Free Grade 3 Definite Integrals in Context Lesson Plans
Free Grade 3 lesson plans 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
Core
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 50:10.[1]
- 2.Simplify the ratio 12:48.[1]
- 3.Simplify the ratio 20:30.[1]
- 4.Simplify the ratio 60:48.[1]
- 5.Share 18 in the ratio 1:5.[2]
- 6.Share 32 in the ratio 2:2.[2]
- 7.Share 96 in the ratio 5:3.[2]
- 8.Share 18 in the ratio 5:4.[2]
- 9.Share 36 in the ratio 1:5.[3]
- 10.Share 36 in the ratio 1:3.[3]
- 11.Share 100 in the ratio 5:5.[3]
- 12.Share 28 in the ratio 1:6.[3]
Show answers and working
1. 5:1
HCF of 50 and 10 is 10. Divide both parts by it: 5:1.
2. 1:4
HCF of 12 and 48 is 12. Divide both parts by it: 1:4.
3. 2:3
HCF of 20 and 30 is 10. Divide both parts by it: 2:3.
4. 5:4
HCF of 60 and 48 is 12. Divide both parts by it: 5:4.
5. 3 and 15
Total parts: 1 + 5 = 6. One part: 18 ÷ 6 = 3. 1 × 3 = 3, 5 × 3 = 15.
6. 16 and 16
Total parts: 2 + 2 = 4. One part: 32 ÷ 4 = 8. 2 × 8 = 16, 2 × 8 = 16.
7. 60 and 36
Total parts: 5 + 3 = 8. One part: 96 ÷ 8 = 12. 5 × 12 = 60, 3 × 12 = 36.
8. 10 and 8
Total parts: 5 + 4 = 9. One part: 18 ÷ 9 = 2. 5 × 2 = 10, 4 × 2 = 8.
9. 6 and 30
Total parts: 1 + 5 = 6. One part: 36 ÷ 6 = 6. 1 × 6 = 6, 5 × 6 = 30.
10. 9 and 27
Total parts: 1 + 3 = 4. One part: 36 ÷ 4 = 9. 1 × 9 = 9, 3 × 9 = 27.
11. 50 and 50
Total parts: 5 + 5 = 10. One part: 100 ÷ 10 = 10. 5 × 10 = 50, 5 × 10 = 50.
12. 4 and 24
Total parts: 1 + 6 = 7. One part: 28 ÷ 7 = 4. 1 × 4 = 4, 6 × 4 = 24.
Worked examples
Simplify the ratio 20:16.
- HCF of 20 and 16 is 4.
- Divide both parts by it: 5:4.
- Answer: 5:4
Share 18 in the ratio 3:6.
- Total parts: 3 + 6 = 9.
- One part: 18 ÷ 9 = 2.
- 3 × 2 = 6, 6 × 2 = 12.
- Answer: 6 and 12
Share 84 in the ratio 2:5.
- Total parts: 2 + 5 = 7.
- One part: 84 ÷ 7 = 12.
- 2 × 12 = 24, 5 × 12 = 60.
- Answer: 24 and 60
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 in Context
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 Definite Integrals in Context 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 Working with Definite Integrals, 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 Definite Integrals in Context?
- Move on to Reverse Differentiation, Area Under a Curve, which build directly on this idea.
Related resources
Stuck on Definite Integrals in Context? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor