Saturday, September 28, 2013

Day 6 - 28 Sept 2013 Multiplication

I loved the game "Salute" very much as it was both interesting and at the same time, testing your skills in Multiplication.

Game Instruction:
- 3 players will be involved in this activity.
- 2 person will be the players where they have to hold the number card on their forehead, without looking at it.
- The number card will face the player opposite her and the middle person.
- The middle person will multiply the two numbers on the cards and say out the product (answer).

Example: In this picture, Student Green holds a number card 3 and Student Red holds the number card 8.

The middle person, Student Black will say the product of 3 and 8, which is 24.

As soon as she speaks, the two players who are holding the card have to guess what is their own card by looking at the opposite player and listening to the product.

This activity tests and allows the children to be familiar with their the multiplication and division. This game brings thrill to the players and hence lower the stress of Rote - memorizing.

Start with smaller numbers or bigger, depending on the level on the three players.

My main take away for this whole EDU330 Elementary Mathematics is the CPA Approach.
Concrete - Providing concrete materials for learning.
Pictorial - Use pictorial and visual aids to help children to understand.
Abstract - When the child is ready for the next level, we can go to the next level; having abstract problem to stimulate their critical thinking skills

Thank you Dr Yeap for Stimulating my interest for maths and engaging us in all these meaningful activities!

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Friday, September 27, 2013

Day 5 - 27 Sept 2013 Museum Visit & Measurement

My group mates and I went to the Singapore Art Museum (SAM) to look for art pieces for our group work. There are 4 of us. We have enjoyed the trip to the museum as some of the art pieces were breath taking while some are too abstract and we do not know how to comprehend it.

There were a few art pieces which were very interesting. We shared our views on the Art pieces and was rewarded by the Museum volunteers for sharing.

Finally, we short-listed two Art piece which we feel it's link.

Initially, One of my group mate and myself is quite keen in choosing this as our Group Art piece to work with as we are able to relate to it more. We thought we could do sorting, grouping, counting and matching with this.

However, my another 2 group mates were able to relate to this picture more although I felt that some of the pictures inside this Art piece might
not be necessary suitable for children. But then, we still 
give this Art Piece a try after hearing what they plan to do with it.

Next, after we came back from the museum, we started with our series of problems again.

Problem 19
Question: How do we know that a triangle has 3 angles that makes up to 180 degree?

We tried various ways of folding to prove that the triangle has equal parts which can prove that the 3 angles are of equal degree. After which, we put the 3 angles in one line and they form a beautiful 180 degree in a straight line. 

The video below demonstrates how to do it and children can develop more understanding from the video as well. 

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Thursday, September 26, 2013

Day 4 - 26 Sept 2013 Measurement & Geometry

Problem 17
Draw polygons on Geoboard papers to find out how many times is it as large as the square. Rule of the game was, there must be at least 1 dot in the middle of the shape.

Do you think 12 is the answer?

Hints: 2 similar size Triangle can form a square! 

See how all of us were engaged in trying to find the answer.

We Never give up!

Finally after trying for countless times, Dr Yeap told us that actually Georg Alexander Pick came up with the theory that only one method / formula is applicable. And that is the formula -> A = P/2 +i - 1

So 12 is the correct answer! Yeah!

You can show your children the videos below to introduce them to Geometry and Geoboards.


Interesting Facts I have learnt today 
It is not convention to use words like "and" to separate numbers. Example, One hundred and one , it is accurately said as One hundred one. However, we are accustomed to our colonial language so we said as one hundred and one. 
Zoden Dienes's theory on "Play, Structured Learning and Practice". Practice do not always becomes perfect. If we practice everyday the wrong thing, eventually we are still wrong.

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Wednesday, September 25, 2013

Day 3 - 25 Sept 2013 Place Value & Fractions

The Grinch from

Problem 9: 
Using number 0 to 9, form the greatest addition sum and the smallest sum by not repeating the numbers. 

My group and I used the trial and error method to get both the BIGGEST and smallest number we can form, after adding up.

It was interesting exploring the possibilities of forming the sum. We had fun while trying out.                              


Trial & Error Method 

Dr Yeap shared with us that if the children are ready to count by one noun, they will be able to           differentiate blocks of 10s & 1 of 10.

Dr Yeap also shared that it is unwise to get children to use lines to divide the sum. The children should be able to identify which are ones and tens and add accordingly rather to recognize it as numbers without any association.

According to Dr Yeap, the picture on the left is not an appropriate way to teach younger age children to add as the children 
should know that it represent a set. It is two ten 5 ones (twenty five) plus one tens 2 
ones (twelve), hence arriving at the answers of 3 tens 7 ones (37).

It is also better if the sum is written as 25 + 12 = rather than the vertical way of writing them as it is a Procedural Knowledge and some children cannot recall to solve the answer in that form.  

The children can also use Base Ten Blocks in helping them to
understand tens and ones and in addition and subtraction.

The following video, I found it interesting for the children to listen and make connections to the numbers value and the base ten block. 
Have fun Viewing!

