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?
Development
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?
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?