Free Grade 3 Introducing Direct Proportion Lessons
Free Grade 3 lessons for Introducing Direct Proportion: 12 real questions with a full answer key and worked solutions. In direct proportion, when one amount doubles the other doubles too. Find the value of one unit, then scale up.
Free
Higher
35 min
24
Learning objectives
Every objective is checkable, and each one maps to an activity and an assessment.
- RememberIdentify introducing direct proportion
Identify introducing direct proportion accurately in a familiar context.
Assessed by: Exit ticket of four short items
- UnderstandExplain introducing direct proportion
Explain introducing direct proportion accurately in a familiar context.
Assessed by: Exit ticket of four short items
- ApplyCalculate introducing direct proportion
Calculate introducing direct proportion accurately in a familiar context.
Assessed by: Exit ticket of four short items
- AnalyseCompare introducing direct proportion
Compare introducing direct proportion 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 Direct Proportion works
In direct proportion, when one amount doubles the other doubles too. Find the value of one unit, then scale up.
12 practice questions
Easy to hard, 24 marks in total. Try them first, then open the answers.
- 1.3 pens cost $4.50. How much do 3 pens cost?[1]
- 2.5 pens cost $35.00. How much do 11 pens cost?[1]
- 3.5 pens cost $35.00. How much do 7 pens cost?[1]
- 4.4 pens cost $28.00. How much do 5 pens cost?[1]
- 5.3 pens cost $24.00. How much do 9 pens cost?[2]
- 6.2 pens cost $12.00. How much do 6 pens cost?[2]
- 7.3 pens cost $12.00. How much do 7 pens cost?[2]
- 8.3 pens cost $39.00. How much do 9 pens cost?[2]
- 9.3 pens cost $36.00. How much do 12 pens cost?[3]
- 10.4 pens cost $42.00. How much do 9 pens cost?[3]
- 11.3 pens cost $40.50. How much do 3 pens cost?[3]
- 12.4 pens cost $72.00. How much do 10 pens cost?[3]
Show answers and working
1. $4.50
Cost of 1 pen: $4.50 ÷ 3 = $1.50. 3 pens: 3 × $1.50 = $4.50.
2. $77.00
Cost of 1 pen: $35.00 ÷ 5 = $7.00. 11 pens: 11 × $7.00 = $77.00.
3. $49.00
Cost of 1 pen: $35.00 ÷ 5 = $7.00. 7 pens: 7 × $7.00 = $49.00.
4. $35.00
Cost of 1 pen: $28.00 ÷ 4 = $7.00. 5 pens: 5 × $7.00 = $35.00.
5. $72.00
Cost of 1 pen: $24.00 ÷ 3 = $8.00. 9 pens: 9 × $8.00 = $72.00.
6. $36.00
Cost of 1 pen: $12.00 ÷ 2 = $6.00. 6 pens: 6 × $6.00 = $36.00.
7. $28.00
Cost of 1 pen: $12.00 ÷ 3 = $4.00. 7 pens: 7 × $4.00 = $28.00.
8. $117.00
Cost of 1 pen: $39.00 ÷ 3 = $13.00. 9 pens: 9 × $13.00 = $117.00.
9. $144.00
Cost of 1 pen: $36.00 ÷ 3 = $12.00. 12 pens: 12 × $12.00 = $144.00.
10. $94.50
Cost of 1 pen: $42.00 ÷ 4 = $10.50. 9 pens: 9 × $10.50 = $94.50.
11. $40.50
Cost of 1 pen: $40.50 ÷ 3 = $13.50. 3 pens: 3 × $13.50 = $40.50.
12. $180.00
Cost of 1 pen: $72.00 ÷ 4 = $18.00. 10 pens: 10 × $18.00 = $180.00.
Worked examples
2 pens cost $14.00. How much do 3 pens cost?
- Cost of 1 pen: $14.00 ÷ 2 = $7.00.
- 3 pens: 3 × $7.00 = $21.00.
- Answer: $21.00
4 pens cost $12.00. How much do 10 pens cost?
- Cost of 1 pen: $12.00 ÷ 4 = $3.00.
- 10 pens: 10 × $3.00 = $30.00.
- Answer: $30.00
3 pens cost $36.00. How much do 3 pens cost?
- Cost of 1 pen: $36.00 ÷ 3 = $12.00.
- 3 pens: 3 × $12.00 = $36.00.
- Answer: $36.00
Interactive practice
Free, no account required — answer on screen or print it.
Common mistakes
What learners typically get wrong, and how to fix it.
Adds instead of scaling.
Correction: Work out the cost of ONE first.
Rounds the unit price too early.
Correction: Keep the exact unit value until the end.
Teacher tips
- · Use a ratio table to keep working organised.
Parent tips
- · Compare price per item on multipacks.
Real-life applications
- · Best-value shopping, currency conversion.
Assessment objectives
How mastery is evidenced, and which standards it maps to.
Every free resource for Introducing Direct Proportion
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Frequently asked
- Is this Grade 3 Introducing Direct Proportion 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 Ratio. 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 Direct Proportion?
- Move on to Working with Direct Proportion, Direct Proportion in Context, Inverse Proportion, Scale Factors, which build directly on this idea.
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