Subject Mathematics

Grade 5th

Students` Learning Outcomes

  • Define and identify direct and inverse proportion.

Information for Teachers

  • A proportion is two ratios that have been set equal to each other; a proportion is an equation that can be solved.


  • Proportional relationships tell us that two variables scale with each other in a predictable way.

Material / Resources

Writing board, chalk / marker, duster, chart paper, textbook


  • Draw few tables below to be filled by the students for direct proportion. This will help students learn proportional reasoning; i. e. a car covers 50 km in 1 hour:


  • Or 1 British Pound is equal to Rs. 200 



  • Ask students questions and fill the table i.e.
  • Students will answer and fill the table given above.
  • Tell the story;


  • Write students responses on the board and tell them that today we will explore about direct and inverse proportion.




  • Explain to the students that if two things are directly proportional to each other, they will increase and decrease in the same proportion to each other.  While in inverse proportion if one value increases the other decreases (or vice versa) in the same ratio.

Activity 1

    • Show some soap bar rappers to the students and tell them to answer the following questions; suppose the price of one piece of soap is 100 Rs.

§  If a person wants to buy one dozen pieces of soap. How much he would pay?

§  If there he wants to buy two dozen pieces of soap from the shop. How much he would pay?   i


  • Add different number of soap bars so that students can have better understanding.
  • Let students find out that if the person buys more pieces. He has to pay more or he has to pay less if he buys less pieces.
  • Tell students that this kind of relation in two quantities is called direct proportion.
  • Encourage students to give more examples of direct proportion.


Activity 2

  • Ask students to imagine that they are supposed to paint their room by themselves. They have few options as well. Think of these options and choose the best.
  • Think of;


§  How long it would take you to paint your room?

§  How long would it take if you had one friend helping you?

  • You may add as many friends as you want.
  • Discuss the possible outcomes with the students and deduce the relation between the time it takes to paint the room and the number of people painting is an inverse proportion. The more people they have, the less time it takes.
  • Ask students to give you some other situation for the inverse proportion.


Activity 3

After giving the answers in above two activities the students are able to understand some problems.

§  Choose some simple proportion word problems from textbook and left students solve in pairs.

§  Students might come up with answers by using their own methods.

§  They might make a table. Or, they might figure out how to calculate the thing for 1 unit, and then go from there.

§  They might discover the need to know how many-fold the one thing increased or decreased, and then just multiply or divide with that number to get the unknown thing.

§  Recall-RATIO is two things” [number or quantities] compared to each other. For example, “80 rupees per liter” is a ratio. Or, “Rs. 40 for 1 liter Pepsi”. Or, 15 girls versus 14 boys. Or, 569 words in 2 minutes. It is a comparison of two numbers or quantities.

§  Whereas-proportion is when you have two ratios set to be equal to each other. For example in the first table “50 km per hour equals 100 km per 2 hours”. Moreover we can also write like this 50:1:: 100:2, the ‘’::’ sign is for proportions.

§  Assign some selected questions from textbook exercise to do as individual work. After completing their work students will swap their copies for peer assessment.

§  After completing their work students will swap their copies for peer assessment.

Sum up / Conclusion

  • Conclude lesson with following points.


§  If two values are increasing or decreasing at the same time in the given ratio, they are in direct proportion.

§  If two values, such as, one value increasing and other is decreasing at the same time in the given ratio, or vice versa, they are in inverse proportion.

§  Give one example of each type.


  • Ask students to solve and explain their answers of the following;
  • Ask students to give you more examples.

Follow up


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