Free Grade 3 Definite Integrals in Context Lessons
Free Grade 3 lessons for Definite Integrals in Context: 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
Stretch
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain definite integrals in context
Explain definite integrals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate definite integrals in context
Calculate definite integrals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare definite integrals in context
Compare definite integrals in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify definite integrals in context
Justify definite integrals in context 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 in Context 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 10:40.[1]
- 2.Simplify the ratio 20:30.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 32:32.[1]
- 5.Share 15 in the ratio 2:1.[2]
- 6.Share 132 in the ratio 5:6.[2]
- 7.Share 28 in the ratio 1:3.[2]
- 8.Share 121 in the ratio 5:6.[2]
- 9.Share 21 in the ratio 1:6.[3]
- 10.Share 24 in the ratio 3:5.[3]
- 11.Share 22 in the ratio 4:7.[3]
- 12.Share 33 in the ratio 2:1.[3]
Show answers and working
1. 1:4
HCF of 10 and 40 is 10. Divide both parts by it: 1:4.
2. 2:3
HCF of 20 and 30 is 10. Divide both parts by it: 2:3.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 1:1
HCF of 32 and 32 is 32. Divide both parts by it: 1:1.
5. 10 and 5
Total parts: 2 + 1 = 3. One part: 15 ÷ 3 = 5. 2 × 5 = 10, 1 × 5 = 5.
6. 60 and 72
Total parts: 5 + 6 = 11. One part: 132 ÷ 11 = 12. 5 × 12 = 60, 6 × 12 = 72.
7. 7 and 21
Total parts: 1 + 3 = 4. One part: 28 ÷ 4 = 7. 1 × 7 = 7, 3 × 7 = 21.
8. 55 and 66
Total parts: 5 + 6 = 11. One part: 121 ÷ 11 = 11. 5 × 11 = 55, 6 × 11 = 66.
9. 3 and 18
Total parts: 1 + 6 = 7. One part: 21 ÷ 7 = 3. 1 × 3 = 3, 6 × 3 = 18.
10. 9 and 15
Total parts: 3 + 5 = 8. One part: 24 ÷ 8 = 3. 3 × 3 = 9, 5 × 3 = 15.
11. 8 and 14
Total parts: 4 + 7 = 11. One part: 22 ÷ 11 = 2. 4 × 2 = 8, 7 × 2 = 14.
12. 22 and 11
Total parts: 2 + 1 = 3. One part: 33 ÷ 3 = 11. 2 × 11 = 22, 1 × 11 = 11.
Worked examples
Simplify the ratio 20:20.
- HCF of 20 and 20 is 20.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 55 in the ratio 4:1.
- Total parts: 4 + 1 = 5.
- One part: 55 ÷ 5 = 11.
- 4 × 11 = 44, 1 × 11 = 11.
- Answer: 44 and 11
Share 36 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 36 ÷ 3 = 12.
- 2 × 12 = 24, 1 × 12 = 12.
- Answer: 24 and 12
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 Definite Integrals in Context 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 Working with Definite Integrals, Introducing Definite Integrals, 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 Definite Integrals in Context?
- Move on to Reverse Differentiation, Area Under a Curve, which build directly on this idea.
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