Free Grade 3 Working with Determinants Lesson Plans
Free Grade 3 lesson plans for Working with 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
Foundation
30 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify working with determinants
Identify working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain working with determinants
Explain working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate working with determinants
Calculate working with determinants accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare working with determinants
Compare working with 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 Working with 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 20:4.[1]
- 2.Simplify the ratio 20:30.[1]
- 3.Simplify the ratio 30:30.[1]
- 4.Simplify the ratio 24:48.[1]
- 5.Share 45 in the ratio 2:3.[2]
- 6.Share 27 in the ratio 4:5.[2]
- 7.Share 54 in the ratio 1:5.[2]
- 8.Share 24 in the ratio 3:5.[2]
- 9.Share 36 in the ratio 3:3.[3]
- 10.Share 24 in the ratio 1:2.[3]
- 11.Share 27 in the ratio 3:6.[3]
- 12.Share 40 in the ratio 2:6.[3]
Show answers and working
1. 5:1
HCF of 20 and 4 is 4. Divide both parts by it: 5:1.
2. 2:3
HCF of 20 and 30 is 10. Divide both parts by it: 2:3.
3. 1:1
HCF of 30 and 30 is 30. Divide both parts by it: 1:1.
4. 1:2
HCF of 24 and 48 is 24. Divide both parts by it: 1:2.
5. 18 and 27
Total parts: 2 + 3 = 5. One part: 45 ÷ 5 = 9. 2 × 9 = 18, 3 × 9 = 27.
6. 12 and 15
Total parts: 4 + 5 = 9. One part: 27 ÷ 9 = 3. 4 × 3 = 12, 5 × 3 = 15.
7. 9 and 45
Total parts: 1 + 5 = 6. One part: 54 ÷ 6 = 9. 1 × 9 = 9, 5 × 9 = 45.
8. 9 and 15
Total parts: 3 + 5 = 8. One part: 24 ÷ 8 = 3. 3 × 3 = 9, 5 × 3 = 15.
9. 18 and 18
Total parts: 3 + 3 = 6. One part: 36 ÷ 6 = 6. 3 × 6 = 18, 3 × 6 = 18.
10. 8 and 16
Total parts: 1 + 2 = 3. One part: 24 ÷ 3 = 8. 1 × 8 = 8, 2 × 8 = 16.
11. 9 and 18
Total parts: 3 + 6 = 9. One part: 27 ÷ 9 = 3. 3 × 3 = 9, 6 × 3 = 18.
12. 10 and 30
Total parts: 2 + 6 = 8. One part: 40 ÷ 8 = 5. 2 × 5 = 10, 6 × 5 = 30.
Worked examples
Simplify the ratio 8:20.
- HCF of 8 and 20 is 4.
- Divide both parts by it: 2:5.
- Answer: 2:5
Share 49 in the ratio 2:5.
- Total parts: 2 + 5 = 7.
- One part: 49 ÷ 7 = 7.
- 2 × 7 = 14, 5 × 7 = 35.
- Answer: 14 and 35
Share 54 in the ratio 5:4.
- Total parts: 5 + 4 = 9.
- One part: 54 ÷ 9 = 6.
- 5 × 6 = 30, 4 × 6 = 24.
- Answer: 30 and 24
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 Working with 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 Introducing Determinants, Identity Matrix. 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 Working with Determinants?
- Move on to Determinants in Context, Matrix Addition, Matrix Multiplication, Identity Matrix, which build directly on this idea.
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