Free Grade 3 Defining Rational Numbers in Context Word Problems Lessons
Free Grade 3 lessons for Defining Rational Numbers in Context Word Problems: 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
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain defining rational numbers in context word problems
Explain defining rational numbers in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate defining rational numbers in context word problems
Calculate defining rational numbers in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare defining rational numbers in context word problems
Compare defining rational numbers in context word problems accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify defining rational numbers in context word problems
Justify defining rational numbers in context word problems 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 in Context Word Problems 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 6:12.[1]
- 2.Simplify the ratio 12:12.[1]
- 3.Simplify the ratio 24:24.[1]
- 4.Simplify the ratio 60:12.[1]
- 5.Share 64 in the ratio 5:3.[2]
- 6.Share 54 in the ratio 1:5.[2]
- 7.Share 6 in the ratio 1:1.[2]
- 8.Share 42 in the ratio 5:2.[2]
- 9.Share 12 in the ratio 3:1.[3]
- 10.Share 48 in the ratio 3:3.[3]
- 11.Share 36 in the ratio 5:4.[3]
- 12.Share 18 in the ratio 2:4.[3]
Show answers and working
1. 1:2
HCF of 6 and 12 is 6. Divide both parts by it: 1:2.
2. 1:1
HCF of 12 and 12 is 12. Divide both parts by it: 1:1.
3. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
4. 5:1
HCF of 60 and 12 is 12. Divide both parts by it: 5:1.
5. 40 and 24
Total parts: 5 + 3 = 8. One part: 64 ÷ 8 = 8. 5 × 8 = 40, 3 × 8 = 24.
6. 9 and 45
Total parts: 1 + 5 = 6. One part: 54 ÷ 6 = 9. 1 × 9 = 9, 5 × 9 = 45.
7. 3 and 3
Total parts: 1 + 1 = 2. One part: 6 ÷ 2 = 3. 1 × 3 = 3, 1 × 3 = 3.
8. 30 and 12
Total parts: 5 + 2 = 7. One part: 42 ÷ 7 = 6. 5 × 6 = 30, 2 × 6 = 12.
9. 9 and 3
Total parts: 3 + 1 = 4. One part: 12 ÷ 4 = 3. 3 × 3 = 9, 1 × 3 = 3.
10. 24 and 24
Total parts: 3 + 3 = 6. One part: 48 ÷ 6 = 8. 3 × 8 = 24, 3 × 8 = 24.
11. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
12. 6 and 12
Total parts: 2 + 4 = 6. One part: 18 ÷ 6 = 3. 2 × 3 = 6, 4 × 3 = 12.
Worked examples
Simplify the ratio 4:20.
- HCF of 4 and 20 is 4.
- Divide both parts by it: 1:5.
- Answer: 1:5
Share 32 in the ratio 1:3.
- Total parts: 1 + 3 = 4.
- One part: 32 ÷ 4 = 8.
- 1 × 8 = 8, 3 × 8 = 24.
- Answer: 8 and 24
Share 30 in the ratio 1:2.
- Total parts: 1 + 2 = 3.
- One part: 30 ÷ 3 = 10.
- 1 × 10 = 10, 2 × 10 = 20.
- Answer: 10 and 20
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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- Start with Defining Rational Numbers in Context Techniques, Defining Rational Numbers in Context Essentials, Working with Defining Rational Numbers. Each one has its own free lesson, worksheet and quiz.
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- What comes next after Defining Rational Numbers in Context Word Problems?
- Move on to Defining Rational Numbers in Context Common Errors, Introducing Defining Rational Numbers, Working with Defining Rational Numbers, which build directly on this idea.
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