Free Grade 3 Scale Factors in Context Lessons
Free Grade 3 lessons for Scale Factors in Context: 12 real questions with a full answer key and worked solutions. Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
Free
Stretch
20 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain scale factors in context
Explain scale factors in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate scale factors in context
Calculate scale factors in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare scale factors in context
Compare scale factors in context accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify scale factors in context
Justify scale factors in context 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 Scale Factors in Context works
Factors divide a number exactly; multiples are in its times table. The HCF is the biggest shared factor, the LCM the smallest shared multiple.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.List all the factors of 18.[1]
- 2.List all the factors of 20.[1]
- 3.List all the factors of 24.[1]
- 4.List all the factors of 30.[1]
- 5.Find the highest common factor (HCF) of 4 and 4.[2]
- 6.Find the highest common factor (HCF) of 4 and 8.[2]
- 7.Find the highest common factor (HCF) of 48 and 56.[2]
- 8.Find the highest common factor (HCF) of 12 and 18.[2]
- 9.Find the lowest common multiple (LCM) of 36 and 42.[3]
- 10.Find the highest common factor (HCF) of 6 and 6.[3]
- 11.Find the lowest common multiple (LCM) of 8 and 24.[3]
- 12.Find the lowest common multiple (LCM) of 10 and 25.[3]
Show answers and working
1. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
2. 1, 2, 4, 5, 10, 20
Find factor pairs that multiply to 20. 1 × 20 2 × 10 4 × 5
3. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
4. 1, 2, 3, 5, 6, 10, 15, 30
Find factor pairs that multiply to 30. 1 × 30 2 × 15 3 × 10 5 × 6
5. 4
List factors of 4 and 4. The largest factor they share is 4.
6. 4
List factors of 4 and 8. The largest factor they share is 4.
7. 8
List factors of 48 and 56. The largest factor they share is 8.
8. 6
List factors of 12 and 18. The largest factor they share is 6.
9. 252
HCF(36, 42) = 6. LCM = 36 × 42 ÷ 6 = 252.
10. 6
List factors of 6 and 6. The largest factor they share is 6.
11. 24
HCF(8, 24) = 8. LCM = 8 × 24 ÷ 8 = 24.
12. 50
HCF(10, 25) = 5. LCM = 10 × 25 ÷ 5 = 50.
Worked examples
List all the factors of 28.
- Find factor pairs that multiply to 28.
- 1 × 28
- 2 × 14
- 4 × 7
- Answer: 1, 2, 4, 7, 14, 28
Find the highest common factor (HCF) of 28 and 28.
- List factors of 28 and 28.
- The largest factor they share is 28.
- Answer: 28
Find the lowest common multiple (LCM) of 20 and 24.
- HCF(20, 24) = 4.
- LCM = 20 × 24 ÷ 4 = 120.
- Answer: 120
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Mixes up factors and multiples.
Correction: Factors are Few (they fit inside), multiples are Many (they go on forever).
Misses factor pairs.
Correction: Work through 1, 2, 3… in order until the pairs meet.
Teacher tips
- · Use factor rainbows to show pairs.
Parent tips
- · Ask how many ways 24 sweets can be put into equal bags.
Real-life applications
- · Arranging chairs in equal rows, syncing bus timetables (LCM).
Assessment objectives
How mastery is evidenced, and which standards it maps to.
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Frequently asked
- Is this Grade 3 Scale Factors in Context 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 Working with Scale Factors, Introducing Scale Factors, Inverse Proportion. 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 Scale Factors in Context?
- Move on to Direct Proportion, Inverse Proportion, Best Buy Problems, which build directly on this idea.
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