Free Grade 3 Introducing Determinants Common Errors Lessons
Free Grade 3 lessons for Introducing Determinants Common Errors: 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing determinants common errors
Identify introducing determinants common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing determinants common errors
Explain introducing determinants common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing determinants common errors
Calculate introducing determinants common errors accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing determinants common errors
Compare introducing determinants common errors 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 Determinants Common Errors 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 60:12.[1]
- 2.Simplify the ratio 16:8.[1]
- 3.Simplify the ratio 50:50.[1]
- 4.Simplify the ratio 18:6.[1]
- 5.Share 72 in the ratio 2:4.[2]
- 6.Share 56 in the ratio 3:5.[2]
- 7.Share 55 in the ratio 5:6.[2]
- 8.Share 40 in the ratio 5:5.[2]
- 9.Share 10 in the ratio 1:1.[3]
- 10.Share 44 in the ratio 3:1.[3]
- 11.Share 35 in the ratio 3:4.[3]
- 12.Share 12 in the ratio 1:3.[3]
Show answers and working
1. 5:1
HCF of 60 and 12 is 12. Divide both parts by it: 5:1.
2. 2:1
HCF of 16 and 8 is 8. Divide both parts by it: 2:1.
3. 1:1
HCF of 50 and 50 is 50. Divide both parts by it: 1:1.
4. 3:1
HCF of 18 and 6 is 6. Divide both parts by it: 3:1.
5. 24 and 48
Total parts: 2 + 4 = 6. One part: 72 ÷ 6 = 12. 2 × 12 = 24, 4 × 12 = 48.
6. 21 and 35
Total parts: 3 + 5 = 8. One part: 56 ÷ 8 = 7. 3 × 7 = 21, 5 × 7 = 35.
7. 25 and 30
Total parts: 5 + 6 = 11. One part: 55 ÷ 11 = 5. 5 × 5 = 25, 6 × 5 = 30.
8. 20 and 20
Total parts: 5 + 5 = 10. One part: 40 ÷ 10 = 4. 5 × 4 = 20, 5 × 4 = 20.
9. 5 and 5
Total parts: 1 + 1 = 2. One part: 10 ÷ 2 = 5. 1 × 5 = 5, 1 × 5 = 5.
10. 33 and 11
Total parts: 3 + 1 = 4. One part: 44 ÷ 4 = 11. 3 × 11 = 33, 1 × 11 = 11.
11. 15 and 20
Total parts: 3 + 4 = 7. One part: 35 ÷ 7 = 5. 3 × 5 = 15, 4 × 5 = 20.
12. 3 and 9
Total parts: 1 + 3 = 4. One part: 12 ÷ 4 = 3. 1 × 3 = 3, 3 × 3 = 9.
Worked examples
Simplify the ratio 12:36.
- HCF of 12 and 36 is 12.
- Divide both parts by it: 1:3.
- Answer: 1:3
Share 30 in the ratio 5:1.
- Total parts: 5 + 1 = 6.
- One part: 30 ÷ 6 = 5.
- 5 × 5 = 25, 1 × 5 = 5.
- Answer: 25 and 5
Share 108 in the ratio 5:7.
- Total parts: 5 + 7 = 12.
- One part: 108 ÷ 12 = 9.
- 5 × 9 = 45, 7 × 9 = 63.
- Answer: 45 and 63
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.
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Frequently asked
- Is this Grade 3 Introducing Determinants Common Errors 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 Introducing Determinants Word Problems, Introducing Determinants Techniques, Identity Matrix. 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 Determinants Common Errors?
- Move on to Working with Determinants, Determinants in Context, which build directly on this idea.
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