Free Grade 3 Introducing Scale Factors Lessons
Free Grade 3 lessons for Introducing Scale Factors: 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
Higher
15 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing scale factors
Identify introducing scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing scale factors
Explain introducing scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing scale factors
Calculate introducing scale factors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing scale factors
Compare introducing scale factors 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 Scale Factors 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 28.[1]
- 2.List all the factors of 18.[1]
- 3.List all the factors of 40.[1]
- 4.List all the factors of 24.[1]
- 5.Find the highest common factor (HCF) of 20 and 30.[2]
- 6.Find the highest common factor (HCF) of 8 and 20.[2]
- 7.Find the highest common factor (HCF) of 12 and 15.[2]
- 8.Find the highest common factor (HCF) of 24 and 28.[2]
- 9.Find the lowest common multiple (LCM) of 12 and 20.[3]
- 10.Find the lowest common multiple (LCM) of 12 and 21.[3]
- 11.Find the lowest common multiple (LCM) of 6 and 9.[3]
- 12.Find the lowest common multiple (LCM) of 28 and 35.[3]
Show answers and working
1. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
2. 1, 2, 3, 6, 9, 18
Find factor pairs that multiply to 18. 1 × 18 2 × 9 3 × 6
3. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
4. 1, 2, 3, 4, 6, 8, 12, 24
Find factor pairs that multiply to 24. 1 × 24 2 × 12 3 × 8 4 × 6
5. 10
List factors of 20 and 30. The largest factor they share is 10.
6. 4
List factors of 8 and 20. The largest factor they share is 4.
7. 3
List factors of 12 and 15. The largest factor they share is 3.
8. 4
List factors of 24 and 28. The largest factor they share is 4.
9. 60
HCF(12, 20) = 4. LCM = 12 × 20 ÷ 4 = 60.
10. 84
HCF(12, 21) = 3. LCM = 12 × 21 ÷ 3 = 84.
11. 18
HCF(6, 9) = 3. LCM = 6 × 9 ÷ 3 = 18.
12. 140
HCF(28, 35) = 7. LCM = 28 × 35 ÷ 7 = 140.
Worked examples
List all the factors of 30.
- Find factor pairs that multiply to 30.
- 1 × 30
- 2 × 15
- 3 × 10
- 5 × 6
- Answer: 1, 2, 3, 5, 6, 10, 15, 30
Find the highest common factor (HCF) of 15 and 9.
- List factors of 15 and 9.
- The largest factor they share is 3.
- Answer: 3
Find the highest common factor (HCF) of 30 and 30.
- List factors of 30 and 30.
- The largest factor they share is 30.
- Answer: 30
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 Introducing Scale Factors 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 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 Introducing Scale Factors?
- Move on to Working with Scale Factors, Scale Factors in Context, Direct Proportion, Inverse Proportion, which build directly on this idea.
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