Free Grade 3 Scalar Multiples Lessons
Free Grade 3 lessons for Scalar Multiples: 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
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain scalar multiples
Explain scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate scalar multiples
Calculate scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare scalar multiples
Compare scalar multiples accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify scalar multiples
Justify scalar multiples 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 Scalar Multiples 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 40.[1]
- 2.List all the factors of 36.[1]
- 3.List all the factors of 12.[1]
- 4.List all the factors of 28.[1]
- 5.Find the highest common factor (HCF) of 12 and 6.[2]
- 6.Find the highest common factor (HCF) of 9 and 9.[2]
- 7.Find the highest common factor (HCF) of 8 and 14.[2]
- 8.Find the highest common factor (HCF) of 32 and 48.[2]
- 9.Find the lowest common multiple (LCM) of 35 and 14.[3]
- 10.Find the lowest common multiple (LCM) of 56 and 40.[3]
- 11.Find the highest common factor (HCF) of 18 and 18.[3]
- 12.Find the lowest common multiple (LCM) of 42 and 18.[3]
Show answers and working
1. 1, 2, 4, 5, 8, 10, 20, 40
Find factor pairs that multiply to 40. 1 × 40 2 × 20 4 × 10 5 × 8
2. 1, 2, 3, 4, 6, 9, 12, 18, 36
Find factor pairs that multiply to 36. 1 × 36 2 × 18 3 × 12 4 × 9 6 × 6
3. 1, 2, 3, 4, 6, 12
Find factor pairs that multiply to 12. 1 × 12 2 × 6 3 × 4
4. 1, 2, 4, 7, 14, 28
Find factor pairs that multiply to 28. 1 × 28 2 × 14 4 × 7
5. 6
List factors of 12 and 6. The largest factor they share is 6.
6. 9
List factors of 9 and 9. The largest factor they share is 9.
7. 2
List factors of 8 and 14. The largest factor they share is 2.
8. 16
List factors of 32 and 48. The largest factor they share is 16.
9. 70
HCF(35, 14) = 7. LCM = 35 × 14 ÷ 7 = 70.
10. 280
HCF(56, 40) = 8. LCM = 56 × 40 ÷ 8 = 280.
11. 18
List factors of 18 and 18. The largest factor they share is 18.
12. 126
HCF(42, 18) = 6. LCM = 42 × 18 ÷ 6 = 126.
Worked examples
List all the factors of 24.
- Find factor pairs that multiply to 24.
- 1 × 24
- 2 × 12
- 3 × 8
- 4 × 6
- Answer: 1, 2, 3, 4, 6, 8, 12, 24
Find the highest common factor (HCF) of 32 and 40.
- List factors of 32 and 40.
- The largest factor they share is 8.
- Answer: 8
Find the lowest common multiple (LCM) of 42 and 28.
- HCF(42, 28) = 14.
- LCM = 42 × 28 ÷ 14 = 84.
- Answer: 84
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.
Every free resource for Scalar Multiples
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Frequently asked
- Is this Grade 3 Scalar Multiples 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 Adding Vectors, Vector Notation, Calculus. 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 Scalar Multiples?
- Move on to Magnitude of a Vector, Vector Geometry, which build directly on this idea.
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