Free Grade 3 Definite Integrals Lesson Plans
Free Grade 3 lesson plans for 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 definite integrals
Identify definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain definite integrals
Explain definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate definite integrals
Calculate definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare definite integrals
Compare 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 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 24:40.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 40:30.[1]
- 4.Simplify the ratio 24:60.[1]
- 5.Share 15 in the ratio 1:4.[2]
- 6.Share 70 in the ratio 3:4.[2]
- 7.Share 66 in the ratio 4:2.[2]
- 8.Share 12 in the ratio 2:4.[2]
- 9.Share 48 in the ratio 1:3.[3]
- 10.Share 24 in the ratio 2:6.[3]
- 11.Share 48 in the ratio 4:4.[3]
- 12.Share 32 in the ratio 3:5.[3]
Show answers and working
1. 3:5
HCF of 24 and 40 is 8. Divide both parts by it: 3:5.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 4:3
HCF of 40 and 30 is 10. Divide both parts by it: 4:3.
4. 2:5
HCF of 24 and 60 is 12. Divide both parts by it: 2:5.
5. 3 and 12
Total parts: 1 + 4 = 5. One part: 15 ÷ 5 = 3. 1 × 3 = 3, 4 × 3 = 12.
6. 30 and 40
Total parts: 3 + 4 = 7. One part: 70 ÷ 7 = 10. 3 × 10 = 30, 4 × 10 = 40.
7. 44 and 22
Total parts: 4 + 2 = 6. One part: 66 ÷ 6 = 11. 4 × 11 = 44, 2 × 11 = 22.
8. 4 and 8
Total parts: 2 + 4 = 6. One part: 12 ÷ 6 = 2. 2 × 2 = 4, 4 × 2 = 8.
9. 12 and 36
Total parts: 1 + 3 = 4. One part: 48 ÷ 4 = 12. 1 × 12 = 12, 3 × 12 = 36.
10. 6 and 18
Total parts: 2 + 6 = 8. One part: 24 ÷ 8 = 3. 2 × 3 = 6, 6 × 3 = 18.
11. 24 and 24
Total parts: 4 + 4 = 8. One part: 48 ÷ 8 = 6. 4 × 6 = 24, 4 × 6 = 24.
12. 12 and 20
Total parts: 3 + 5 = 8. One part: 32 ÷ 8 = 4. 3 × 4 = 12, 5 × 4 = 20.
Worked examples
Simplify the ratio 30:40.
- HCF of 30 and 40 is 10.
- Divide both parts by it: 3:4.
- Answer: 3:4
Share 27 in the ratio 1:2.
- Total parts: 1 + 2 = 3.
- One part: 27 ÷ 3 = 9.
- 1 × 9 = 9, 2 × 9 = 18.
- Answer: 9 and 18
Share 132 in the ratio 5:6.
- Total parts: 5 + 6 = 11.
- One part: 132 ÷ 11 = 12.
- 5 × 12 = 60, 6 × 12 = 72.
- Answer: 60 and 72
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 Definite Integrals
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Frequently asked
- Is this Grade 3 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, 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 Definite Integrals?
- Move on to Area Under a Curve, Differentiation, which build directly on this idea.
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