Logical Thinking Revision - it.iitb.ac.in

RevisionLesson

Logical Thinking

5

In this lesson you will learn:Step by step approach and reasoning to solve problems.How to use what you already know to solve problems.How to tackle a task when you do not know anything about it.How logical thinking can help solve problems.

mAi

1. We know: There are four types of fruits Apples, oranges, bananas and grapes.2. Goal: I have to pick two fruits 3. There are some conditions: a cross mark for apple + orange, apple + grapes. 4. I like apples. What other fruit can I take? 5. Answer: And a tick mark for apple and banana.

Tejas: Fruits! I like fruits. They are good for health.Moz: Correct. You can have them. Each one of you pick two types of fruits. Note the following: If you pick apple you cannot pick orange. If you pick orange you cannot pick banana. If you pick grapes you cannot pick apple.

Jyoti: With orange we cannot pick banana or apple. Hence I picked orange and grapes.

Moz: Very good logical thinking. Can I pick banana and grapes?Tejas and Jyoti: Yes you can!

Moz: Now let us look at another example. You are walking towards a play ground. But the playground is on the other side of the road. So what do you do?Jyoti: We know that we have to first reach a zebra crossing where there are traffic lights.

Read the problem carefully.Ex problem: What comes next in the sequence?

As you are reading make a note of the following:1. The information available A sequence of geometrical shapes is given In the sequence the first shape has 3 sides, the second 4 sides and the third 5 sides.2. Are there any conditions ? There is a difference of one side between two shapes. The number of sides is increasing by 1 in the sequence.3. What is the goal? To find the fourth shape in the sequence. 4. Achieve the goal using data and conditions. The fourth shape has 5+1 = 6 sides.

CONCEPTS

Tejas: With apple we cannot pick an orange or grapes hence I picked apple and banana.

Tejas: We check that the vehicles on both sides have stopped before crossing.Jyoti: The condition is that we should follow traffic light rules so that accidents do not happen. Moz: Good. It is very important to learn about the traffic rules and follow them.

1. We have a task on hand. Crossing the road.2. What are the rules that I know to perform the task? Cross the road when the green signal for crossing is on and the vehicles stop moving. If you do not know the rules then ask parents, teachers and from other elders whom you know. observe others who are performing the task. Observe, how people wait till the green signal to cross is on. When all the vehicles to both the directions stop, they cross.3. Why should I follow the rules? Accidents can happen if I cross the road when the vehicles are moving.

What, when and why are questions that can help you take an action logically. What and when makes you recall what has been learnt. Why makes you understand the importance of following the facts you know.

CONCEPTS

Jyoti: Here is a problem. There are three groups of children on the play ground. Group A has 3 children, B has 5 children and C has 2 children. The teacher wants to know the total number of children on the play ground.

Tejas: There are 10 children in the play ground.Moz: Ok. Now consider the another problem. Group A has 5 children, Group B has 5 children and Group C also has 5 children. How many children are there in the playground?

Tejas: There are 10 children in the play ground.Moz: Ok. Now look at this. Group A has 5 children, Group B has 5 children and Group C also has 5 children. How many children are there in the playground?

We know: Group A = 3 children, Group B = 5 children and Group c = 2 children Goal: Find total number of children. Answer: Add the three numbers

We know: There are three groups and each group has 5 children each.Goal: Find total number of children.Answer: Multiply 5x3

+ +A B C

+

Jyoti: There are 15 children.Moz: Why did you add in the first problem and multiply in the second problem.Tejas: In the first problem the numbers are unequal. So we have to add each one of them.Jyoti: In the second problem also we can add. But since the same number appears three times we can simply multiply to get the result.

Moz: Very good. Here are a few pieces of my birthday cake. The cake was cut into 8 pieces. I gave one piece to my father and one to my mother. Can you tell me how many pieces are left now?

Jyoti: We know, there were 8 pieces of cake. one piece was given to father and one piece to mother.Tejas: Now let us find the number of pieces left.

Step 1: Find the total number of pieces that were given away.Add 1+1 = 2 Step 2: Take away the pieces that were given away from the total number of pieces. Subtract 2 from 8 = 6

Tejas: 6 pieces are left now.

Jyoti: 2 pieces each!Moz: Very good. You have been able to solve the problems very easily. You already know how to think logically. I met a farmer yesterday who has a problem. Let us together find a solution.

