28 Sept...last session

This is the last session of Elementary Mathematics module.  I have enjoyed 1st session to the last session of this module.  Dr.Yeap has introduced alot of Math activities which help us to understand current primary school's Math concepts.  I have indeed learned alot of Math methods which I have never been introduced to during my school days.

Do you know area of triangle? 

Area of traingle -> 1/2 x base x height

But Dr. Yeap has taught other method which enlightened us.....

 

We were taught to think of other methods and Dr. Yeap showed us to cut part of triangle to place it on top portion of triangle to form a rectangle.  We will then be able to find area by using length x breadth. 

 

We were then been asked to set Math questions during our quiz.  It was quite tough yet fun as we need to use proper English sentence structure to make sure the other party able to understand the sentences and solve the problem.

 

Overall, Math is a subject which you can't memorize all the methods but to understand the concept.  It depends alot on your thinking skills using the right concept.......

 

27 sept...Tangrams and BODMAS

Today, my group mates and I visited Singapore Art Museum for our group assignment.  It was a fruitful trip as I saw quite a number of abstract Art pieces at the galleries.  Hmmmm....i was wondering, how did these artists come up with such ideas and transfer them into their artworks.

After returning to our class, Dr. Yeap told us to use tangrams to form squares.  So what is tangrams?
This is what I have searched.....

The tangram is among the most popular of all dissection puzzles that exist today. A tangram is an ancient, unique, Chinese puzzle that consists of seven (geometric) pieces: one square, five triangles and one parallelogram. When all pieces are put together, they form one big square, when they are sperated, they form what is called a tan. Of the five triangles there are two large, two small and one medium in size. "The large triangle is twice the area of the medium triangle. The medium triangle, the square, and the parallelogram are each twice the area of the small triangle. Each angle of the square measures 90 degrees. Each triangle contains a 90 degree and two 45 degree angles, which makes them isosceles right triangles. The parallelogram contains 45 degree and 135 degree angles" (Bohning, G., et al., 1997, p. 3).

The relationship among the pieces enables them to fit together to form many figures and arrangements. However, the tangram is more than a seven piece square. When it comes to tangrams, the challenge is to arrange the pieces to form additional shapes. The seven pieces can be arranged to make anything form a rabbit, to the alphabet, to a person. "The tangram is the opposite of a jigsaw puzzle. Instead of fitting the pieces together in only one way, the seven tangram pieces can be arranged to make a great number of different figures" (Bohning, G., et al., 1997, p. 4).

 My groupmates and I have formed different sizes of squares using tangrams:

After the tangram activities, we were introduced to "BODMAS"...Have you heard of it?

If you've not heard about it, please read the text below:

Order of Operations - BODMAS

Operations

"Operations" mean things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation.

But, when you see something like...

7 + (6 × 5² + 3)

... what part should you calculate first?

Start at the left and go to the right?
Or go from right to left?

Calculate them in the wrong order, and you will get a wrong answer !

So, long ago people agreed to follow rules when doing calculations, and they are:

Order of Operations

Do things in Brackets First. Example:

		6 × (5 + 3)	=	6 × 8	=	48
		6 × (5 + 3)	=	30 + 3	=	33	(wrong)

Exponents (Powers, Roots) before Multiply, Divide, Add or Subtract. Example:

		5 × 22	=	5 × 4	=	20
		5 × 22	=	102	=	100	(wrong)

Multiply or Divide before you Add or Subtract. Example:

		2 + 5 × 3	=	2 + 15	=	17
		2 + 5 × 3	=	7 × 3	=	21	(wrong)

Otherwise just go left to right. Example:

		30 ÷ 5 × 3	=	6 × 3	=	18
		30 ÷ 5 × 3	=	30 ÷ 15	=	2	(wrong)

How Do I Remember It All ... ? BODMAS !

B	Brackets first
O	Orders (ie Powers and Square Roots, etc.)
DM	Division and Multiplication (left-to-right)
AS	Addition and Subtraction (left-to-right)

Divide and Multiply rank equally (and go left to right).

Add and Subtract rank equally (and go left to right)

After you have done "B" and "O", just go from left to right doing any "D" or "M" as you find them. Then go from left to right doing any "A" or "S" as you find them.

Here are some BODMAS questions for you to answer, enjoy......

Question 1

 

What is the value of 3 + 6 ÷ 3 × 2 ?

A    7       B    6       C    4     D  1.5

Question 2

What is the value of 5 × 3 - 12 ÷ 4 + 8

A   3        B    4       C   14      D   20

 

Question 3

 

What is the value of 5 × 4 - 2 × 3 + 16 ÷ 4

A   10      B  11½    C   18      D   34

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

26 Sept...Fraction, Multiplication and Geometry

Teaching Mathematics is all about formulas, steps, four operations knowledge...but today, I enjoyed the topic on fraction.  Dr. Yeap played a short nursery music video "Three Little Pigs" which I enjoyed alot.  After enjoying the sond, Dr. Yeap gave us a fraction problem to solve:

3 little pigs share 4 pizzas equally....how much should each little pig get?

 



 

 

 

These are my methods of solving this question...do you have other methods?

Polygon

Do you know what is a polygon?

A polygon is a plane shape with straight sides.

Is it a Polygon?

