Students` Learning Outcomes

  • Solve real life problems involving direct and inverse proportion [by unitary method]

Information for Teachers

  • In unitary method we deal with the following;

§  Finding the price of more things when price of one thing is given.


§  Finding the price of 1 thing if price of more things are given.

§  Finding the price of given number of things if the price of other number of same things is given.

§  During lesson where necessary also consult with textbook.

Material / Resources

Writing board, chalk / marker, duster, chart paper, packets or tins of food items, textbook          


  • Show students a packet of juice and read the information for ingredients.
  • The label on juice pack shows this information
  • Apple juice 440 ml. each 440 ml provides;

o   Energy 226 calories.

o   Carbohydrates 6.6g.

o   Vitamin C 20 mg

  • Ask the students that if 440 ml of juice provides 226 calories how many calories 100 ml of juice will provide?
  • Ask students to decide is it direct or inverse proportion question, can they show the working? If they are unable to do, then show working on the board.
  • Solution:

440 ml of juice contains calories = 226

1 ml of juice contains calories = 226 + 440

100 ml will contain = 226/440 x 100 = 56.5 cal.

  • Ask again is it direct or inverse proportion and why?


Activity 1

  • Discuss the following questions with the whole class.
  • What is ratio?

o   A ratio shows the relative sizes of two or more values.

o   Ratio means a relation between part to part or part to whole.

  • What is proportion?

o   When two ratios are equal they are said to be in proportion.

  • If increased in one quantity causes decrease in other quantity or decrease in one quantity, then we say that both quantities are inversely related.
  • Two values are in “direct proportion” with each other if the following relationship holds: whenever one variable doubles, the other variable doubles, the other variable doubles. Whenever one variable triples, the other variable triples and so on.
  • Ask the students “Do you remember the proportion tables we did in the previous lessons?”
  • Show them following tables and recollect the information about direct and inverse proportion.


  • Solve table 2 on the board with the help of the students.



  • Change the number of workers and practice further.
  • After completing the examples give students in pairs, questions from textbook exercise.
  • While students are working, keep roaming in the class, correct students if they make any mistake.


Activity 2

  • Write some statements of the questions for direct and inverse proportion on paper slips.
  • o   These questions can be taken from textbook or you can make this yourself.
  • Prepare enough slips that each student gets one slip.
  • Distribute these slips in the students.
  • Ask students to read the statement, write is it direct or inverse proportion? And then solve the question.
  • Collect back the solved slips shuffle and redistribute among students, to read and check the question of each other.

Sum up / Conclusion

  • Conclude the lesson with the following points;

o   All mathematical concepts are lying as situations in out daily life.

o   When two values are increasing or decreasing at the same time in the same ratio, it is direct proportion.

o   When two values are in relation such that one value increases other decreases, it is inverse proportion.


  • Ask students to solve the following questions in their notebooks.


Follow up

  • Ask students to suggest solutions for following situations;


Ask students to suggest solutions for following situations;

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