Tejas and Jyoti discuss the problem and work out the solution as follows:Tejas: There is a fox, a chicken and some corn. Jyoti: There is a river and a boat and a farmer.Tejas: The goal is to take the chicken, fox and the corn to the other side of the river in the boat.

Farmer’s problem:Kishan, the farmer has to take a fox, a chicken, and a bag of corn safely across a river in a boat. He can take only one thing at a time in the boat. He cannot leave the fox and the chicken together on either side of the river, or the fox will eat the chicken. Likewise, he cannot leave the chicken alone with the bag of corn or the chicken will eat the corn. How can the farmer get everything across the river without anything being eaten?

Moz: I want to distribute these pieces equally among three of us.

Jyoti: The conditions are: The farmer can take at a time only one of the fox, chicken or corn in his boat. On either side of the river the farmer cannot leave fox and chicken together Chicken and corn together But he can leave fox and corn together.

Tejas: Suppose Kishan takes the chicken first and leaves it on the other side.Jyoti: Then he comes back and takes the corn.Tejas: But he cannot leave the corn and chicken together.Jyoti: So he leaves the corn and brings back the chicken.Tejas: Now he takes the fox and leaves it on the other side.Moz: Good. So the fox and corn on the other side can be left together.

Jyoti. Now, he comes back and then takes the chicken.Tejas: Kishan’s problem solved. That was fun to solve.Moz: See how easy it is to solve a problem by first understanding.Jyoti: And then solve it step by step!

Moz: Let us meet tomorrow and use what you learned today and build some interesting games using scratch. Chin Chinaki...

Step wise thinking is mostly detailing out a solution. There may be only one rule to follow.Logical reasoning is about understanding the goal and conditions of a problem and then solving it in a step-wise manner to reach the end.

CONCEPTS

Lesson

Outcome

After you have studied this lesson,

you will be able to:

Understand the problem

Identify goal and conditions

Solve the problem

WORKSHEETSBook III Lesson 5

1. Solve anagrams and match the columns. In anagrams, alphabets in a word are presented in jumbled order. You have to set it in correct order to form the word. For instance, an anagram as ‘D R E’ would mean ‘RED’.a. Following are some things you carry to the school everyday. Solve the anagrams by matching the columns.

S.No. Anagram Word

1 K B O O

2 F I T F I N

3 G A B

4 C I P E N L

5 X O B


b. Following are names of the vehicles that are used for transportation. Solve the anagrams by matching the columns.

S.No Anagram Word

1 R N T I A

2 P S I H

3 L C Y E C

4 S B U

5 R A C


2. Chiku, the rabbit has to hop his way to find the carrots on the island. With each hop, he crosses five tiles. How many times will he have to hop to reach the carrots.

3. Complete the following series:a) 9, 10, 12, 15,?

b) 1, 2, 4, 7,?

c) 10, 9, 7, 4, ?

d) 12, 8, 5, 3, ?

a) 19

a) 10 b) 11

b) 1 c) 2

c) 1

d) 0

d) 7b) 10

c) 5 d) 12

a) 8

a) 2

b) 17(Hint: 9+1=10, 10+2=12, 12+3=15, 15+4=19)

c) 25 d) 20


4. Munmun, the squirrel has to eat the groundnut. Help her reach reach it.

5. Can you help Jyoti to solve the folowing puzzles.

a. Some figures are given below. Observe them

Now match the shapes with their colour

YELLOW RED BLUE GREEN


b. Observe the following figures.

c. Study the following figures.

Now colour the triangles in the grid below, so that the Red triangle is between yellow and blue triangles. The first triangle is the Yellow one.

Now colour the squares in the following grid. The Red square comes in between the brown and yellow squares. Blue square is the first square in the grid. Black square is directly above the yellow square.

6. Can you tell what comes next? Circle the correct option.


i.

ii.

7. Solve the following puzzles:a. Kartar, Seema and Rahul are collectors. One collects stamps, one collects insect pictures and one collects toy car pictures. Rahul swapped his car pictures for insect pictures. Seema doesn’t like cars but likes getting letters. Kartar thinks insects are too small to worry about. What do Kartar, Seema and Rahul collect?

b. Amina, Manish, and Jeet each ate something different for breakfast. One had toast, one had chapatti, and one had an apple for breakfast. What did each person have for breakfast? i) Amina likes to eat either an apple or toast for breakfast. ii) Only Manish and Jeet like chapati for breakfast. iii) Jeet did not have chapatti or toast for breakfast.


