Free Grade 3 Working with Definite Integrals Lesson Plans
Free Grade 3 lesson plans for Working with 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with definite integrals
Identify working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with definite integrals
Explain working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with definite integrals
Calculate working with definite integrals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with definite integrals
Compare working with 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 Working with 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 12:24.[1]
- 2.Simplify the ratio 8:24.[1]
- 3.Simplify the ratio 12:18.[1]
- 4.Simplify the ratio 24:30.[1]
- 5.Share 16 in the ratio 3:1.[2]
- 6.Share 30 in the ratio 4:2.[2]
- 7.Share 54 in the ratio 5:1.[2]
- 8.Share 70 in the ratio 4:3.[2]
- 9.Share 90 in the ratio 3:6.[3]
- 10.Share 20 in the ratio 4:6.[3]
- 11.Share 63 in the ratio 4:5.[3]
- 12.Share 120 in the ratio 5:7.[3]
Show answers and working
1. 1:2
HCF of 12 and 24 is 12. Divide both parts by it: 1:2.
2. 1:3
HCF of 8 and 24 is 8. Divide both parts by it: 1:3.
3. 2:3
HCF of 12 and 18 is 6. Divide both parts by it: 2:3.
4. 4:5
HCF of 24 and 30 is 6. Divide both parts by it: 4:5.
5. 12 and 4
Total parts: 3 + 1 = 4. One part: 16 ÷ 4 = 4. 3 × 4 = 12, 1 × 4 = 4.
6. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
7. 45 and 9
Total parts: 5 + 1 = 6. One part: 54 ÷ 6 = 9. 5 × 9 = 45, 1 × 9 = 9.
8. 40 and 30
Total parts: 4 + 3 = 7. One part: 70 ÷ 7 = 10. 4 × 10 = 40, 3 × 10 = 30.
9. 30 and 60
Total parts: 3 + 6 = 9. One part: 90 ÷ 9 = 10. 3 × 10 = 30, 6 × 10 = 60.
10. 8 and 12
Total parts: 4 + 6 = 10. One part: 20 ÷ 10 = 2. 4 × 2 = 8, 6 × 2 = 12.
11. 28 and 35
Total parts: 4 + 5 = 9. One part: 63 ÷ 9 = 7. 4 × 7 = 28, 5 × 7 = 35.
12. 50 and 70
Total parts: 5 + 7 = 12. One part: 120 ÷ 12 = 10. 5 × 10 = 50, 7 × 10 = 70.
Worked examples
Simplify the ratio 16:12.
- HCF of 16 and 12 is 4.
- Divide both parts by it: 4:3.
- Answer: 4:3
Share 36 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 36 ÷ 6 = 6.
- 5 × 6 = 30, 1 × 6 = 6.
- Answer: 30 and 6
Share 21 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 21 ÷ 7 = 3.
- 4 × 3 = 12, 3 × 3 = 9.
- Answer: 12 and 9
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 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 Introducing Definite Integrals, 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 Working with Definite Integrals?
- Move on to Definite Integrals in Context, Reverse Differentiation, Area Under a Curve, which build directly on this idea.
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