Free Grade 3 Introducing Rational Number Line Lessons
Free Grade 3 lessons for Introducing 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
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing rational number line
Explain introducing rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing rational number line
Calculate introducing rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing rational number line
Compare introducing rational number line accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing rational number line
Justify introducing 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 Introducing 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 12:18.[1]
- 2.Simplify the ratio 40:8.[1]
- 3.Simplify the ratio 12:12.[1]
- 4.Simplify the ratio 10:50.[1]
- 5.Share 18 in the ratio 1:1.[2]
- 6.Share 14 in the ratio 5:2.[2]
- 7.Share 72 in the ratio 4:4.[2]
- 8.Share 8 in the ratio 1:3.[2]
- 9.Share 14 in the ratio 1:6.[3]
- 10.Share 44 in the ratio 4:7.[3]
- 11.Share 21 in the ratio 4:3.[3]
- 12.Share 88 in the ratio 1:7.[3]
Show answers and working
1. 2:3
HCF of 12 and 18 is 6. Divide both parts by it: 2:3.
2. 5:1
HCF of 40 and 8 is 8. Divide both parts by it: 5:1.
3. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
4. 1:5
HCF of 10 and 50 is 10. Divide both parts by it: 1:5.
5. 9 and 9
Total parts: 1 + 1 = 2. One part: 18 ÷ 2 = 9. 1 × 9 = 9, 1 × 9 = 9.
6. 10 and 4
Total parts: 5 + 2 = 7. One part: 14 ÷ 7 = 2. 5 × 2 = 10, 2 × 2 = 4.
7. 36 and 36
Total parts: 4 + 4 = 8. One part: 72 ÷ 8 = 9. 4 × 9 = 36, 4 × 9 = 36.
8. 2 and 6
Total parts: 1 + 3 = 4. One part: 8 ÷ 4 = 2. 1 × 2 = 2, 3 × 2 = 6.
9. 2 and 12
Total parts: 1 + 6 = 7. One part: 14 ÷ 7 = 2. 1 × 2 = 2, 6 × 2 = 12.
10. 16 and 28
Total parts: 4 + 7 = 11. One part: 44 ÷ 11 = 4. 4 × 4 = 16, 7 × 4 = 28.
11. 12 and 9
Total parts: 4 + 3 = 7. One part: 21 ÷ 7 = 3. 4 × 3 = 12, 3 × 3 = 9.
12. 11 and 77
Total parts: 1 + 7 = 8. One part: 88 ÷ 8 = 11. 1 × 11 = 11, 7 × 11 = 77.
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 99 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 99 ÷ 9 = 11.
- 5 × 11 = 55, 4 × 11 = 44.
- Answer: 55 and 44
Share 12 in the ratio 1:3.
- Total parts: 1 + 3 = 4.
- One part: 12 ÷ 4 = 3.
- 1 × 3 = 3, 3 × 3 = 9.
- Answer: 3 and 9
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 Introducing Rational Number Line lesson really free?
- Yes. Every lessons 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 Defining Rational Numbers. Each one has its own free lesson, worksheet and quiz.
- How is the lesson 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 Introducing Rational Number Line?
- Move on to Working with Rational Number Line, Rational Number Line in Context, Defining Rational Numbers, Operations with Rationals, which build directly on this idea.
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