Book III Lesson 5

1. Play puzzles in the Educational suite Gcompris. Within the educational suite gcompris, explore “go to discovery activities” and “puzzles”. There are several activities within each of them. For instance, if you click on miscellaneous activities, you will see the following game.

2. Connect the following nine dots, Use only 4 straight lines traced without lifting your pencil.

. . . . . . . . .

Group activity:Divide the class into groups of five students each. Each group is given a theme around which to construct a story. For example, one group can write a story about the talk between flowers, another group can write a story about the talk between objects in the school bag. The teacher can also give pictures of animals with varied expressions to triger the imagination of children to construct the story. One student says a sentence and the second student adds another line. In this way, the story gets constructed by the students. The following questions can help students in framing the story: 1. What is happening in the picture?2. What are the different characters doing?3. What has happend before?4. What will happen next?After students have made the story, the teacher discusses the emotions experienced and values demonstrated by the different characters in the story.

Book III Lesson 5

Explore!1. A shoe can be used for several activities besides covering your feet. Write 20 different uses of a shoe.

Teacher’sCornerStart the class by revising the step-wise thinking lesson. Now bring out the importance of thinking capabilities. Ask students what they do to keep physically fit. They may say, ‘We exercise our body to remain physically fit’. Tell them, that exercise of mind is important for mental fitness. Tell them that solving puzzles, mental sums, stories and computer games can be an effective mechanism for exercise of the mind.

To teach logical thinking, discuss examples where in children use logical thinking in every day life. For instance, you may ask the students, why they do not cross the road when vehicles are moving. You can elaborate that while crossing the road, they reason out that they should not cross the road when the green signal is on as the vehicles are passing and they may be hit if they are not careful. They wait for the signal to be red, so that the vehicles stop and they cross the road safely.

Ask several ‘WHY’ questions. For example: Why are vegetables washed before cooking? Why do you not put your finger in the flame of a burning candle? Why should we learn good manners? Why should we help others? Why should we speak truth?

Explain that in step wise thinking, they detail out the solution and there may be only one rule to follow. For logical reasoning, they have to understand the rules and conditions. You can give the example of cooking a vegetable. First ask them about the steps to follow. Tell them that this is an example of making a vegetable. Now question them on why to follow the steps in the order. Tell them the questionning is an example of logical thinking.

Narrate a story to the students that highlights logical thinking. Ask them questions that require logical reasoning after you have told them the story. Summarize the lesson emphasizing the importance of thinking logically. You can narrate the following story in the class:

Unity is Strength Once upon a time, there was a flock of doves that flew in search of food led by their king. One day, they had flown a long distance and were very tired. The dove king encouraged them to fly a little further. The smallest dove picked up speed and found some rice scattered Priyaeath a banyan tree. So all the doves landed and began to eat. Suddenly a net fell over them and they were all trapped. They saw a hunter approaching carrying a huge club. The doves desperately fluttered their wings trying to get out, but to no avail. The king had an idea. He advised all the doves to fly up together carrying the net with them. He said that there was strength in unity. Each dove picked up a portion of the net and together they flew off carrying the net with them. The hunter looked up in astonishment. He tried to follow them, but they were flying high over hills and valleys. They flew to a hill near a city of temples where there lived a mouse who could help them. He was a faithful friend of the dove king.

Book IIILesson 5

Teacher’sCorner

When the mouse heard the loud noise of their approach, he went into hiding. The dove king gently called out to him and then the mouse was happy to see him. The dove king explained that they had been caught in a trap and needed the mouse’s help to gnaw at the net with his teeth and set them free. The mouse agreed saying that he would set the king free first. The king insisted that he first free his subjects and the king last. The mouse understood the king’s feelings and compled with his wishes. He began to cut the net and one by one all the doves were freed including the dove king.They all thanked the mouse and flew away together, united in their strength. Questions to be asked: How were the doves saved? What would have happened if all the doves did not listen to their king? Why is it important to be united?

Furhter Reading :http://www.kidsdomain.com/kids/links/Puzzles.htmlhttp://www.indiaparenting.com/stories/panchatantra/panch010.shtmlhttp://www.aimsedu.org/Puzzle/fencingNum/fence1.htmlhttp://wwwcsi.unian.it/educa/problemsolving/stice_ps.htmlwww.micsymposium.org/mics_2004/Sinapova.pdfhttp://www.det.wa.edu.au/education/gifttal/activities/ideas.htm

Book IIILesson 5

Logical Thinking Revision - it.iitb.ac.in

Documents