Free Grade 3 Introducing Proper Fractions Lessons
Free Grade 3 lessons for Introducing Proper Fractions: 12 real questions with a full answer key and worked solutions. A fraction describes equal parts of a whole. The denominator (bottom) is how many equal parts there are; the numerator (top) is how many we are talking about.
Free
Stretch
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain introducing proper fractions
Explain introducing proper fractions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing proper fractions
Calculate introducing proper fractions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing proper fractions
Compare introducing proper fractions accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify introducing proper fractions
Justify introducing proper fractions 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 Proper Fractions works
A fraction describes equal parts of a whole. The denominator (bottom) is how many equal parts there are; the numerator (top) is how many we are talking about.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.A shape is split into 5 equal parts and 4 are shaded. What fraction is shaded, and what fraction is not?[1]
- 2.A shape is split into 8 equal parts and 4 are shaded. What fraction is shaded, and what fraction is not?[1]
- 3.A shape is split into 3 equal parts and 2 are shaded. What fraction is shaded, and what fraction is not?[1]
- 4.A shape is split into 7 equal parts and 4 are shaded. What fraction is shaded, and what fraction is not?[1]
- 5.A shape is split into 12 equal parts and 2 are shaded. What fraction is shaded, and what fraction is not?[2]
- 6.A shape is split into 4 equal parts and 2 are shaded. What fraction is shaded, and what fraction is not?[2]
- 7.A shape is split into 11 equal parts and 2 are shaded. What fraction is shaded, and what fraction is not?[2]
- 8.A shape is split into 8 equal parts and 6 are shaded. What fraction is shaded, and what fraction is not?[2]
- 9.A shape is split into 10 equal parts and 7 are shaded. What fraction is shaded, and what fraction is not?[3]
- 10.A shape is split into 6 equal parts and 4 are shaded. What fraction is shaded, and what fraction is not?[3]
- 11.A shape is split into 10 equal parts and 8 are shaded. What fraction is shaded, and what fraction is not?[3]
- 12.A shape is split into 15 equal parts and 7 are shaded. What fraction is shaded, and what fraction is not?[3]
Show answers and working
1. 4/5 shaded, 1/5 not shaded
Denominator = total equal parts = 5. Numerator = shaded parts = 4. Unshaded: 5 − 4 = 1, so 1/5.
2. 4/8 shaded, 4/8 not shaded
Denominator = total equal parts = 8. Numerator = shaded parts = 4. Unshaded: 8 − 4 = 4, so 4/8.
3. 2/3 shaded, 1/3 not shaded
Denominator = total equal parts = 3. Numerator = shaded parts = 2. Unshaded: 3 − 2 = 1, so 1/3.
4. 4/7 shaded, 3/7 not shaded
Denominator = total equal parts = 7. Numerator = shaded parts = 4. Unshaded: 7 − 4 = 3, so 3/7.
5. 2/12 shaded, 10/12 not shaded
Denominator = total equal parts = 12. Numerator = shaded parts = 2. Unshaded: 12 − 2 = 10, so 10/12.
6. 2/4 shaded, 2/4 not shaded
Denominator = total equal parts = 4. Numerator = shaded parts = 2. Unshaded: 4 − 2 = 2, so 2/4.
7. 2/11 shaded, 9/11 not shaded
Denominator = total equal parts = 11. Numerator = shaded parts = 2. Unshaded: 11 − 2 = 9, so 9/11.
8. 6/8 shaded, 2/8 not shaded
Denominator = total equal parts = 8. Numerator = shaded parts = 6. Unshaded: 8 − 6 = 2, so 2/8.
9. 7/10 shaded, 3/10 not shaded
Denominator = total equal parts = 10. Numerator = shaded parts = 7. Unshaded: 10 − 7 = 3, so 3/10.
10. 4/6 shaded, 2/6 not shaded
Denominator = total equal parts = 6. Numerator = shaded parts = 4. Unshaded: 6 − 4 = 2, so 2/6.
11. 8/10 shaded, 2/10 not shaded
Denominator = total equal parts = 10. Numerator = shaded parts = 8. Unshaded: 10 − 8 = 2, so 2/10.
12. 7/15 shaded, 8/15 not shaded
Denominator = total equal parts = 15. Numerator = shaded parts = 7. Unshaded: 15 − 7 = 8, so 8/15.
Worked examples
A shape is split into 2 equal parts and 1 are shaded. What fraction is shaded, and what fraction is not?
- Denominator = total equal parts = 2.
- Numerator = shaded parts = 1.
- Unshaded: 2 − 1 = 1, so 1/2.
- Answer: 1/2 shaded, 1/2 not shaded
A shape is split into 4 equal parts and 3 are shaded. What fraction is shaded, and what fraction is not?
- Denominator = total equal parts = 4.
- Numerator = shaded parts = 3.
- Unshaded: 4 − 3 = 1, so 1/4.
- Answer: 3/4 shaded, 1/4 not shaded
A shape is split into 9 equal parts and 4 are shaded. What fraction is shaded, and what fraction is not?
- Denominator = total equal parts = 9.
- Numerator = shaded parts = 4.
- Unshaded: 9 − 4 = 5, so 5/9.
- Answer: 4/9 shaded, 5/9 not shaded
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Counts unequal parts as fractions.
Correction: Parts must be the same size.
Swaps numerator and denominator.
Correction: The denominator is down — it is the total number of parts.
Teacher tips
- · Fold paper strips into equal parts and label them.
Parent tips
- · Ask what fraction of the family is wearing blue.
Real-life applications
- · Sharing food fairly, telling the time (quarter past).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Introducing Proper Fractions 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 Unit Fractions. 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 Proper Fractions?
- Move on to Working with Proper Fractions, Proper Fractions in Context, Introduction to Fractions, Parts of a Fraction, which build directly on this idea.
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