Day 6

Is there an universal symbol for division?
The symbol that we knew since young is

But Dr Yeap told us that half of the people in the world used this symbol to represent division and the other half of the world used this   :    as the symbol for division.
This is an insight for me as I never knew this before.

Today we are going to find the area of a triangle.

I used three different methods to find out the area of this triangle and got the same answer for these three methods.

 

You may try the links to know more........

http://www.mathsisfun.com/algebra/trig-area-triangle-without-right-angle.html

http://www.wikihow.com/Calculate-the-Area-of-a-Triangle

http://www.mathplayground.com/howto_area_triangle.html

Day 5

Do you know how to make squares using tangrams?
What are the different ways that you can make a square?
These are some of the "squares" that I have made during class.

 

I used 4 pieces of tangrams to make a square.

 

Dr Yeap challenged us to make a bigger square using the seven pieces of tangrams that he has given us. This is what I came out with..........

 

 

 



Do you have any other ways to make a square using the seven pieces of tangrams?

 

 

Do you know how many types of triangles are there?

 

 

 

 

The sum of angles in a right angle triangle is 180 degree and this is how I prove it.......

 

 

I folded in the two sides to form a right angle and therefore, the sum of the triangle is 180 degree.

 

What about other triangles that are not a right-angle triangle?

 

I tried another method...........

 

 

 

Do you have any other ways to find out the sum of angles in a triangle?

 

There are some of the websites that you can gain more insights:

http://www.freemathhelp.com/feliz-angles-triangle.html

http://www.mathsisfun.com/proof180deg.html

http://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof---sum-of-measures-of-angles-in-a-triangle-are-180

http://www.mathsteacher.com.au/year7/ch09_polygons/02_anglesum/sum.htm

 

Day 4 - Measurement and Geometry

Have you heard of the story of "Three Little Pigs"?
What do you think when 4 pizzas are shared among the 3 of them and how many pizzas will each of them get?

I took my pencil and drew 4 long blocks, symbolizing 4 pizzas. I divide one of the block into 3 equal parts and got the answer as 1 whole and 1 thirds.

After discussion with the other classmates, there was another method of solving this question, which is breaking the 4 wholes into 12 thirds and further divide it by 3. The answer will be the same as what I got earlier - 4 thirds which is the same as 1 whole and 1 thirds.

 

 

I find it easier to grasp the concept with visual aids which coincide with CPA approach. The children will get to revisit this concept every year as they learn another new layer of knowledge on top of what they have already learnt which is what the primary schools in Singapore is advocating - Spiral Curriculum. 

Have you ever tried making shapes using a geoboard?

A geo-board is a math manipulative used to support early geometric, measurement and numeracy concepts. A geo-board is a square board with pegs that children attach rubber bands to.

Children enjoyed "playing" with it and through exploring, they gain the necessary concepts.

 

These are some of the questions that can be used when children are exploring with the geo-boards.

What is the largest or smallest square you can make on your geo-board?

Show a square with 5 square units.

Show a square with 10 square units.

What is the largest or smallest triangle you can make on your geo-board?
 

 

 

You would like to try the links to download the geo-board app and try it out but beware as it is super additive!!!

https://itunes.apple.com/en/app/geoboard-by-math-learning/id519896952?mt=8

http://www.mathlearningcenter.org/web-apps/geoboard/

You may also use dot paper to draw out the different shapes.

Dr Yeap drew a square on the dot paper and then a polygon which has one dot in it. He challenged us to draw other shapes that also has one dot in the polygon. This is some of the polygons that I drew!

 

 

Dr Yeap further challenged us to find out how many squares are there is the polygons that we drew.

 

 

So can you find out how many squares are there is the polygons that I drew?
There is an easy way to find out......... (well........ it's Georg Alexander Pick who found out first!)
Just count the number of dots that the polygon is made up with and divide the number of dots by 2, and you will get the answer.....


Example:

Number of dots: 12

12 divide by 2 = 6

Therefore, there are 6 square in this polygon.

 

 

Isn't it easy??? After all, mathematics is about having the ability to use skills like patterning to figure out things!

 

A good quote to end the day.......

 

Day 3 - Fractions

A fraction represents a part of a whole, or any number of equal parts. Dr Yeap challenged the class to share a piece of chocolate/cake/pizza (up to your imagination of what you wanted the piece of paper to be) equally among 4 persons.

