Free Grade 3 Working with Rational Number Line Lesson Plans
Free Grade 3 lesson plans for Working with Rational Number Line: 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
Stretch
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain working with rational number line
Explain working with rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with rational number line
Calculate working with rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with rational number line
Compare working with rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify working with rational number line
Justify working with rational number line 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 Rational Number Line 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 12:24.[1]
- 2.Simplify the ratio 60:60.[1]
- 3.Simplify the ratio 24:12.[1]
- 4.Simplify the ratio 30:6.[1]
- 5.Share 36 in the ratio 1:2.[2]
- 6.Share 18 in the ratio 5:1.[2]
- 7.Share 16 in the ratio 1:3.[2]
- 8.Share 27 in the ratio 4:5.[2]
- 9.Share 66 in the ratio 2:4.[3]
- 10.Share 110 in the ratio 3:7.[3]
- 11.Share 120 in the ratio 5:7.[3]
- 12.Share 80 in the ratio 5:5.[3]
Show answers and working
1. 1:2
HCF of 12 and 24 is 12. Divide both parts by it: 1:2.
2. 1:1
HCF of 60 and 60 is 60. Divide both parts by it: 1:1.
3. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
4. 5:1
HCF of 30 and 6 is 6. Divide both parts by it: 5:1.
5. 12 and 24
Total parts: 1 + 2 = 3. One part: 36 ÷ 3 = 12. 1 × 12 = 12, 2 × 12 = 24.
6. 15 and 3
Total parts: 5 + 1 = 6. One part: 18 ÷ 6 = 3. 5 × 3 = 15, 1 × 3 = 3.
7. 4 and 12
Total parts: 1 + 3 = 4. One part: 16 ÷ 4 = 4. 1 × 4 = 4, 3 × 4 = 12.
8. 12 and 15
Total parts: 4 + 5 = 9. One part: 27 ÷ 9 = 3. 4 × 3 = 12, 5 × 3 = 15.
9. 22 and 44
Total parts: 2 + 4 = 6. One part: 66 ÷ 6 = 11. 2 × 11 = 22, 4 × 11 = 44.
10. 33 and 77
Total parts: 3 + 7 = 10. One part: 110 ÷ 10 = 11. 3 × 11 = 33, 7 × 11 = 77.
11. 50 and 70
Total parts: 5 + 7 = 12. One part: 120 ÷ 12 = 10. 5 × 10 = 50, 7 × 10 = 70.
12. 40 and 40
Total parts: 5 + 5 = 10. One part: 80 ÷ 10 = 8. 5 × 8 = 40, 5 × 8 = 40.
Worked examples
Simplify the ratio 4:8.
- HCF of 4 and 8 is 4.
- Divide both parts by it: 1:2.
- Answer: 1:2
Share 54 in the ratio 1:5.
- Total parts: 1 + 5 = 6.
- One part: 54 ÷ 6 = 9.
- 1 × 9 = 9, 5 × 9 = 45.
- Answer: 9 and 45
Share 42 in the ratio 2:4.
- Total parts: 2 + 4 = 6.
- One part: 42 ÷ 6 = 7.
- 2 × 7 = 14, 4 × 7 = 28.
- Answer: 14 and 28
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 Rational Number Line 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 Rational Number Line, Defining Rational Numbers. 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 Rational Number Line?
- Move on to Rational Number Line in Context, Defining Rational Numbers, Operations with Rationals, which build directly on this idea.
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