There are 100 zeros at the end of 100!. To determine this, one must count the number of factors of 2 and 5 in the expression. There are more factors of 2 than 5. The number of 5s is determined by adding the number of 5s in the tables of 5 and 25 (which is counted twice). This gives a total of 24 5s. Since there are more zeros for each factor of 5, there are 24 zeros at the end of 100!.

1. How Many zeros are there in
the end if we will expand the
expression 100 factorial (100!)
Bloom’s Taxonomy of Instructional
Objectives
By
Bhaskar Lohumi

2. Benjamin Bloom’s Taxonomy
In 1956, Benjamin Bloom formulated a classification
“the goals of the educational processes”
It has means of expressing qualitatively different kinds of thinking
It has been adapted for classroom use as a planning tool
It continues to be one of the most universally applied models
It provides a way to organise thinking skills into six levels, from the
most basic to the more complex levels of thinking
It is taxonomy of Cognitive Objectives

3. Bloom’s Revised Taxonomy
1990s Lorin Anderson (former student of Bloom) revisied
the Bloom’s taxonomy
Comprehension and synthesis were retitled to understanding and
creating respectively, in order to better reflect the nature of the thinking
defined in each category.
The names of six major categories were changed from noun to verb
forms.
As the taxonomy reflects different forms of thinking and thinking is an
active process verbs were used rather than nouns.
The subcategories of the six major categories were also replaced by
verbs and some subcategories were reorganised.
The knowledge category was renamed. The word knowledge was
inappropriate to describe a category of thinking and was replaced with
the word remembering instead.

4. Original Terms New Terms
Evaluation Creating
Knowledge Remembering
Comprehension Understanding
Application Applying
Analysis Analysing
Synthesis Evaluating

5. BLOOM’S REVISED TAXONOMY
Creating: Generating new ideas, products, or ways of viewing things,
Designing, constructing, planning, producing, inventing.
Remembering: Recalling information, Recognizing, listing,
describing, retrieving, naming, finding
Understanding: Explaining ideas or concepts, Interpreting,
summarising, paraphrasing, classifying, explaining
Applying: Using information in another familiar situation,
Implementing, carrying out, using, executing
Analysing: Breaking information into parts to explore understandings
and relationships, Comparing, organizing, deconstructing, interrogating,
finding
Evaluating: Justifying a decision or course of action, Checking,
Hypothesising, critiquing, experimenting, judging

6. Bloom’s Taxonomy
Knowledge or Remembering:
Here the student recall or remembers statements?
Define, Duplicate, List, Memorize
N! factorial = N.(N - 1).(N - 2).(N - 3). … .(3).(2).(1)
6! factorial = (6).(5).(4).(3).(2).(1) = 720
5! factorial = (5).(4).(3).(2).(1) = 120
4! factorial = (4).(3).(2).(1) = 24
3! factorial = (3).(2).(1) = 6
2! factorial = (2).(1) = 2 1! factorial = (1) = 1
𝒙 = Integral part of x

7. Bloom’s Taxonomy
Comprehension or Understanding:
Here the student explain ideas or concepts?
Classify, Describe, Discuss, Explain,
Identify, Locate, Recognize, Report,
Translate, Paraphrase
A zero is obtained by multiplying 2 and 5
2 × 5 = 10
So We have to count how many 2 and 5 are there in
100! (100 Factorial)

8. Bloom’s Taxonomy
Application or Applying:
Here the student use the information in a new way?
Choose, Demonstrate, Dramatize,
Employ, Illustrate, Interpret, Operate,
Schedule, Sketch, Solve, Use, Write
64 = 26, 32 = 25, 16 = 24, 8 = 23, 4 = 22, 2 = 21
Similarly 25 = 52, 5 = 51

9. Bloom’s Taxonomy
Appraise, Compare, Contrast, Criticize,
Differentiate, Discriminate, Distinguish,
Examine, Experiment, Question, Test
Analysis or Analysing:
Here the student distinguish between the different parts?
Number of 2s will be more than number of 5s in the
expression 100!(100 Factorial)
So We will only count 5s as the less number of digits
available will make less number of zeros in the end

10. Bloom’s Taxonomy
Evaluate or Evaluating:
Here the student justify a stand or decision?
Appraise, Argue, Defend, Judge, Select,
Support, Value, Evaluate
How to count number of 5s in the expression
100!(100 Factorial)
So he will see in the table of 5, 5 comes once and in
the table of 25, 5 comes twice which we have to
count again as it was counted once in the table of 5

11. Bloom’s Taxonomy
Synthesis or Creating:
Here the student create new product or point of view?
Assemble, Construct, Create, Design,
Develop, Formulate, Write
Hence Number of 5s in 100! will be
𝟏𝟎𝟎
𝟓
+
𝟏𝟎𝟎
𝟓𝟐 = 𝟐𝟎 + 𝟒 = 𝟐𝟒
So number of primes p in N! will be
𝑵
𝒑
+
𝑵
𝒑𝟐 +
𝑵
𝒑𝟑 +
𝑵
𝒑𝟒 +…

