Free Grade 3 Introducing Determinants Techniques Lessons
Free Grade 3 lessons for Introducing Determinants Techniques: 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
Higher
25 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing determinants techniques
Identify introducing determinants techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing determinants techniques
Explain introducing determinants techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing determinants techniques
Calculate introducing determinants techniques accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing determinants techniques
Compare introducing determinants techniques 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 Techniques 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 30:12.[1]
- 2.Simplify the ratio 32:24.[1]
- 3.Simplify the ratio 6:6.[1]
- 4.Simplify the ratio 16:20.[1]
- 5.Share 44 in the ratio 1:3.[2]
- 6.Share 77 in the ratio 2:5.[2]
- 7.Share 88 in the ratio 2:6.[2]
- 8.Share 48 in the ratio 3:1.[2]
- 9.Share 88 in the ratio 4:7.[3]
- 10.Share 72 in the ratio 3:5.[3]
- 11.Share 20 in the ratio 4:6.[3]
- 12.Share 60 in the ratio 3:3.[3]
Show answers and working
1. 5:2
HCF of 30 and 12 is 6. Divide both parts by it: 5:2.
2. 4:3
HCF of 32 and 24 is 8. Divide both parts by it: 4:3.
3. 1:1
HCF of 6 and 6 is 6. Divide both parts by it: 1:1.
4. 4:5
HCF of 16 and 20 is 4. Divide both parts by it: 4:5.
5. 11 and 33
Total parts: 1 + 3 = 4. One part: 44 ÷ 4 = 11. 1 × 11 = 11, 3 × 11 = 33.
6. 22 and 55
Total parts: 2 + 5 = 7. One part: 77 ÷ 7 = 11. 2 × 11 = 22, 5 × 11 = 55.
7. 22 and 66
Total parts: 2 + 6 = 8. One part: 88 ÷ 8 = 11. 2 × 11 = 22, 6 × 11 = 66.
8. 36 and 12
Total parts: 3 + 1 = 4. One part: 48 ÷ 4 = 12. 3 × 12 = 36, 1 × 12 = 12.
9. 32 and 56
Total parts: 4 + 7 = 11. One part: 88 ÷ 11 = 8. 4 × 8 = 32, 7 × 8 = 56.
10. 27 and 45
Total parts: 3 + 5 = 8. One part: 72 ÷ 8 = 9. 3 × 9 = 27, 5 × 9 = 45.
11. 8 and 12
Total parts: 4 + 6 = 10. One part: 20 ÷ 10 = 2. 4 × 2 = 8, 6 × 2 = 12.
12. 30 and 30
Total parts: 3 + 3 = 6. One part: 60 ÷ 6 = 10. 3 × 10 = 30, 3 × 10 = 30.
Worked examples
Simplify the ratio 8:24.
- HCF of 8 and 24 is 8.
- Divide both parts by it: 1:3.
- Answer: 1:3
Share 77 in the ratio 3:4.
- Total parts: 3 + 4 = 7.
- One part: 77 ÷ 7 = 11.
- 3 × 11 = 33, 4 × 11 = 44.
- Answer: 33 and 44
Share 110 in the ratio 3:7.
- Total parts: 3 + 7 = 10.
- One part: 110 ÷ 10 = 11.
- 3 × 11 = 33, 7 × 11 = 77.
- Answer: 33 and 77
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 Techniques 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 Essentials, 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 Techniques?
- Move on to Introducing Determinants Word Problems, Introducing Determinants Common Errors, Working with Determinants, Determinants in Context, which build directly on this idea.
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