Free Grade 3 Introducing Definite Integrals Essentials Lessons
Free Grade 3 lessons for Introducing Definite Integrals Essentials: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing definite integrals essentials
Identify introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing definite integrals essentials
Explain introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing definite integrals essentials
Calculate introducing definite integrals essentials accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing definite integrals essentials
Compare introducing definite integrals essentials 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 Introducing Definite Integrals Essentials 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 32:8.[1]
- 2.Simplify the ratio 20:12.[1]
- 3.Simplify the ratio 8:4.[1]
- 4.Simplify the ratio 6:24.[1]
- 5.Share 27 in the ratio 3:6.[2]
- 6.Share 110 in the ratio 5:6.[2]
- 7.Share 20 in the ratio 4:1.[2]
- 8.Share 84 in the ratio 5:2.[2]
- 9.Share 18 in the ratio 4:5.[3]
- 10.Share 21 in the ratio 2:5.[3]
- 11.Share 64 in the ratio 1:7.[3]
- 12.Share 80 in the ratio 2:6.[3]
Show answers and working
1. 4:1
HCF of 32 and 8 is 8. Divide both parts by it: 4:1.
2. 5:3
HCF of 20 and 12 is 4. Divide both parts by it: 5:3.
3. 2:1
HCF of 8 and 4 is 4. Divide both parts by it: 2:1.
4. 1:4
HCF of 6 and 24 is 6. Divide both parts by it: 1:4.
5. 9 and 18
Total parts: 3 + 6 = 9. One part: 27 ÷ 9 = 3. 3 × 3 = 9, 6 × 3 = 18.
6. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
7. 16 and 4
Total parts: 4 + 1 = 5. One part: 20 ÷ 5 = 4. 4 × 4 = 16, 1 × 4 = 4.
8. 60 and 24
Total parts: 5 + 2 = 7. One part: 84 ÷ 7 = 12. 5 × 12 = 60, 2 × 12 = 24.
9. 8 and 10
Total parts: 4 + 5 = 9. One part: 18 ÷ 9 = 2. 4 × 2 = 8, 5 × 2 = 10.
10. 6 and 15
Total parts: 2 + 5 = 7. One part: 21 ÷ 7 = 3. 2 × 3 = 6, 5 × 3 = 15.
11. 8 and 56
Total parts: 1 + 7 = 8. One part: 64 ÷ 8 = 8. 1 × 8 = 8, 7 × 8 = 56.
12. 20 and 60
Total parts: 2 + 6 = 8. One part: 80 ÷ 8 = 10. 2 × 10 = 20, 6 × 10 = 60.
Worked examples
Simplify the ratio 16:32.
- HCF of 16 and 32 is 16.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 54 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 54 ÷ 6 = 9.
- 4 × 9 = 36, 2 × 9 = 18.
- Answer: 36 and 18
Share 56 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 56 ÷ 8 = 7.
- 5 × 7 = 35, 3 × 7 = 21.
- Answer: 35 and 21
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
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Frequently asked
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- What should a learner already know before this?
- Start with 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 Introducing Definite Integrals Essentials?
- Move on to Introducing Definite Integrals Techniques, Introducing Definite Integrals Word Problems, Introducing Definite Integrals Common Errors, Working with Definite Integrals, which build directly on this idea.
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