# Problems involving Average

Lesson Planning of Solve Real Life Problems involving Average

Subject Mathematics

Students` Learning Outcomes

• Define an average (arithmetic mean)
• Find an average of given numbers.
• Solve real life problems involving average

Information for Teachers

• Data set is a collection of data, usually presented in tabular form.

• The resulted obtained by adding several quantities together and then dividing this total by the number of quantities is called average.

• An average of a data set is a measure of the “middle” value of the data set.

• PROCEDURE: To calculate the average, first add all of the numbers to find the sum. Then divide the sum by the amount of numbers in your set. The result is the average of your numbers.
• SAMPLE PROBLEM: Suppose the ages of four students are given below. We can find their average age through following steps:

9, 10, 7, 6

• Step 1: Find the sum

9 + 10 + 7+ 6+ =32

• Step 2:  Divide the sum by the amount of numbers in your set. Because there are four numbers in your set, divide the sum by 4.

32 ÷ 4 = 8

• The average of the numbers is 8.

Material / Resources

Writing board, chalk / marker, duster, coin, six – sided die, pencil, pen textbook

Introduction

• This lesson provides students with an opportunity to identify and apply average.
• Ask the students do they have any information regarding average? What do we man by average?
• Listen their views and write them on the board.
• Explain them what an average is and how we find average of different numbers?
• Explain about average by giving real life examples.
• Consult textbook at all the steps wherever required.

Development

Activity 1

• Write an example on the board and ask the students to be attentive.
• Ask the students that this time we will find average of these three numbers 7, 3, 5

Solution:

• Step 1: add all the three numbers, such as; 7 + 3 + 5 = 15
• Step 2: divide the sum by the total numbers [Total numbers are three] such as;
• 15 ÷ 3 = 5
• Hence, 5 is the average of numbers 7, 3 and 5
• Similarly repeat another example to further strengthen their understanding, such as;

Activity 2

• Now describe some real life examples, e.g. write heights of Rabia, Alia and Arena on the board like following table.
 Students Height [ft] Rabia 5 Aalia 4 Arena 3
• Call one of the students and help him / her to find average height of the three students.
• Step 1: Add all the height = 5 + 4 + 3 = 12
• Step 2: Divide the sum by the total number of students = 12 ÷ 3 = 4
• Hence, 4 is the average height of the three students.

Sum up / Conclusion

• Tell the students that today we have discussed about average that how we can find average in real life problems. Repeat the key points.

• The result obtained by adding several quantities together and then dividing this total by the number of quantities is called average.
• Average can be found through this formula:

• In simple terms average can be obtained” by dividing the sum of the numbers in your list by the number of items in your list”

Assessment

• Write the following questions on the board and ask students to solve these on their notebooks.
• If four students Jamal, Nassir, Ali and Osama scored 40, 10, 90, and 60 marks respectively in mathematics class test. Then what will be the average of the marks (Expected answer may be as; 25)
 Student Number Jamal 40 Nassir 10 Ali 90 Osama 60
• Let them think and respond accordingly. Help them step by step if they found any problem.