Free Grade 3 Working with Operations with Rationals Lesson Plans
Free Grade 3 lesson plans for Working with 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
Core
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with operations with rationals
Explain working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with operations with rationals
Calculate working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with operations with rationals
Compare working with operations with rationals accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with operations with rationals
Justify working with 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 Working with 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 30:20.[1]
- 2.Simplify the ratio 12:16.[1]
- 3.Simplify the ratio 24:12.[1]
- 4.Simplify the ratio 12:18.[1]
- 5.Share 110 in the ratio 5:6.[2]
- 6.Share 42 in the ratio 4:3.[2]
- 7.Share 72 in the ratio 5:3.[2]
- 8.Share 72 in the ratio 4:4.[2]
- 9.Share 72 in the ratio 3:5.[3]
- 10.Share 22 in the ratio 4:7.[3]
- 11.Share 33 in the ratio 2:1.[3]
- 12.Share 12 in the ratio 3:1.[3]
Show answers and working
1. 3:2
HCF of 30 and 20 is 10. Divide both parts by it: 3:2.
2. 3:4
HCF of 12 and 16 is 4. Divide both parts by it: 3:4.
3. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
4. 2:3
HCF of 12 and 18 is 6. Divide both parts by it: 2:3.
5. 50 and 60
Total parts: 5 + 6 = 11. One part: 110 ÷ 11 = 10. 5 × 10 = 50, 6 × 10 = 60.
6. 24 and 18
Total parts: 4 + 3 = 7. One part: 42 ÷ 7 = 6. 4 × 6 = 24, 3 × 6 = 18.
7. 45 and 27
Total parts: 5 + 3 = 8. One part: 72 ÷ 8 = 9. 5 × 9 = 45, 3 × 9 = 27.
8. 36 and 36
Total parts: 4 + 4 = 8. One part: 72 ÷ 8 = 9. 4 × 9 = 36, 4 × 9 = 36.
9. 27 and 45
Total parts: 3 + 5 = 8. One part: 72 ÷ 8 = 9. 3 × 9 = 27, 5 × 9 = 45.
10. 8 and 14
Total parts: 4 + 7 = 11. One part: 22 ÷ 11 = 2. 4 × 2 = 8, 7 × 2 = 14.
11. 22 and 11
Total parts: 2 + 1 = 3. One part: 33 ÷ 3 = 11. 2 × 11 = 22, 1 × 11 = 11.
12. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
Worked examples
Simplify the ratio 10:50.
- HCF of 10 and 50 is 10.
- Divide both parts by it: 1:5.
- Answer: 1:5
Share 42 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 42 ÷ 7 = 6.
- 3 × 6 = 18, 4 × 6 = 24.
- Answer: 18 and 24
Share 88 in the ratio 5:3.
- Total parts: 5 + 3 = 8.
- One part: 88 ÷ 8 = 11.
- 5 × 11 = 55, 3 × 11 = 33.
- Answer: 55 and 33
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 Working with 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 Introducing Operations with Rationals, Rational Number Line. 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 Working with Operations with Rationals?
- Move on to Operations with Rationals in Context, Defining Rational Numbers, Rational Number Line, which build directly on this idea.
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