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Polygon (straight sides)	Not a Polygon (has a curve)	Not a Polygon (open, not closed)

Polygon comes from Greek. Poly- means "many" and -gon means "angle".

I have learnt the way of finding area of a polygon using the formula....it is amazing indeed!

 

Fraction

A fraction represents a part of a whole or, more generally, any number of equal parts. The numerator represents a number of equal parts, and the denominator, which cannot be zero, indicates how many of those parts make up a unit or a whole. 

I have learnt from Dr. Yeap that when we say a fraction term e.g. 1/4, we cannot say 1 upon 4 or 1 out of 4, we have to say it - one fourth or one quarter.  Hmm...I wonder how these terms derived in our daily lives?

Dr. Yeap then challenged us on a fraction problem - sharing a piece of cake equally among 4 persons using the paper he has provided for us.  My classmates and I folded the paper into three different types of fraction(see figures of rectangles) easily.

Dr. Yeap continued to challenge us by asking us is it possible to divide them into other shapes equally and this is how we derive by having Triangles(see figures of triangles).  He further asked are there anymore shapes we can derive.  Some of our classmates have come up with some shapes and Dr. Yeap asked if these shapes are of equal portion?  Initially I thought it was not as the shapes are uneven from a glance.  Later, I tried doing it on the piece of paper, I realised they are of equal portions(paper is divided into 16 parts and each portion consist of 4 parts).

 

 

 

We do not visualise to determine the equal portion but need to work it out on concrete materials.  Math is really a fun subject to explore!

 

Here are some fraction activities you may wish to try:

 

http://www.sheppardsoftware.com/mathgames/fractions/Balloons_fractions1.htm
http://www.glencoe.com/sec/math/studytools/cgi-bin/msgQuiz.php4?isbn=1-57039-850-X&chapter=3&lesson=1
http://www.interactivestuff.org/sums4fun/efrac1.html

Uses of Whole Number

What is a whole number?

In google term, it is known as positive interger(1,2,3.....) and not a partial number, fraction or percentage.

 

 

But today in 2nd day of Dr. Yeap's lesson, I have learnt different classification of whole numbers.

 

1) Cardinal Number,

 

2) Nominal Number,

 

3) Ordinal Number and

 

4) Measurement Number.

 

Besides that, the interesting part of the lesson is the 10 frames using "Jack n The Beanstalk" musical story.  It is interesting to understand that there are many ways to solve the problems with three numbers involved.  This will enhance children's creative thinking in deriving various solution methods and not only focus on one method which I was being taught during my Primary school years.

So how many ways are you able to do this addition?  Try it....

 

 

 

 



Day 1 - Own Experience in solving problems

Today is the first lesson of Elementary mathematics.  Four problems in one lesson : one adjective to describe - FUN!!!

 From Rote Counting to Card Trick to Textbook Problem and lastly Tangram Problem, I had fun sloving these problems.  I particularly like the Tangram activity as it really engage me into thinking mode to shift the shapes to form different sizes of rectangles.  There is always a sense of achievement when my peers and I managed to form rectangles using different sizes.  I have realised in order to solve problems, we need to explore, working in group, using concrete materials.

 

 

I have also learnt that there is even a story about Tangram and I google it to learn more about it.  I'll share definitely share this story with my centre's children.

 



Chapter 1 & 2

A note to Parent...

Many a times, when children have problem or struggling solving Mathematics questions, parents will comment," I remembered my Math subject was the worst among all subjects, that is why my children follow my learning style. I think it is very important for parents to engage in their children's education from as early as Pre-K to their college level as in the present society, it focus on education, career and life readiness.

To kickstart with parent engagement, we will introduce one of the most important features of Principles and Standards for School Mathematics.  They are:

1) The Equity Principle - all students must have the opportunity and adequate support to learn Mathematics "regardless of personal characteristics, background, or physical challenges"
2) The Curriculum Principle - Students must be helped to see that Mathematics is an integrated whole, not a collection of isolated bits and pieces.
3) The Teaching Principle - Effective Mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well(NCTM,2000,p.16)
4) The Learning Principle - Mathematics today requires not only computational skills but also the ability to think and reason mathematically to solve new problems and learn new ideas that students will face in future.
5) The Assessment Principle - Assessment should be a major factor in making instructional decision.  Teachers can better make the daily decisions that support student learning by continuously gathering data on students' undertsanding of the Mathe concept.
6) The Technology Principle - Calculators, computers and other merging technologies are essential tools for doing and learning Mathematics.

With these six principles, teachers will create an environment where students take risks and share and defend Mathematical ideas, they will be actively engaged in problem solving through teachers' guidance.  First is the language of doing mathematics: children in traditional Mathematics classes often describe Mathematics as imitating what the teacher shows them.  These are low-level thinking activities and do not adequately prepare students for the real act of doing Mathematics.  In contrast, we need to engage students in doing Mathematics with the following- compare, explain, explore, predict, investigate, verify and solve.  These verbs lead to higher-level thinking and encompass 'making sense' and 'figuring out'.

Next is the classroom environment for doing mathematics: classrooms where students are making sense of Mathematics do not happen by accident - they happen because the teacher establishes practices and expectations that encourage risk taking, reasoning, sharing.

Parents... start learning Mathematics with your children now, it is definitely a fun and interesting subject!!!