Averages
Aptitude (Numeracy & Reasoning) 21st century literacies
Average
Lesson Plan
Objective:


Total Time: 90 Minutes 

Instructor Note: This unit would deal with the basic nuances of the everimportant topic average. Owing to its importance, it becomes inevitable to form a strong foundation and holistic learning of the same. Learners get to understand basic concepts of average and its practical usage. It would enable them to analyze the deviations of individual data from the mean of the given set under observation. Trainer is required to deliver this unit under an engaging environment by using practical examples and competitive activities. (After concept discussion & practice) Display/distribute handout consisting of questions. Foundation section will compromise 4 questions, instruct students that they will be given 8 minutes to discuss among themselves & solve these 4 questions, whichever group solves maximum problems wins maximum points on the points table (refer opening protocol). Award 5 marks for each correct answer given by a group. Move around the class to check procedures used by students to solve problems. Once time is up, provide solutions and explanations for each question. Switch to moderate level. This section comprises 3 questions and the cumulative time allotted will be 10 minutes. All other instructions remain the same. Switch to HOTS. This section comprises 3 questions and cumulative time allotted will be 15 minutes. All other instructions remain the same. 

Opening Protocol:

3 Minutes 

Opening Activity:
Trainer’s role:

15 Minutes 

Section 1:
Then the average number of students in the rooms is calculated as [(20+10+15)/3] = 15. So, average refers to the sum of observations divided by the number of observations. We got 15 as the average number of students in three rooms, what does that mean? What is “15” trying to say? Let’s have a look. We had three numbers (20,10,15) whose average is 15. Let’s say below is a line representing “15” (Average value). In this figure you can see that 20 is above the average, 10 is below the average and 15 is on the average line. Let us see how much deviation 20 & 10 has from the average number.
Net deviation = Positive deviation + Negative deviation i.e. [(+5) + (5)] =0
Oh! Did we get a zero? Isn’t that interesting? Yes, it is! Average of an observation is such a number which equals the net deviation of the whole observation to “zero”. So, if there is no deviation in any of the numbers in an observation, then what does that mean? It means that the whole set of observations has the same value. So, in the above case when you got 15 as the average number of students in three rooms, you can consider that each room has 15 students. This statement can also be represented as: Now, if I tell you to calculate the sum of observations in the above figure, what will you do? Since you have to sum 15 three times so you will directly write 15*3=45 or you can rearrange this equation to 15=45/3. Can you observe this equation? This is exactly what you write as formula: Average = Sum of observations/total number of observations Now did you get an idea that if you know the concept, there is no need to memorize formulas because ultimately these formulas were derived from the concepts. Also, average has many practical applications in our daily life, so if we understand the concept, we can utilize them. Section 2:
Solution: According to the question, the average of five numbers is 29. Now, using the concepts learnt above, Let’s suppose that the value of all five numbers is 29 as shown in the figure below. Now in the second arrangement, the numbers become 27. Originally, they were 29, now how do we calculate the lost/excluded number? Here is our observation: Looking at both the figures we can clearly deduce that initially we had five boxes with value 29 and now we have four boxes with value 27, so we have clearly lost a number/box with value “29”. But Is 29 my excluded number? No, try to find other changes between two arrangements. Can you see that apart from one missing box of value “29”, now every box has lost two units each. So, total number of units lost from all the four remaining boxes will be 4*2=8. So, now you can say that the total number excluded/lost is 29+8=37. What is the textual method to solve the above problem by using formulas? Average of five numbers =29, Let us consider five numbers be A, B, C, D, E. Now according to the formula, Average= Sum of observations/Total number of observations. Applying formula, we can write (A+B+C+D+E)/5=29 or A+B+C+D+E= 145—Eq1, Since one number is excluded, we can write (A+B+C+D)/4=27 or A+B+C+D=108— Eq2. Putting value of Eq2 in Eq1 we get A= (145108) = 37. Now, tell me, is it required to perform the above mathematical operation to reach a solution? Leave back your traditional approaches and start visualizing these problems. This will help you solve real life problems based on averages quickly without using pen & paper. Section 3:
Solution: Just visualize along. There are 7 people whose average weight is 12 kg, so we can consider that each of them weighs 12 kg. If the weight of the teacher is excluded, the average weight is reduced by 5 kg, so now there are 6 people who weigh 7 kg each. Now, let’s calculate total weight loss= [12 kg (teacher’s weight which was excluded)] + [30kg (5kgs each of 6 students)]. So, the excluded weight was 30+12=42 kg and whose weight was excluded? It was the teacher. Thus, the teacher weighed 42 kg. 
25 Minutes 
Section 4: Foundation
Section 5: Moderate
Section 6: HOTS – HIGH ORDER THINKING SKILLS

8 minutes Answers (1) 76 (2) 8700 (3) 89.85 (4) 11.6 10 minutes Answers (1) 50 (2) 100 (3) 20 15 minutes Answers (1) 85 (2) 2 (3) 1536.07 EXPLANATION 10 Minutes 
Closing activity:

1 Minutes 
Closing Protocol:

Postsession 