Free Grade 3 Definite Integrals in Context Worksheets
Free Grade 3 worksheets 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
30 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 60:24.[1]
- 2.Simplify the ratio 16:12.[1]
- 3.Simplify the ratio 50:10.[1]
- 4.Simplify the ratio 30:30.[1]
- 5.Share 48 in the ratio 2:4.[2]
- 6.Share 36 in the ratio 1:5.[2]
- 7.Share 20 in the ratio 4:1.[2]
- 8.Share 132 in the ratio 5:6.[2]
- 9.Share 24 in the ratio 3:3.[3]
- 10.Share 55 in the ratio 3:2.[3]
- 11.Share 16 in the ratio 1:3.[3]
- 12.Share 77 in the ratio 1:6.[3]
Show answers and working
1. 5:2
HCF of 60 and 24 is 12. Divide both parts by it: 5:2.
2. 4:3
HCF of 16 and 12 is 4. Divide both parts by it: 4:3.
3. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
4. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
5. 16 and 32
Total parts: 2 + 4 = 6. One part: 48 ÷ 6 = 8. 2 × 8 = 16, 4 × 8 = 32.
6. 6 and 30
Total parts: 1 + 5 = 6. One part: 36 ÷ 6 = 6. 1 × 6 = 6, 5 × 6 = 30.
7. 16 and 4
Total parts: 4 + 1 = 5. One part: 20 ÷ 5 = 4. 4 × 4 = 16, 1 × 4 = 4.
8. 60 and 72
Total parts: 5 + 6 = 11. One part: 132 ÷ 11 = 12. 5 × 12 = 60, 6 × 12 = 72.
9. 12 and 12
Total parts: 3 + 3 = 6. One part: 24 ÷ 6 = 4. 3 × 4 = 12, 3 × 4 = 12.
10. 33 and 22
Total parts: 3 + 2 = 5. One part: 55 ÷ 5 = 11. 3 × 11 = 33, 2 × 11 = 22.
11. 4 and 12
Total parts: 1 + 3 = 4. One part: 16 ÷ 4 = 4. 1 × 4 = 4, 3 × 4 = 12.
12. 11 and 66
Total parts: 1 + 6 = 7. One part: 77 ÷ 7 = 11. 1 × 11 = 11, 6 × 11 = 66.
Worked examples
Simplify the ratio 40:40.
- HCF of 40 and 40 is 40.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 49 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 49 ÷ 7 = 7.
- 3 × 7 = 21, 4 × 7 = 28.
- Answer: 21 and 28
Share 16 in the ratio 1:1.
- Total parts: 1 + 1 = 2.
- One part: 16 ÷ 2 = 8.
- 1 × 8 = 8, 1 × 8 = 8.
- Answer: 8 and 8
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 worksheet really free?
- Yes. Every worksheets 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 worksheet 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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