Free Grade 3 Operations with Rationals Lesson Plans
Free Grade 3 lesson plans for Operations with Rationals: 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
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify operations with rationals
Identify operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain operations with rationals
Explain operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate operations with rationals
Calculate operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare operations with rationals
Compare operations with rationals 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 Operations with Rationals 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 6:18.[1]
- 2.Simplify the ratio 8:12.[1]
- 3.Simplify the ratio 20:30.[1]
- 4.Simplify the ratio 36:12.[1]
- 5.Share 36 in the ratio 1:2.[2]
- 6.Share 77 in the ratio 5:2.[2]
- 7.Share 81 in the ratio 4:5.[2]
- 8.Share 30 in the ratio 5:1.[2]
- 9.Share 72 in the ratio 5:1.[3]
- 10.Share 16 in the ratio 5:3.[3]
- 11.Share 48 in the ratio 3:1.[3]
- 12.Share 18 in the ratio 3:3.[3]
Show answers and working
1. 1:3
HCF of 6 and 18 is 6. Divide both parts by it: 1:3.
2. 2:3
HCF of 8 and 12 is 4. Divide both parts by it: 2:3.
3. 2:3
HCF of 20 and 30 is 10. Divide both parts by it: 2:3.
4. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
5. 12 and 24
Total parts: 1 + 2 = 3. One part: 36 ÷ 3 = 12. 1 × 12 = 12, 2 × 12 = 24.
6. 55 and 22
Total parts: 5 + 2 = 7. One part: 77 ÷ 7 = 11. 5 × 11 = 55, 2 × 11 = 22.
7. 36 and 45
Total parts: 4 + 5 = 9. One part: 81 ÷ 9 = 9. 4 × 9 = 36, 5 × 9 = 45.
8. 25 and 5
Total parts: 5 + 1 = 6. One part: 30 ÷ 6 = 5. 5 × 5 = 25, 1 × 5 = 5.
9. 60 and 12
Total parts: 5 + 1 = 6. One part: 72 ÷ 6 = 12. 5 × 12 = 60, 1 × 12 = 12.
10. 10 and 6
Total parts: 5 + 3 = 8. One part: 16 ÷ 8 = 2. 5 × 2 = 10, 3 × 2 = 6.
11. 36 and 12
Total parts: 3 + 1 = 4. One part: 48 ÷ 4 = 12. 3 × 12 = 36, 1 × 12 = 12.
12. 9 and 9
Total parts: 3 + 3 = 6. One part: 18 ÷ 6 = 3. 3 × 3 = 9, 3 × 3 = 9.
Worked examples
Simplify the ratio 10:10.
- HCF of 10 and 10 is 10.
- Divide both parts by it: 1:1.
- Answer: 1:1
Share 110 in the ratio 5:6.
- Total parts: 5 + 6 = 11.
- One part: 110 ÷ 11 = 10.
- 5 × 10 = 50, 6 × 10 = 60.
- Answer: 50 and 60
Share 14 in the ratio 4:3.
- Total parts: 4 + 3 = 7.
- One part: 14 ÷ 7 = 2.
- 4 × 2 = 8, 3 × 2 = 6.
- Answer: 8 and 6
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 Operations with Rationals
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 Operations with Rationals 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 Rational Number Line, Defining Rational Numbers, Percentages. 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 Operations with Rationals?
- Move on to Whole Numbers, Counting, Number Recognition, Number Formation, which build directly on this idea.
Related resources
Stuck on Operations with Rationals? The AI Tutor already knows this page, its prerequisites and its common mistakes.
Open the free AI Tutor