Free Grade 3 Defining Rational Numbers Lesson Plans
Free Grade 3 lesson plans for Defining Rational Numbers: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain defining rational numbers
Explain defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate defining rational numbers
Calculate defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare defining rational numbers
Compare defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify defining rational numbers
Justify defining rational numbers 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 Defining Rational Numbers 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 12:20.[1]
- 2.Simplify the ratio 16:8.[1]
- 3.Simplify the ratio 36:12.[1]
- 4.Simplify the ratio 50:30.[1]
- 5.Share 36 in the ratio 5:1.[2]
- 6.Share 60 in the ratio 4:2.[2]
- 7.Share 60 in the ratio 3:3.[2]
- 8.Share 42 in the ratio 3:3.[2]
- 9.Share 40 in the ratio 2:3.[3]
- 10.Share 60 in the ratio 1:5.[3]
- 11.Share 60 in the ratio 5:7.[3]
- 12.Share 54 in the ratio 2:7.[3]
Show answers and working
1. 3:5
HCF of 12 and 20 is 4. Divide both parts by it: 3:5.
2. 2:1
HCF of 16 and 8 is 8. Divide both parts by it: 2:1.
3. 3:1
HCF of 36 and 12 is 12. Divide both parts by it: 3:1.
4. 5:3
HCF of 50 and 30 is 10. Divide both parts by it: 5:3.
5. 30 and 6
Total parts: 5 + 1 = 6. One part: 36 ÷ 6 = 6. 5 × 6 = 30, 1 × 6 = 6.
6. 40 and 20
Total parts: 4 + 2 = 6. One part: 60 ÷ 6 = 10. 4 × 10 = 40, 2 × 10 = 20.
7. 30 and 30
Total parts: 3 + 3 = 6. One part: 60 ÷ 6 = 10. 3 × 10 = 30, 3 × 10 = 30.
8. 21 and 21
Total parts: 3 + 3 = 6. One part: 42 ÷ 6 = 7. 3 × 7 = 21, 3 × 7 = 21.
9. 16 and 24
Total parts: 2 + 3 = 5. One part: 40 ÷ 5 = 8. 2 × 8 = 16, 3 × 8 = 24.
10. 10 and 50
Total parts: 1 + 5 = 6. One part: 60 ÷ 6 = 10. 1 × 10 = 10, 5 × 10 = 50.
11. 25 and 35
Total parts: 5 + 7 = 12. One part: 60 ÷ 12 = 5. 5 × 5 = 25, 7 × 5 = 35.
12. 12 and 42
Total parts: 2 + 7 = 9. One part: 54 ÷ 9 = 6. 2 × 6 = 12, 7 × 6 = 42.
Worked examples
Simplify the ratio 8:12.
- HCF of 8 and 12 is 4.
- Divide both parts by it: 2:3.
- Answer: 2:3
Share 45 in the ratio 3:2.
- Total parts: 3 + 2 = 5.
- One part: 45 ÷ 5 = 9.
- 3 × 9 = 27, 2 × 9 = 18.
- Answer: 27 and 18
Share 48 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 48 ÷ 6 = 8.
- 5 × 8 = 40, 1 × 8 = 8.
- Answer: 40 and 8
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 Defining Rational Numbers 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 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 Defining Rational Numbers?
- Move on to Rational Number Line, Operations with Rationals, Whole Numbers, Counting, which build directly on this idea.
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