Free Grade 3 Working with Definite Integrals Lessons
Free Grade 3 lessons 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 30:40.[1]
- 2.Simplify the ratio 36:12.[1]
- 3.Simplify the ratio 30:50.[1]
- 4.Simplify the ratio 12:20.[1]
- 5.Share 33 in the ratio 5:6.[2]
- 6.Share 18 in the ratio 1:1.[2]
- 7.Share 36 in the ratio 4:5.[2]
- 8.Share 30 in the ratio 4:2.[2]
- 9.Share 16 in the ratio 1:1.[3]
- 10.Share 20 in the ratio 1:4.[3]
- 11.Share 20 in the ratio 3:2.[3]
- 12.Share 77 in the ratio 5:6.[3]
Show answers and working
1. 3:4
HCF of 30 and 40 is 10. Divide both parts by it: 3:4.
2. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
3. 3:5
HCF of 30 and 50 is 10. Divide both parts by it: 3:5.
4. 3:5
HCF of 12 and 20 is 4. Divide both parts by it: 3:5.
5. 15 and 18
Total parts: 5 + 6 = 11. One part: 33 ÷ 11 = 3. 5 × 3 = 15, 6 × 3 = 18.
6. 9 and 9
Total parts: 1 + 1 = 2. One part: 18 ÷ 2 = 9. 1 × 9 = 9, 1 × 9 = 9.
7. 16 and 20
Total parts: 4 + 5 = 9. One part: 36 ÷ 9 = 4. 4 × 4 = 16, 5 × 4 = 20.
8. 20 and 10
Total parts: 4 + 2 = 6. One part: 30 ÷ 6 = 5. 4 × 5 = 20, 2 × 5 = 10.
9. 8 and 8
Total parts: 1 + 1 = 2. One part: 16 ÷ 2 = 8. 1 × 8 = 8, 1 × 8 = 8.
10. 4 and 16
Total parts: 1 + 4 = 5. One part: 20 ÷ 5 = 4. 1 × 4 = 4, 4 × 4 = 16.
11. 12 and 8
Total parts: 3 + 2 = 5. One part: 20 ÷ 5 = 4. 3 × 4 = 12, 2 × 4 = 8.
12. 35 and 42
Total parts: 5 + 6 = 11. One part: 77 ÷ 11 = 7. 5 × 7 = 35, 6 × 7 = 42.
Worked examples
Simplify the ratio 30:24.
- HCF of 30 and 24 is 6.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 42 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 42 ÷ 6 = 7.
- 4 × 7 = 28, 2 × 7 = 14.
- Answer: 28 and 14
Share 36 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 36 ÷ 6 = 6.
- 4 × 6 = 24, 2 × 6 = 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.
Every free resource for Working with Definite Integrals
One concept, one ecosystem — all of it free.
Goes deeper
The entities below this one, each with the same complete free resource set.
Sibling concepts
Related concepts
Lateral links, including across subjects.
Next topics
All free formats for this concept
Every kind below is a real page, generated from this entity.
Learn — Meet the idea.
Practice — Build fluency.
Revise — Keep it in memory.
Assess — Prove mastery.
Apply — Use it in context.
Teach — Deliver it to a class.
Frequently asked
- Is this Grade 3 Working with 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 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 Working with Definite Integrals?
- Move on to Definite Integrals in Context, Reverse Differentiation, Area Under a Curve, which build directly on this idea.
Related resources
Stuck on Working with Definite Integrals? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor