Assignment Code: AMT-01/TMA/2021

Course Code: AMT-01

Assignment Name: Teaching of Primary School Mathematics

Year: 2020-2021

Verification Status: Unverified

Valid Until: December 31, 2021

Q1) a) Give one example each, with justification, to support the following statements.

i)Children in early primary school have a problem with handling formal arithmetic.

Ans) Children have problems with conventional methods because the formal code is much too abstract to master at this stage. Relating the problem to a concrete real-life experience helps children to rely on their own intuitive understanding, and thus invent a strategy to arrive at a solution.

There is also another reason why children in early primary school have a problem with handling formal arithmetic. In the formal code of arithmetic the operations proceed from right to left, whereas reading in English proceeds from left to right. Many primary school children continue to make the error in going from left to right while doing arithmetical operations. This indicates the need to develop their spatial thinking ability before and along with other arithmetical abilities.

ii) Repetition is not the same as rote learning.

Ans) Repetition can be imaginative. It can involve the children in enjoyable activities, which could even be initiated by the children themselves. In these repetitions the participating children observe and experience something new and different each time.

Rote learning, on the other hand, does not allow for variety because it is not the process which is being repeated, but the `information' which is being repeated mechanically (for example, memorising multiplication tables mechanically).

iii) Objects of different shapes may have the same volume?

Ans) Yes, objects of different shapes may have the same volume. As in the case of length and area, the standard unit for measuring volume may be introduced. Small unit cubes of measurement 1 cm. x 1 cm. x 1 cm. may be used for the purpose. The problem here is that children, even after understanding the concept of the occupied volume of solid and its conservation do not understand the notion that volumes can be compared using interpretation of a unit cube. One of the major difficulties experienced by the children in thinking of solids as built of hit cub, is that many of the cubic units & cannot be seen, such as those in the centre of a cuboid. You can overcome this problem to some extent by making, them do the activity which they might have done in their childhood while playing with wooden blocks. Dismantling and assembling blocks to form various shapes. Show them a block made up by putting small cubes together. Let them find out how many cubes this block consists of.

Q1) b) Evaluation at every step, through immediate feedback, should form part of teaching – learning process. Explain this statement in the context of each, teaching and learning of place-value. Further give three distinct multiple assessment techniques for evaluation in the context given.

Ans) Evaluation plays an enormous role in the teaching-learning process. It helps teachers and learners to improve teaching and learning. Evaluation is a continuous process and a periodic exercise. It helps in forming the values of judgement, educational status, or achievement of student. Evaluation in one form or the other is inevitable in teaching-learning, as in all fields of activity of education judgements need to be made.

In learning, it contributes to formulation of objectives, designing of learning experiences and assessment of learner performance. Besides this, it is very useful to bring improvement in teaching and curriculum. It provides accountability to the society, parents, and to the education system.

We can draw following characteristics of evaluation:

1. Evaluation implies a systematic process which omits the casual uncontrolled observation of pupils.

2. Evaluation is a continuous process. In an ideal situation, the teaching- learning process on the one hand and the evaluation procedure on the other hand, go together. It is certainly a wrong belief that the evaluation procedure follows the teaching-learning process.

3. Evaluation emphasises the broad personality changes and major objectives of an educational programme. Therefore, it includes not only subject-matter achievements but also attitudes, interests and ideals, ways of thinking, work habits and personal and social adaptability.

4. Evaluation always assumes that educational objectives have previously been identified and defined. This is the reason why teachers are expected not to lose sight of educational objectives while planning and carrying out the teaching-learning process either in the classroom or outside it.

5. A comprehensive programme of evaluation involves the use of many procedures (for example, analytico-synthetic, heuristic, experimental, lecture, etc.); a great variety of tests (for example, essay type, objective type, etc.); and other necessary techniques (for example, socio-metric, controlled-observation techniques, etc.).

6. Learning is more important than teaching. Teaching has no value if it does not result in learning on the part of the pupils.

7. Objectives and accordingly learning experiences should be so relevant that ultimately they should direct the pupils towards the accomplishment of educational goals.

Purposes and Functions of Evaluation:

Evaluation plays a vital role in teaching learning experiences. It is an integral part of the instructional programmes. It provides information’s on the basis of which many educational decisions are taken. We are to stick to the basic function of evaluation which is required to be practiced for pupil and his learning processes.

Evaluation has the following functions:

1. Placement Functions:

1. Evaluation helps to study the entry behaviour of the children in all respects.

2. That helps to undertake special instructional programmes.

3. To provide for individualisation of instruction.

4. It also helps to select pupils for higher studies, for different vocations and specialised courses.

2. Instructional Functions:

1. A planned evaluation helps a teacher in deciding and developing the ways, methods, techniques of teaching.

2. Helps to formulate and reformulate suitable and realistic objectives of instruction.

3. Which helps to improve instruction and to plan appropriate and adequate techniques of instruction.

4. And also helps in the improvement of curriculum.

5. To assess different educational practices.

6. Ascertains how far could learning objectives be achieved.

7. To improve instructional procedures and quality of teachers.

8. To plan appropriate and adequate learning strategies.

3. Diagnostic Functions:

1. Evaluation has to diagnose the weak points in the school programme as well as weakness of the students.

2. To suggest relevant remedial programmes.

3. The aptitude, interest and intelligence are also to be recognised in each individual child so that he may be energised towards a right direction.

4. To adopt instruction to the different needs of the pupils. 

5. To evaluate the progress of these weak students in terms of their capacity, ability and goal.

6. Guidance Functions:

1. Assists a person in making decisions about courses and careers.

2. Enables a learner to know his pace of learning and lapses in his learning.

3. Helps a teacher to know the children in details and to provide necessary educational, vocational and personal guidance.

Q1) c) How would you convince a child that any number multiplied by 0 is 0, using a teaching aid.

Ans) Students learn the meaning of a number times zero, or zero times a number, both as regards to equal-size groups and number line jumps. The exercises involve filling in the table of zero and the table of one, and some miscellaneous multiplication problems.

Q2) a) Illustrate with examples why “classification” and “seriation” are pre number concepts. Develop a series of three distinct activities at different levels of difficulty, to assess how for children have ability to perform any one of these two processes. Explain how these activities are at different levels of ability.

Ans) Classification:

Classification (also called grouping) involves putting together things that have some characteristic in common. We can say that a child is able to classify only if she is able to decide upon the criterion for classification, and maintain it throughout the activity. This ability forms a basis for the development of logical and mathematical concepts.

Children often classify while doing everyday activities. When a child is asked to put a doll's clothes in one bag and the doll's ornaments in another, or to put the unclean plates in one tub and the clean ones in another, or to separate squares and triangles from paper cutouts, she is classifying. But we need to give children more opportunities for classification, to develop this ability in them. This can be done very easily through play.

While organising a task for a child, we must keep in mind what she is familiar with, and her capabilities. It is important to observe a child in different situations before coming to any conclusions about her abilities. We must encourage children to talk about what they are doing in an activity. This helps us to know how far the children have understood the concept of classification. In the initial, activities the basis for classification should be one property only.

Some activities that can be organised with pre-schoolers to develop their ability to classify are:

You could start by giving children different items to enjoy with. While playing, they spontaneously think of ways of 'arranging' them. Of course, their 'classification' may 'seem quite arbitiary to you, but that doesn't matter. What is important is that they are getting an opportunity to handle a variety of materials, and 'organise' them in some manner. At this stage the children may not be ready to classify on the basis of even one criterion.

At the next stage you could ask them to classify objects that are familiar to them on the basis of one, physical characteristic like colour, or shape, or texture. You could explain-what has to be done - "Put together all the objects which are red in colour", "Put together all the sticks like this one", etc. Initially you may have to form the groups to show the children how to do the activity.

You could make available a variety of leaves/stones/pulses/balls, and ask children to sort them into groups. Let children evolve their own criteria for classification and group them jn any way they like. Once they complete the activity, talk to them about the criteria they have evolved by asking them questions like "Why are these together?", "Why not put this here ?", etc.

While children are having a meal, you could ask them which foods taste sweet, and which are salty.

A more complex game would be to divide up some objects yourself, based on some criterion. Then you could give the children a few chances to guess what your criterion is.

Seriation:

Ordering a set of objects means to arrange them in a sequence according to some rule. This arrangement could be on the basis of size, shape, colour or any other attribute. For example, you could order a set of red and green leaves on the basis of colour - one red, one green, one red

Seriation is a particular type of ordering in which the objects are arranged according to an increase (or decrease) in some attribute like length, shape, weight, and so on. For example, you could seriate a set of stones according to their weight - the heaviest one coming first, and then the next heavy one, and so on, ending with the lightest one.

For Example, 4-year-old Bachi was given five sticks of different lengths, and asked to order thein according to length. To do so she placed the first stick next to herself. Then she picked up another and placed it with reference to the first one. This was alright so far. While placing the third stick, she referred to the previous two sticks, and placed it correctly. Now, while placing the fourth stick, she referred only to the third stick, instead of looking at the total arrangement. So, finally her arrangement looked like the one it should have.

Bachi could seriate three objects. But, when it came to the fourth, she couldn't relate it to all the previous sticks. She couldn't see that it is longer than the second, but shorter than the third, and therefore, must come in between them. After the third stick, she perceived each subsequent one only in relation to the previous stick that had been put in the sequence.

The above Example also brings out the need to be clear about the logical processes involved in any task given to a child. In particular, before we expect a child to perform seriation tasks, we should see if she is able to:

• order in two directions (e.g., apply the relations 'bigger than' and 'smaller than' at the same time),

• understand the logic of transitivity (i.e., if A is more than B and B is more than C, then A is more than C).

The simplest ordering activity is asking children to copy a pattern. For example, make a row of alternating chalk and pencils, and ask children to make a similar row using chalk and pencils from a heap.

At a higher level of difficulty, you could ask children to continue a pattern. For example, place a twig and two beads, repeat this unit a few times, 'and then ask children to continue it.

The question to be answered in ordering activities is "what comes next ?"

At the next level of difficulty is asking children to seriate a collection of objects on the basis of some attribute. You could begin by giving children three objects to seriate and then gradually increase the number. Initially you may need to prompt them by asking questions such as "Which is the smallest?", "Which is the longest?", and explain how to do the task. If children put objects in a series incorrectly, ask them questions like "Is A (pointing to the object) thinner than C (pointing to the object )?" or "This one looks bigger, shouldn't it come here?". This will help them to analyse the arrangement and develop the concepts involved.

When carrying out seriation activities, using words like 'last', 'first' and 'before' helps children develop these concepts. Such activities will also help them to see that attributes are relative. A button which may be the largest in one set, may be the smallest in another. Thus, there are no absolute dimensions.

Q2) b) Illustrate the use of each of the following in learning the concept of “fraction”.

i) an outdoor activity

Ans) A very simple outdoor challenge for children to try, is to find a thin stick, break it into a number of pieces, e.g. four and put it back together correctly. This is a nature jigsaw. It’s much harder than it sounds. A similar activity can happen with leaves.

Recently, I saw this challenge taken a step further. The teacher decided her class needed more practice and understanding about how fractions are part of a whole. The children had to work in groups to create a fraction wall.

This turned into quite a problem solving activity. Firstly, sticks had to be found of similar lengths. Otherwise the fractions were not equal on every line…

The next tricky bit was remembering to put the sticks close together rather than spread them out as in the above photo. There had to be one whole stick, two half sticks, a stick broken into thirds, then a stick in quarters, etc.

he groups tended to work as a team, with one or two members finding and fetching sticks and others working on the structure of the fraction wall.

ii) newspapers and magazines                                                   

Ans) Students are given various lengths of paper strips or pieces of paper streamers. Ask the students to fold their paper strips into halves and ask a question such as: “How do you know you have folded your strip into halves?” Ask students to compare their half strips with those of other students. Students are then shown other students’ attempts to show one half of a rectangle

Ask questions such as:

1. Which of these students have success- fully shaded their rectangles to shows one half? (Some students will not recog- nise that Mike’s rectangle is showing one half as they think the left hand side is one half and the right hand side is two halves.)

2. Why is Jackson’s half different to Mike’s half?

3. Why do you think Jen has shaded her rectangle how she has?

Q3) a) What could be the logic behind the following subtraction done by a child:

1.39

4.6

3.45

−

Does this shows that the child has not understood the process of subtraction of

numbers? Give reasons for your answer. How will you help her to correct her

mistake

Ans) In the above example, it is clear that the above result given by the child is a mistake. The correct answer should be -1.15. What the student has done here is that they have not accounted for the 4.6 to be as 4.60. Adding that zero at the end makes the units places clear to understand. Hence, when doing the subtraction, they have done “45 - 6” which is equal to 39 as they have written in their answer. However, the correct answer should be .15 as 45 has to be minused from .60. When we do this, we arrive at the correct answer.

The other mistake done by the student is not adding the minus sign in the answer. Their current answer is 1.39 when it should be -1.15.

From this, we understand that the student has got an understanding of the process of subtraction but there are a few things that need to be corrected. I would help the student understand the above concept with adding a 0 at the end of a decimal point. For example, 4.6 should be written as 4.60 in order for it to be done correctly. Another thing that needs to be fixed is the – sign at the beginning of the answer. We need to explain to her that when the lower number is higher than the upper number the final answer automatically starts with a minus sign. This can also be explained with the help of objects.

Q3) b) Analyze any chapter of the mathematics text book for class 3 children and identify two portions in it where the language of mathematics is not appropriate to the level of children. You reword the portions of it, to make it simpler for children to learn it better. Present the original portion and the changed portion with necessary explanation which justifies the changes.

Ans)Arguably one of the biggest challenges for most primary teachers is the struggle to address the many components of the mathematics curriculum within the confines of a daily timetable. How many times have you felt there just isn’t enough time to teach every outcome and every ‘dot point’ in the entire mathematics curriculum for your grade in one year? It is my belief that one of the biggest issues in mathematics teaching at the moment stems from misconceptions about what and how we’re supposed to be teaching, regardless of which curriculum or syllabus you are following.  The way we, as teachers, perceive the content and intent of our curriculum influences whether students engage and achieve success in mathematics. The way we experienced the curriculum when we were at school also influences how mathematics is taught in our own classrooms.

This struggle arises partially from the common perception that every outcome (in NSW) or Content Descriptor (from the Australian Curriculum) must be addressed as an individual topic, often because of the way the syllabus/curriculum is organised (this is not a criticism – the content has to be organised in a logical manner). This often results in mathematical concepts being taught in an isolated manner, without any real context for students. A result of this is a negative impact on student engagement. Students fail to see how the mathematics relates to their real lives and how it is applied to various situations. They also fail to see the connections amongst and within the mathematical concepts.

This leads me to my second point and what I believe is happening in many classrooms as a result of misunderstanding the intention of the mathematics curriculum. If students are experiencing difficulties or need more time to understand basic concepts, you don’t have to cover every aspect of the syllabus. It is our responsibility as teachers to ensure we lay strong foundations before continuing to build – we all know mathematics is hierarchical – if the foundations are weak, the building will collapse. If students don’t understand basic concepts such as place value, it doesn’t make sense to just place the ‘strugglers’ in the ‘bottom’ group and move on to the next topic.

Q4) a) A class 4 teacher wants to help her students understand the 3 categories of division of numbers. Construct one word problem of each category corresponding to the division 32 ÷ 8 = 4. Which of these categories of word problems is usually considered difficult for a primary school child to understand? Give reasons for your answer.

Ans) In division we will see the relationship between the dividend, divisor, quotient and remainder. The number which we divide is called the dividend. The number by which we divide is called the divisor. The result obtained is called the quotient. The number left over is called the remainder.

Division is breaking a number up into an equal number of parts. Example: 32 divided by 8 = ? If you take 32 things and put them into eight equal sized groups, there will be 4 things in each group. The answer is 4.

Signs for Division There are a number of signs that people may use to indicate division. The most common one is ÷, but the backslash / is also used. Sometimes people will write one number on top of another with a line between them. This is also called a fraction. Example signs for "a divided by b": a ÷ b

Dividend = 32

Divisor = 8

Quotient = 4

Q4) b) Devise a game for a group of appropriate level of children to help them develop the ability to estimate volume.

Ans) Firstly, there are three boxes in a kit. Each has been exactly measured so it fits a certain number of blocks. Children need to cut out and put together each box (I had them in groups of 3 so each group member made one box).

Then you fill each of the blocks up with place value cubes (1cm cubes) and measure the volume of the box. You can see the little A on the side of the box, each box is numbered.

Here is the larger box. There is also a worksheet peeking out from the corner!

After children have filled up the three boxes and counted the blocks they fill in some questions about how many times blocks fit inside.

The thing I really liked about this activity is that when I was wondering around, some children had different strategies for working out the volume of the box. (For example only measure length, then height, then width!) It was wonderful to see the children's thinking!

If you need a volume activity, you can't go past this one - it is a simple buy, print and copy off - no other preparation required by you. There are a couple of extra surprises in the pack too!

Q5) a) What is a magic square? Complete entries in the following and make it a magic square.

Ans) In the magic square trick, an audience names any two digit number between 22 and 99 and after you fill in the 16 boxes there will be 28 possible combinations where the boxes will add up to the given number.

The trick to drawing the magic square is to realize that the numbers in a 4 by 4 magic square are always fixed as shown. (Look at the following video to see how to remember the numbers and their places in the square). Only the four numbers A, B, C, D are dependent on the number given by the audience.

Q5) b) Explain two implications for teaching mathematics of the fact that mathematical knowledge is hierarchically constructed. Give examples in support of your answers in the context of teaching negative numbers.

Ans) The hierarchy of concepts also has implications for the way concepts are learnt. If you look at the historical development of any concept, hierarchically lower concepts usually came before hierarchically higher concepts. The learning of concepts by children is also, broadly, on the same pattern. Therefore, it is usually better to introduce a child to an hierarchy of ideas the way they developed. Unfortunately, this does not always happen.

For example, a square is a particular type of rectangle, and a rectangle is a particular case of a parallelogram. But many children in Class 2 are taught these concepts at the same time, without even relating them to each other. What is the result? Even two years later many of them will say that a square is not a parallelogram.

So, to really understand a new mathematical idea a person requires a proper understanding of mathematical concepts that come before it. This is what we mean when we say mathematics is an hierarchically structured discipline. In the following exercise we ask you to consider the implications of this fact for teaching.

Q5) c) i) What is the pattern used by the student?

Ans) the student has multiplied the first digit of the first number with the first digit of the second number and then placed the numbers next to each other to formulate the final answer

ii) Explain why it works?

Ans) It works because of the way numbers work with each other in an ambiguous way.

iii) Describe how it helps to encourage mathematical thinking.

Ans) Using this technique can help the students to think in a visual and mathematic way. This is because when they see the numbers interacting with each other they realise they can do the same pattern with other numbers as well. This helps them develop their mathematical thinking.

Q6) b)  Prove that the sum of the first n even numbers is an even number. Is the kind of logic used in proving this is inductive, deductive or both? Justify your answer.

Ans) Let n= 2k for some integer k

Then, in a series of even integers we obtain

2+4+6+...+2k=k(k+1)2+4+6+...+2k=k(k+1)

P(k)=1(1+1)=2,P(k)=1(1+1)=2, where k=1

P(k+1)=2+...+2(k+1)P(k+1)=2+...+2(k+1)

=k(k+1)+2(k+1)=k(k+1)+2(k+1)

=k^2+k+2k+2=k

2 +k+2k+2

=k^2+3k+2=k

2 +3k+2

=k(k+1)[(k+1)+1]=k(k+1)[(k+1)+1] Q.E.D

This shows the prove that the sun of n even numbers is even.

This is inductive proof.

The inductive step involves assuming the statement is true for one number, then proving it for the next number. ... If somehow integers came in two chunks with 0 in the first chunk, then mathematical induction would only work to prove that the statement is true in the first chunk.

Q6)c) What could be the possible reasons for giving such answers? Suggest a class room activity that helps children explore and learn the concept of angle and also helps children to articulate reasons and construct arguments discussed in Sec. 18.3 of Block 5.

Ans)  I love teaching angles - it's short and sweet, and the students always have a lot of success with it - which makes it all the better.

Tables, Whiteboards and Washi Tape: Get the tape out and get ready for some hands-on fun!  (You don't have to use washi tape - masking tape works perfectly fine, too).  To introduce angles at the beginning of our unit, we did a full group lesson on classifying angles.  I taped up a table, armed students with a whiteboard marker, and let them classify (acute, right, obtuse, and straight) as many angles as they could.  They LOVED this activity!  So everyone could fit around the table, I paired up the students so they could take turns marking angles on the table. Once we were masters at classifying angles, we could move on to measuring angles.  This is such a fun activity - perfect for practice at math centers!  We just used some fun washi tape to "draw" lines on our whiteboards.

 We used 5 pieces of tape - and I told them the tape had to be straight and go across the board from one side to the other.  From there, students measured the angles made by the tape.  You could just leave it at this, but I turned this activity into a game by pairing up the students.  Each student had a different color of whiteboard marker.  The first student measured an angle (any angle of their choice) and wrote down the measurement using their color.  Then, the second student checked the answer.  If it was correct, they left it alone.  If it was incorrect, they erased the first answer and wrote the correct answer using their color (the second student).  The second student then got a chance to pick and measure an angle of their choice - recording the answer in their color.  At the end of the activity, the student with the most answers in their color (most correct answers) wins! 

Q7)a) A class 5 child believe that the division always makes a number smaller. Describe an activity that could help her correct her misconceptions. Also describe an activity to assess how far the activity is effective.

Ans) Division is an operation that takes two numbers. Sometimes we call the first number the dividend and the second the divisor. When the same problem or expression is written as a fraction we call the first the numerator, the second, the denominator.

Numerator/Denominator = answer

Division is also the inverse operation of multiplication. Thus, the answer to our division problem when multiplied by the denominator must equal the original numerator.

When the denominator is a number greater than one, the answer is always smaller than the numerator.

For example if I have 12 eggs and I divide them up among four people I am able to give them three eggs each. 12 is the Numerator, 4 is the Denominator and 3 is the answer.

12/4 = 3 or 12 eggs divided by 4 people = 3 eggs per person = 3 eggs/person.

Checking our answer using multiplication we see that our answer, 3, when multiplied by the denominator, 4 yields 12, the original numerator. Since 3*4=12, Then 12/4=3

If 2*5=10, then 10/5=2

If 7*8=56 then 56/8=7

And if A*B=C, then C/B=A

We can look at three cases based on the size of the denominator compared to 1.

Case 1, denominator greater than 1

Case 2, denominator equal to 1

Case 3, denominator less than 1.

Looking at Case 1, denominator greater than 1

This, while extremely common is the only case where the answer is smaller than the numerator.

12/3=4

12/4=3

12/6=2

12/2=6

Looking at case 2, denominator equal to 1

In every case, the answer is equal in size to the numerator.

12/1=1

100/1=1

6/1=6

Case 3, denominator less than 1.

This is the only case where the answer is greater than the numerator. This is the reason when the quora question assumes something false. Examples:

12/0.5=24

12/0.25 = 48

12/0.1=120

12/0.01=1200

In all these cases, the denominator is less than 1. The smaller you make the denominator, the larger the answer!

Practically speaking, lets say you have 12 apples. If you want to divide the apples into halves (1/2 = 0.5) as in our first example you can give a half apple to each of 24 people.

If you want to feed 48, you can give each only 1/4=0.25 of an apple as in our 2nd example. Checking we see that 48 * 0.25 = 48 * 1/4 = 12

This is when when you divide by numbers less than 1, you end up with a number greater than the numerator. Each piece is the size of the denominator and therefore when the size is less than 1 you will need more of them to equal the original numerator.

Q7) b) What is an equation? Does all the equation involve a variable. Give an example of an equation with a variable in it and which does not have a variable in it.

Ans) In mathematics, an equation is a statement that asserts the equality of two expressions, which are connected by the equals sign "=" The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any equality is an equation.

Solving an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variable. A conditional equation is only true for particular values of the variables.

Q7) b) ii) Here is a think of a number game: ‘Think of a number, then double it, add six to the sum, divide the sum by half and then subtract 3 from it the number’. Did you receive the same number you had started with? Why? Justify.

Ans) It happens because this mathematical puzzle is independent of the number you chose. It is only dependent on the amount you added (six in this case). Final result is half of the amount you added.

So, now I am applying the conditions put in the question to prove my statement.

Let the number to be “x”.

Now, I’m doubling it and adding six so it becomes 2x +6

Now, I’m dividing it by half so it becomes x +3

Now, I’m subtracting the number from which I started; so x + 3 - x = 3

See, we got the answer 3 as all the operations are designed in a way that the end result is independent of the number we chose.

Q8) Which of the following statements are true or false?

i) Pre-operational thinking is the characteristic of a two year old child - False

ii) Each mathematical problem have a unique solution. - False

iii) ‘Today is a bright day’ is an unambiguous statement. – True

iv) The sum of the interior angles of a Pentagon is 450o. – False (540)

v) If the capacity of a 3D-objects increases, then the volume also increases. - True