Free Grade 3 Determinants Lesson Plans
Free Grade 3 lesson plans for Determinants: 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 determinants
Identify determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain determinants
Explain determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate determinants
Calculate determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare determinants
Compare determinants 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 Determinants 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 24:12.[1]
- 2.Simplify the ratio 24:24.[1]
- 3.Simplify the ratio 12:16.[1]
- 4.Simplify the ratio 20:20.[1]
- 5.Share 36 in the ratio 5:4.[2]
- 6.Share 72 in the ratio 4:4.[2]
- 7.Share 77 in the ratio 2:5.[2]
- 8.Share 15 in the ratio 1:2.[2]
- 9.Share 20 in the ratio 1:4.[3]
- 10.Share 121 in the ratio 4:7.[3]
- 11.Share 60 in the ratio 3:7.[3]
- 12.Share 48 in the ratio 2:2.[3]
Show answers and working
1. 2:1
HCF of 24 and 12 is 12. Divide both parts by it: 2:1.
2. 1:1
HCF of 24 and 24 is 24. Divide both parts by it: 1:1.
3. 3:4
HCF of 12 and 16 is 4. Divide both parts by it: 3:4.
4. 1:1
HCF of 20 and 20 is 20. Divide both parts by it: 1:1.
5. 20 and 16
Total parts: 5 + 4 = 9. One part: 36 ÷ 9 = 4. 5 × 4 = 20, 4 × 4 = 16.
6. 36 and 36
Total parts: 4 + 4 = 8. One part: 72 ÷ 8 = 9. 4 × 9 = 36, 4 × 9 = 36.
7. 22 and 55
Total parts: 2 + 5 = 7. One part: 77 ÷ 7 = 11. 2 × 11 = 22, 5 × 11 = 55.
8. 5 and 10
Total parts: 1 + 2 = 3. One part: 15 ÷ 3 = 5. 1 × 5 = 5, 2 × 5 = 10.
9. 4 and 16
Total parts: 1 + 4 = 5. One part: 20 ÷ 5 = 4. 1 × 4 = 4, 4 × 4 = 16.
10. 44 and 77
Total parts: 4 + 7 = 11. One part: 121 ÷ 11 = 11. 4 × 11 = 44, 7 × 11 = 77.
11. 18 and 42
Total parts: 3 + 7 = 10. One part: 60 ÷ 10 = 6. 3 × 6 = 18, 7 × 6 = 42.
12. 24 and 24
Total parts: 2 + 2 = 4. One part: 48 ÷ 4 = 12. 2 × 12 = 24, 2 × 12 = 24.
Worked examples
Simplify the ratio 8:32.
- HCF of 8 and 32 is 8.
- Divide both parts by it: 1:4.
- Answer: 1:4
Share 42 in the ratio 4:2.
- Total parts: 4 + 2 = 6.
- One part: 42 ÷ 6 = 7.
- 4 × 7 = 28, 2 × 7 = 14.
- Answer: 28 and 14
Share 88 in the ratio 5:6.
- Total parts: 5 + 6 = 11.
- One part: 88 ÷ 11 = 8.
- 5 × 8 = 40, 6 × 8 = 48.
- Answer: 40 and 48
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 Determinants lesson plan really free?
- Yes. Every lesson plans 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 Identity Matrix, Matrix Multiplication, Vectors. Each one has its own free lesson, worksheet and quiz.
- How is the lesson plan 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 Determinants?
- Move on to Inverse Matrices, which build directly on this idea.
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