Lesson Plan of Direct and Inverse Proportion Involving in Real Life Problems Mathematics Grade V

Lesson Plan of Direct and Inverse Proportion Involving in Real Life Problems

Mathematics Grade V

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 =16x5

                          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?