.[3]
Show answers and working
1. 2:1
HCF of 40 and 20 is 20. Divide both parts by it: 2:1.
2. 5:2
HCF of 60 and 24 is 12. Divide both parts by it: 5:2.
3. 3:2
HCF of 12 and 8 is 4. Divide both parts by it: 3:2.
4. 5:3
HCF of 40 and 24 is 8. Divide both parts by it: 5:3.
5. 21 and 42
Total parts: 3 + 6 = 9. One part: 63 ÷ 9 = 7. 3 × 7 = 21, 6 × 7 = 42.
6. 15 and 18
Total parts: 5 + 6 = 11. One part: 33 ÷ 11 = 3. 5 × 3 = 15, 6 × 3 = 18.
7. 36 and 72
Total parts: 3 + 6 = 9. One part: 108 ÷ 9 = 12. 3 × 12 = 36, 6 × 12 = 72.
8. 28 and 7
Total parts: 4 + 1 = 5. One part: 35 ÷ 5 = 7. 4 × 7 = 28, 1 × 7 = 7.
9. 6 and 12
Total parts: 2 + 4 = 6. One part: 18 ÷ 6 = 3. 2 × 3 = 6, 4 × 3 = 12.
10. 21 and 28
Total parts: 3 + 4 = 7. One part: 49 ÷ 7 = 7. 3 × 7 = 21, 4 × 7 = 28.
11. 40 and 10
Total parts: 4 + 1 = 5. One part: 50 ÷ 5 = 10. 4 × 10 = 40, 1 × 10 = 10.
12. 21 and 7
Total parts: 3 + 1 = 4. One part: 28 ÷ 4 = 7. 3 × 7 = 21, 1 × 7 = 7.
Worked examples
Simplify the ratio 40:16.
- HCF of 40 and 16 is 8.
- Divide both parts by it: 5:2.
- Answer: 5:2
Share 66 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 66 ÷ 6 = 11.
- 1 × 11 = 11, 5 × 11 = 55.
- Answer: 11 and 55
Share 14 in the ratio 5:2.
- Total parts: 5 + 2 = 7.
- One part: 14 ÷ 7 = 2.
- 5 × 2 = 10, 2 × 2 = 4.
- Answer: 10 and 4
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 really free?
- Yes. Every lessons 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 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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