Problem - Solving
OBJECTIVES
· Students will be develop the ability to understand what the goal of the problem is and what rules could be applied that represent the key to solving the problem.
· They will develop abstract thinking and creative approach.
INTRODUCTION
The process of working through details of a problem to reach a solution. Problem solving may include mathematical or systematic operations and can be a gauge of an individual's critical thinking skills.
Four Stages of Problem Solving
Stage 1: Understand and explore the problem;
Stage 2: Find a strategy;
Stage 3: Use the strategy to solve the problem;
Stage 4: Look back and reflect on the solution.
Example 1:
Jay is 85 cm tall. His father is twice as tall as Jay. How tall is Jay's mother if she is 15 cm shorter than his father?
(a) 1 m 55 cm (b) 1 m 66 cm
(c) 1 m 72 cm (d) 1 m 90 cm
Ans. (a)
Explanation:
Jay's height = 85 cm
His father's height \[=85\times 2=170\]cm
His mother's height = 170 - 15 = 155 cm
= 1 m 55 cm.
Example 2:
There are 18 pupils in a group. There are 10 boys and the rest are girls 7 pupils are wearing glasses. If 3 girls are wearing glasses, how many boys are not wearing glasses?
(a) 3 (b) 6
(c) 8 (d) 9
Ans. (b)
Explanation:
more...

Estimation
OBJECTIVES
· Students will be able to generate a range of possible outcomes.
· They will be able to judge the size, amount and cost of something.
INTRODUCTION
Estimation is a rough calculation of the value, number, quantity, or extent something.
Example 1:
2 litres is most likely the amount of liquid in a ______.
(a) Bathtub
(b) Pond
(c) Large bottle of soda
(d) Swimming pool
Ans. (c)
Explanation: 2 litres is most likely the amount in a large bottle of soda.
Example 2:
What is the closest estimate of how much longer the back of truck is than the front?
(a) 60 feet (b) 70 feet
(c) 50 feet (d) 40 feet
Ans. (c)
Explanation: Nearest Estimation is 70 - 20 = 50 feet.
Example 3:
How many 250 ml cartons of milk would it take to fill the 11 carton?
(a) 2 (b) 3
(c) 4 (d) 5
Ans. (c)
Explanation:
Example 4:
The amount of water in a bath tub is about 50 _______.
(a) mililitres (b) litres
(c) centilitres (d) kilograms
Ans. more...

Logical Diagram
OBJECTIVES
· Students will be able to find out the relation between some times of a group by diagrams.
· They will be able to compare and contrast groups of things.
INTRODUCTION
A Venn Diagram is a visual brainstorming tool used to compare and contrast two (sometimes three) different things. Comparing is looking at traits that things have in common, while contrasting is looking at how they differ from each other.
A Venn Diagram is made up of two large circles that intersect with each other to form a space in the middle. Each circle represents something that you want to compare and contrast. Where the two circles intersect, you would write traits that the two things have in common. In either side of the intersecting space, you would write the differences among the two things.
TYPE-I: Different Types of Questions Based on Venn Diagrams
CASE 1:
When one group of items is completely included in the second group of items and the second, again completely belongs to the third group, they are represented as shown.
Examples 1
Tree, Forest, Leaf
Explanation:
Venn diagram would be as follows: Clearly, leaf is apart of tree and tree is a part of forest.
CASE 2:
If the items evidently belong to three different groups, i.e., they are not correlated with each other in any way. They are represented as shown.
Example 2
Whale, Crocodile, Bird
Explanation:
They all belong to different categories.
CASE 3:
If the three items are partly related to each other, they are represented as shown.
more...

Geometrical Shapes
OBJECTIVES
· To identify different objects with represent some kind of geometrical shapes which we are coming across our day to day life. (Both 2D and 3D)
· To recognize difference parts of various geometrical shapes such as vertex and sides of a particular geometrical pattern.
· Use of different geometrical shapes for creating Tangrams.
· Knowledge of line of symmetry. (Horizontal and vertical)
GEOMETRIC SHAPES
Geometric Shape is defined as a set of points or vertices and sides connecting to the point to form a closed entry. There are various kinds of geometrical shapes. Basing upon the number of vertices and sides they are identified.
2d Geometrical Shapes