So this is my imagination of the piece of paper........



I tried different ways of dividing the "piece of chocolate" among 4 persons and this is what I derived to.......

 

 

Some of my classmates suggested other methods of dividing into 4 equal parts that will result in  mixed shape solution, like these....................

 

These diagrams are very creative as the equal parts does not be of the same shape!

 

Dr Yeap further challenged us to share 3 fourths equally between 2 persons.

After pondering for quite a while, I came up with 2 diagrams with 2 different methods of getting the answer. However, I find it easier to understand fractions with visual aids. (Haha! Guess that we can't run away from CPA approach as fractions are better understood when seen)

 

 

 

 

There are some links that are useful to enhance children's knowledge on fractions and have fun!

 

http://sg.ixl.com/promo?gclid=CITf4dyE57kCFfFg4godYmMAGg&partner=google&redirect=%2Fmath%2Ffractions&campaign=1230&adGroup=fractions

 

http://www.sheppardsoftware.com/mathgames/fractions/fracTut1.htm

 

http://www.coolmath4kids.com/fractions/

Day 2 - Whole Numbers

Today is the second day of class and the topic that I've learnt is on "Whole Numbers".

I find that the usage of Ten-Frames is very helpful in developing number sense in children. Research has shown that both children and adults have the innate ability to subitize - to instantaneously recognise the number of objects in a small group. Ten-Frames can help to organise numbers in groups of 5 and 10 to match the base ten-number system.

Once the children the system of Ten-Frames, they are ready to proceed to other mathematical concepts like addition. You may like to try this link to play games using the Ten-Frames. 
http://illuminations.nctm.org/ActivityDetail.aspx?ID=75

Day 1

Today is the first lesson of elementary maths. I was actually looking forward to the lesson, hoping to gain more knowledge of teaching mathematics to young children.

I enjoyed the problems that Dr Yeap posted and began to reflect on how I looked at maths problems. I tends to look for a pattern between the numbers and try to solve the problem by trial and error.

I liked the card trick problem as I had the chance to explore with concrete materials and realised that basic mathematics skills can be used to engaged high-level thinking. Maths is simply magically!

The "shredder" problem actually got me stuck for a while as I can't visualise that both shredder work at the same time. From this exercise, I reflected that both children and adults need concrete materials to explore and play with.

There are also many strategies that can be used to solve a problem, just like the Tangram. For instance, there are several ways of forming a rectangle using different shapes. From this activity, it gave me an opportunity to explore and play with the materials and the discussion with my classmates brought a different angle to the way I think when putting the pieces together to form a rectangle.



 In short, learning mathematics is fun and I must really say that I had a lot of fun in class today!

Dear Parents,

Welcome to the first issue of e-newsletter on Elementary Mathematics.

First of all………

1.       Do you have a fear for mathematics when you were young?

2.       Do you hate rote learning and memorizing the multiplication table?

3.       Do you know how to explain mathematic concepts to your young children?

Do not panic. You can gain more insights on the guiding principles on how the teachers will be teaching mathematics to young children.

There are six fundamental principles to high-quality mathematic education which are Equity, Curriculum, Teaching, Learning, Assessment and Technology.

Through these six principles, there is a common set of five content standards, which are Number and Operations, Algebra, Geometry, Measurement and Data Analysis and Probability. The teachers will teach mathematics through the guiding principles and standards.

The children will learn mathematics through these five process standards:

1.       Problem solving

2.       Reasoning and Proof

3.       Communication

4.       Connection

5.       Representation

 

Can you see a pattern and wonder the relationship between them?

                                                      6 + 6

                                                      5 + 7

                                                      3 + 9                   

                                                

The children are encouraged to actively engage in problem solving problems by exploring, figuring that there are many strategies in finding an answer, observing the patterns and order, even though the process takes time for the children and teacher.

The teachers will ensure that maths lesson is a fun and enjoyable session by providing hands-on experiences. Tools and manipulatives like unifix cubes, counters and spinners will be provided to illustrate and discover mathematic concepts. The manipulatives can be a testing ground for young children to better grasp a mathematic concept as “seeing is believing”.

So do not fear mathematics and start to embrace it with confidence and fun!!!

 

 

www.i-teach-k.blogspot.com