12. Applying: Explain why some vehicles are large and others small. Write a story about the uses of both.
Survey 10other children to see whatbikes theyride. Displayon a chartorgraph.
Creating: Invent a vehicle. Draw or construct itafter careful planning. What sortof transport will there
be in twenty years time? Discuss, write about itand report to the class. Write a song about traveling in
different formsof transport.
Developing Lessons around BLOOM’S TAXONOMY
Travel
Remembering:How many wayscan you travel from one place to another? List and draw allthe
waysyou know. Describe one of the vehicles from your list,draw a diagram and label the parts.
Collect “transport” pictures from magazines-- make a poster with info.
Understanding: How do you get from school to home? Explainthe method of traveland draw a
map. Writea play about a form of modern transport. Explain how you felt the firsttime you rode a
bicycle. Make yourdeskinto a formof transport.
Analysing: Make a jigsaw puzzle of children using bikessafely. What problems are there with
modern formsof transport and theiruses-write a report. Use a Venn Diagram to compare boats to
planes, orhelicoptersto bicycles.
Evaluating: What changes would you recommend to road rules to prevent traffic accidents?
Debate whether we should be able to buy fuel at a cheaper rate. Rate transport from slow to fast etc.

13. Level I: Remembering (Knowledge)
List the planets in our solar system
List 3-5 characteristics of each planet
List the characteristics of comets, meteorites, and asteroids
Level II: Understanding (Comprehension)
Explain in your own words the theories of Ptolemy, Copernicus, Galileo, and Newton as they
relate to the structure of our solar system.
Describe how most scientists believe the solar system first formed
Level III: Applying (Application)
Classify these “mystery planets” as either Inner or Outer planets based on their characteristics.
Using your knowledge of mathematics, figure out how much you would weigh on each of the
planets in our solar system.
Developing Lessons around BLOOM’S TAXONOMY
Our Solar System

14. Level IV: Analysing (Analysis)
Compare/contrast the photos of landforms on Earth and Mars. How might the features on Mars
have formed?
Based on the data, what can you say about the relationship between a planet’s distance from the
sun and its speed of revolution?
Level V: Evaluating (Evaluation)
Design an experiment to investigate how the speed of a meteorite affects the size of a crater.
Construct a scale model of the solar system using materials from home.
Create a game that will teach young children about the solar system.
Level VI: Creating (Synthesis)
What were some sources of error in your experiment with craters?
Write an essay arguing for or against manned missions to Mars. Use research to back up your
opinion.
Developing Lessons around BLOOM’S TAXONOMY
Our Solar System

15. Creating: write your own problem
Developing Lessons around BLOOM’S TAXONOMY
System of Linear Equations in Two Variables
Remembering: Identifying the steps to solve System of
Linear Equations in two variables.
Understanding: Describe what we are looking for and why –
zeros, values of x and y, intersection, etc.
Applying: Solve the given System of Linear Equations in two
variables or draw their graph
Analysing: Compare, Contrast, and Classify different pairs of
Linear Equations in two variables
Evaluating: explain and defend your solution

16. Developing Lessons around BLOOM’S TAXONOMY
Area

17. Developing Lessons around BLOOM’S TAXONOMY
Prime Numbers

18. Creative thinking Exercise 1.1
• Connect the nine dots using only 4 straight
lines

19. Creative thinking Exercise 1.1
Solution

20. Creative thinking Exercise 1.2
Connect the nine dots using only 3 straight
lines

21. Creative thinking Exercise 1.2
Solution

22. There are 127 tennis players playing
in a knock-out tournament. Find the
minimum number of matches to be
played in order to select a winner.
Creative thinking Exercise 1.3

23. Total = 126
Minimum matches means the loser never plays after
losing.
Players Matches
126 63
64 32
32 16
16 8
8 4
4 2
2 1
Creative thinking Exercise 1.3
Solution

24. Player 1 Plays Matches
2 1
3
4
2
3
It doesn’t matter who wins. So lets assume
player 1 wins all matches.
127 126
Creative thinking Exercise 1.3
Solution

25. To make 1 player out of 127 win,
how many should lose ?
? ?
?
?
?
?
?
126
Creative thinking Exercise 1.3
Solution

26.  SACHIN in his previous birth was on JUPITER
 RAHUL in his previous birth was NOT on JUPITER
 VINOD in his previous birth was NOT on SATURN
If EXACTLY ONE of above three
predictions is correct then
Who came from Jupiter?
SACHIN, RAHUL and VINOD are believed to be
on three different planets JUPITER, MARS and
SATURN in their previous births
Creative thinking Exercise 1.4

27. case 1 if prediction 1 is true then it contradicts with
prediction 2 being false simultaneously.
case 2 if prediction 2 is true then it contradicts with
prediction 3 being false simultaneously.
Therefore prediction 3 is true which concludes that
RAHUL came from Jupiter.
Creative thinking Exercise 1.4
Solution

28. And All the Best!