· Triangle has three sides. · It has three vertices. | |

· Squares have 4 equal sides and 4 right angles.
· They have 4 lines of symmetry.
· All squares belong to the rectangle family.
· All squares belong to the rhombus family.
· more...
Embedded Figure
OBJECTIVES
· It will measure cognitive functioning and style of students.
· Students will be able to find shapes within the large more complex image.
INTRODUCTION
A figure is said to be embedded in figure (X), if figure (X) contains a part of that figure.
Types of Questions
Type I: Identify the Small Part hidden in given figure:
In such type of problem, figure (X), is given, followed by four parts, such that one of them is hidden in figure (X), students have to identify that part.
Example 1:
Identify which shape is hidden in the Figure (X).
(a) (b)
(c) (d)
Ans. (b)
Type II: Identify the Figure in Which Given Part is Hidden
In such problems, a figure X is given which is followed by four alternative of complex figures in such a way that figure (X) is hidden or embedded in one and only one of them. Student have to identify that particular figure in which the figure (X) is hidden.
Example 2:
(a) (b)
(c) (d)
Ans. (a)
Mirror/Water Image
OBJETIVES
· Students will learn how different objects are seen when they get reflected both in mirror and in Water.
INTODUCTION
The reflection of object into the mirror is called its mirror image. It is obtained by inverting an object laterally. If we combine the original figure and mirror image together they form symmetry.
MIRROR IMAGES
Mirror Images of Capital letters
· The capital letters which have the same mirror images are:
A, H, I, M, 0, T, U, V, W, X, Y
Mirror Images of Small letters
· The small letters which have the same mirror images are:
i, l, o, v, w, x
Mirror Images of Numbers
· 0 and 8 numbers have the same mirror images.
Mirror Image of Clock Time
For mirror image of clock time, the given time shall be subtracted from 12 00 or 11.60.
Example 1:
What will be the mirror image of clock time 3:40?
Explanation:
By using simple trick
WATER IMAGE
INTRODUCTION
more...
Logical Reasoning
OBJECTIVES
· To identify relationships, similarities and difference between shapes and patterns.
· To recognize visual sequences and relationships between objects and remembering these.
INTRODUCTION
Visual reasoning is the process of manipulating one's mental image of an object to reach a certain conclusion.
Types of Questions
The chapter includes:
1. Grouping of figures.
2. Paper folding and cutting.
3. Merging and splitting of images.
4. Finding difference between two images.
5. Clock wise and anticlock wise rotation of objects.
6. Tessellation puzzle.
7. Completion of image.
8. Corresponding image.
9. Different sections of image.
10. Symmetry
11. Rule detection
Paper Folding and Cutting
In this type of questions, there are three or four figures given in one line. Each figure followed a pattern. Each figure consists of a dotted line along which it is to be folded and the arrow shows the side which it is to be folded.
After folding, the paper is cut or punched and then students have to visualize the correct figure that will be produced when the paper is unfolded.
Direction (Example 1): In the following example, a piece of paper is folded and cut and then unfolded. One of more...
Type I: How to arrange the numbers given to the
corresponding letter so that they form a meaningful word?
Arrange the letters in the different combinations given in options
to find a meaningful word.
Type II: Finding the word from
the options that can/cannot be formed from the given letters.
Students have to observe carefully all the letters given in the
question and find the combination of letters from the given options that
contains or does not contains letters.
Type III: How to form a meaningful
word and find the category of word?
Arrange the given jumbled letters in a meaningful word and
identify the category in which formed word lies.
Type IV: How to identify the
combination of letters that has same number of skipped letters between the
adjacent letters?
Write the alphabetical series in order, then observe carefully all
the options.
EXAMPLE
1. In the question, some letters are given which are
numbered 1, 2, 3, 4, 5 and 6 followed by four options containing combinations
of these numbers. Find the combination of numbers so that letters arranged
accordingly to form a meaningful word.
R F W E L O
1 2 3 4 5 6
(a) 2, 5, 6, 3, 1, 4 (b)
2, 5, 6. 3, 4, 1
(c) 1, 5, 6, 4,
3, 1 (d) 2, 5, 6, 1, 3, 4
Explanation (b):
First go through each option:
(a) 256314 = FLOWRE;
(b) 256341= FLOWER
(c) 256431 = FLOEWR;
(d) 256134= FLORWE
Meaningful word: FLOWER.'. Combination: 2, 5, 6, 3, 4, 1
2. Which word cannot be
made from the letters of the given word?
TEMPERAMENT
(a) METER (b)
PETER (c) TENT (d) TESTER
Explanations (d): S of the word TESTER
is not in the given word.
Type I:
How to find the missing term or next term in (number or letter) series to continue the given series?
- Identify the (descending or ascending) order of series. Observe the pattern using operations: addition, subtraction, multiplication, and division, skip counting and reverse counting.
- Identify the order of alphabetical series either from A to Z or Z to A.
- Numbering of alphabets either starts from A or starts from Z.
- Skipping letters.
- To find the missing term in the given pattern, identify the rule followed in rest of the given terms in pattern using mathematical operations (+,- ,x, ~), skip counting and reverse counting.
- Complete the figure pattern by drawing its incomplete part in the pattern.
How to decode the questions given in coded language?
In these type of questions, some particular words are assigned certain substituted names.
Then a question is asked that is to be answered in the substituted code language.
EXAMPLE
1. If' Wrist watch' is called 'Nail'; 'Nail' is called 'Phone' and 'Phone' is called 'Newspaper', then what do we wear on wrist?
(a) Wrist watch
(b) Nail
(c) Phone
(d) Newspaper
Explanation (b):
Wrist watch is worn on wrist and Wrist watch is called Nail.
2. If B means C, C means D and D means E, which alphabet is a vowel?
(a) B
(b) C
(c) D
(d) E
Explanation (c):
E is a vowel and D means E.
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