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

Solution:

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 Weight (in pounds) No. of workers Days to complete work 0 0 5 16 1 165 8 10 2 330 10 8 3 475 20 4 4 655 30 2
·         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

Assessment

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?