Direct and Inverse Proportion

Students’ Learning Outcomes

·         Solve real life problems involving direct and inverse proportion (by unitary method)

Information for Teacher

·         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 is given
·         Finding the price of given number of things if the price of other number of same things is given
·           Ratio:                   A ration shows the relative sizes of two or more values
                                              Ration means a relation between part to part or part to whole
·           Proportion:          when two rations are equal they are said to be in proportion
·         During lesson where and when necessary consult textbook

Resources / Material

Board, chalk/marker, chart paper, packets or tins of food items, textbook

Worm up activity

·         Show students a packet of juice and read the information for ingredients
·         The label on a juice pack shows this information
·         Apple juice 440ml, each 440ml provides:
o   Energy 226 calories,
o   Carbohydrate 6.6g,
o   Vitamin c20mg
·         Ask the students that if 440 ml of juice provides 226 calories how many calories 100ml of juice will provide?
·         Ask students to decide is it direct or inverse proportion question, can they show the working? If they are unable, show working on the board


                     440 ml of juice contains calories =226
                     I ml of juice contains calories = 226 /440                                           
                     100 ml 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 ration?
o   A ration shows the relative sizes of two or more values
o   Ration means a relation between part to part or part to whole
·         What is proportion?
o   When two rations 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
·         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 lesson?
·         Show them following tables and recollect the information about direct and inverse proportion
Table 1
Table 2
Number of men
(in pounds)
No. of workers
Days to complete work
·         Solve table on the board with the help of the students
·         If 5 workers complete a job in 16 days, then 8 workers will complete the same job in how many days?                                                                     
                           5 worker complete the job in = 16 days
                          1 worker will complete the job in =16×5
                          8 workers will complete the job in
                                                                                       = 16 x 5 / 8 = 10 days
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 these 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:
·         All the mathematical concepts are lying as situations in our daily life
·         When two values are increasing or decreasing at the same time in the same ratio, it is direct proportion
·         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
·         If the cost of 4 light bulbs is PRs 60.00, work out the cost of 3 light bulbs?
·         The cost of 3 pens is PRs. 45; work out the cost of 7 pens?
·         24 workers can construct a house in 15 days. But the owner would like to finish the work in 12 days. How many workers should he employ?
·         If 7 electricians cam wire some new houses in 17 days, how many electricians would be required to do the job in 9 days?
·         A car traveling at 45km/hrs. takes 33 minutes for a journey. How long does a car traveling at 55km/hrs. Take for the same journey?

Follow up

Ask students to suggest solutions for following situations:
·         It takes 14 hours with 1 tap with a flow of 18 liters per minute to fill a reservoir with water. How long will it take if its flow is reduced to 7 liters per minute?
·         If ¼ of a tank can be filled in 2 minutes, how many minutes will it take to fill the whole tank?

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