Free Grade 3 Matrix Operations Lessons
Free Grade 3 lessons for Matrix Operations: 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
Core
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- UnderstandExplain matrix operations
Explain matrix operations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate matrix operations
Calculate matrix operations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare matrix operations
Compare matrix operations accurately in a familiar context.
Assessed by: Exit ticket of four short items
- EvaluateJustify matrix operations
Justify matrix operations 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 Matrix Operations 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 30:10.[1]
- 2.Simplify the ratio 12:60.[1]
- 3.Simplify the ratio 12:20.[1]
- 4.Simplify the ratio 40:50.[1]
- 5.Share 14 in the ratio 2:5.[2]
- 6.Share 30 in the ratio 4:6.[2]
- 7.Share 24 in the ratio 1:3.[2]
- 8.Share 20 in the ratio 4:1.[2]
- 9.Share 120 in the ratio 5:7.[3]
- 10.Share 60 in the ratio 3:3.[3]
- 11.Share 55 in the ratio 1:4.[3]
- 12.Share 12 in the ratio 4:2.[3]
Show answers and working
1. 3:1
HCF of 30 and 10 is 10. Divide both parts by it: 3:1.
2. 1:5
HCF of 12 and 60 is 12. Divide both parts by it: 1:5.
3. 3:5
HCF of 12 and 20 is 4. Divide both parts by it: 3:5.
4. 4:5
HCF of 40 and 50 is 10. Divide both parts by it: 4:5.
5. 4 and 10
Total parts: 2 + 5 = 7. One part: 14 ÷ 7 = 2. 2 × 2 = 4, 5 × 2 = 10.
6. 12 and 18
Total parts: 4 + 6 = 10. One part: 30 ÷ 10 = 3. 4 × 3 = 12, 6 × 3 = 18.
7. 6 and 18
Total parts: 1 + 3 = 4. One part: 24 ÷ 4 = 6. 1 × 6 = 6, 3 × 6 = 18.
8. 16 and 4
Total parts: 4 + 1 = 5. One part: 20 ÷ 5 = 4. 4 × 4 = 16, 1 × 4 = 4.
9. 50 and 70
Total parts: 5 + 7 = 12. One part: 120 ÷ 12 = 10. 5 × 10 = 50, 7 × 10 = 70.
10. 30 and 30
Total parts: 3 + 3 = 6. One part: 60 ÷ 6 = 10. 3 × 10 = 30, 3 × 10 = 30.
11. 11 and 44
Total parts: 1 + 4 = 5. One part: 55 ÷ 5 = 11. 1 × 11 = 11, 4 × 11 = 44.
12. 8 and 4
Total parts: 4 + 2 = 6. One part: 12 ÷ 6 = 2. 4 × 2 = 8, 2 × 2 = 4.
Worked examples
Simplify the ratio 48:24.
- HCF of 48 and 24 is 24.
- Divide both parts by it: 2:1.
- Answer: 2:1
Share 21 in the ratio 2:1.
- Total parts: 2 + 1 = 3.
- One part: 21 ÷ 3 = 7.
- 2 × 7 = 14, 1 × 7 = 7.
- Answer: 14 and 7
Share 35 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 35 ÷ 7 = 5.
- 3 × 5 = 15, 4 × 5 = 20.
- Answer: 15 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.
Every free resource for Matrix Operations
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Frequently asked
- Is this Grade 3 Matrix Operations 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 Vectors. 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 Matrix Operations?
- Move on to Number Sense, Algebra, Geometry, Measurement, which build directly on this idea.
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