Free Grade 3 Working with Defining Rational Numbers Lesson Plans
Free Grade 3 lesson plans for Working with 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
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with defining rational numbers
Explain working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with defining rational numbers
Calculate working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with defining rational numbers
Compare working with defining rational numbers accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with defining rational numbers
Justify working with 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 Working with 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 6:18.[1]
- 2.Simplify the ratio 24:6.[1]
- 3.Simplify the ratio 8:8.[1]
- 4.Simplify the ratio 30:12.[1]
- 5.Share 63 in the ratio 4:5.[2]
- 6.Share 90 in the ratio 5:4.[2]
- 7.Share 15 in the ratio 1:2.[2]
- 8.Share 70 in the ratio 2:5.[2]
- 9.Share 24 in the ratio 2:2.[3]
- 10.Share 72 in the ratio 3:6.[3]
- 11.Share 40 in the ratio 1:4.[3]
- 12.Share 32 in the ratio 1:3.[3]
Show answers and working
1. 1:3
HCF of 6 and 18 is 6. Divide both parts by it: 1:3.
2. 4:1
HCF of 24 and 6 is 6. Divide both parts by it: 4:1.
3. 1:1
HCF of 8 and 8 is 8. Divide both parts by it: 1:1.
4. 5:2
HCF of 30 and 12 is 6. Divide both parts by it: 5:2.
5. 28 and 35
Total parts: 4 + 5 = 9. One part: 63 ÷ 9 = 7. 4 × 7 = 28, 5 × 7 = 35.
6. 50 and 40
Total parts: 5 + 4 = 9. One part: 90 ÷ 9 = 10. 5 × 10 = 50, 4 × 10 = 40.
7. 5 and 10
Total parts: 1 + 2 = 3. One part: 15 ÷ 3 = 5. 1 × 5 = 5, 2 × 5 = 10.
8. 20 and 50
Total parts: 2 + 5 = 7. One part: 70 ÷ 7 = 10. 2 × 10 = 20, 5 × 10 = 50.
9. 12 and 12
Total parts: 2 + 2 = 4. One part: 24 ÷ 4 = 6. 2 × 6 = 12, 2 × 6 = 12.
10. 24 and 48
Total parts: 3 + 6 = 9. One part: 72 ÷ 9 = 8. 3 × 8 = 24, 6 × 8 = 48.
11. 8 and 32
Total parts: 1 + 4 = 5. One part: 40 ÷ 5 = 8. 1 × 8 = 8, 4 × 8 = 32.
12. 8 and 24
Total parts: 1 + 3 = 4. One part: 32 ÷ 4 = 8. 1 × 8 = 8, 3 × 8 = 24.
Worked examples
Simplify the ratio 24:12.
- HCF of 24 and 12 is 12.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 24 in the ratio 3:1.
- Total parts: 3 + 1 = 4.
- One part: 24 ÷ 4 = 6.
- 3 × 6 = 18, 1 × 6 = 6.
- Answer: 18 and 6
Share 10 in the ratio 1:4.
- Total parts: 1 + 4 = 5.
- One part: 10 ÷ 5 = 2.
- 1 × 2 = 2, 4 × 2 = 8.
- Answer: 2 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 Working with 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 Introducing 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 Working with Defining Rational Numbers?
- Move on to Defining Rational Numbers in Context, Rational Number Line, Operations with Rationals, which build directly on this idea.
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