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Problem 12 Share 3/4 cake equally between 2 person. How much does each gets? The normal way of solving this question for us should be:- 3/4 divide by 2  3/4 x 1/2 = 3/8 3/8 slices of cakes will be shared among 2 person.
However, Dr Yeap did not give us an answer. His explanation was that he did not ask us to change the denominator to do the sum. 
In this case, the above sum could not be solve. 
The point he wants to bring across is: Denominator which is different cannot be put together to discuss and solve. Example was, an apple and an orange. Can you add the two up and says I have 2 appleorange? No we can't.
Points to note when dealing with Fractions:
# Addition & Subtraction only takes place when the noun (denominator)is the same.
Fraction's language alert! 3/4 is read as 3 fourths. Not 3 over 4 or 3 upon 4! We only use 3 in 4 chance or 1 out of 4 chance if we are referring to properties. 
****************************************************************************************** New words I have learnt today 
Acceleration: A new skill concept, a level higher from the current concept.
Enrichment: Remaining at the same concept but scaffold in a different way of learning.
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Tuesday, September 24, 2013

DAY 2 - 24 Sept 2013 Cardinal Numbers

Jack and the Beanstalk from AnimateIt.netBeans, Beans, Beans...

Problem 6: Counting Down Beans

Basically, this game is connected to subtraction as we count backwards. As we take away the bean from the pile, we do mental calculation and call out the existing amount of bean that is left on the table. It is a very interesting game as this is the "play stage" theory by Dienes. The children will be able to play the game without consciously knowing that they are learning about subtraction and doing counting back.

Game Instructions: Taking a set amount of beans of about 20 in our case, we are only allowed to removed 1 or 2 beans per turn, between the 2 players. The last player who takes the last bean will win. 

Throughout the game, I did mental calculation and tried to control the possibility of winning by ensuring that I have either 5 or 3 beans left so that it will be to my advantage. That is when I realized from Dr Yeap that there are good and bad numbers that can control the winning situation. 
I realized that if I take a maximum of 3 beans, the bad number would be in multiples of 4 and if we take maximum of 4 beans, then the bad numbers would be in multiples of 5. The bad numbers would be +1 of the actual maximum no. of bean we are taking. 

My group tried playing with all the beans that were given, around 66 beans in all and we removed to a maximum of 5 beans among 3 players. At the beginning, I just try to clear as many bean as possible until it reaches around 12, I became more cautious and strategized the number of beans would take. 

The red bean game reminds me of the game 
which I played when I was young. We draw 
lines into a pyramid and starts canceling, as 
you can see from the picture on the left. It was a fun game. And never did realized until now that I was actually learning subtraction!!

How Many were going to Saint Ives?

REALIZATION * In Day 2 lesson, I realized that things with different nouns cannot be count together. *When Children cannot count, there are 4 main concerning factors which contributes to the reason:- 1. The children's ability to classify 2. The ability to do rote-counting 3. The ability to do one-to-one correspondent counting 4. The Conceptual understanding of cardinal numbers (at times, the child might not appreciate or know that the last number that was said was to represent the size or quantity of the object.)                                New words I have learnt today 
Subitize: It's the ability to perceive a number of items without actually counting it.  Manyness: The quality of being many or a lot.
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Monday, September 23, 2013

DAY 1 - 23 Sept 2013 Counting

Mathematics Class with Dr Yeap has totally changed my impression about Maths! It was fun and interactive, even for us adults. I am like a little child, playing games after games. Brain storming for the answers was . It thrilled me further when I realized that Dr Yeap walked his talk on how to guide children with us, through implementing and role-modeling for us. We are the children in his class.

It reminds me on Dienes' Theory as I play: " Children learns Mathematical Concept through Informal Learning." And that is exactly what we were doing in the class.

From guessing where the number 99 falls on my name "MICHELLE" was an interesting activity for me and my classmates. We were all very engrossed in calculating and COUNTING all the way to 99 to make sure we got it right. Then it struck us! Hey! Look! There are Patterns that can lead us to the answer!

M   I   C   H   E   L   L   E
 1   2   3   4   5   6   7   8  
15  14  13  12  11  10  9
      16  17  18  19  20  21  22  
29 28  27  26  25  24  23   
      30  31  32  33 34  35  36
43  42  41  40  39  38  37   
Hey hey hey! Am I going to continue to count all the way?
Hahaha! Of course not!! As you can see now, there are patterns that can be found in the above diagram. Can you spot it? 
Well, follow my pink panther below to solve the problem!


Have you spotted the multiples of 14 in the number picture? 

Now I am very near to get my 99!
7 x 14 = ?

Correct, as what you have guessed, 7 x 14 = 98!!
And if 98 is in the row of 'I' then where is 99?
Yes, it is at the alphabet 'M'. the 7th row.

As I was doing this, I cannot help but to agree with Dr Yeap.
1. We should try different ways to solve a problem. 
Although counting does help in finding answers, it's not always necessary. I managed not to count all the way to 99!

2. Look for patterns behind the mass of numbers. Don't Panic. 
Very true indeed! A Lot of times, we panic when we see lots of numbers flowing towards us. We should relax and try to spot if there are any patterns that can relate to on another.

3. The articulation of our thinking helps us in contrasting and reflecting. 
When I speak my thoughts out or discuss with my peers, it helps me to understand my sums better and I can better understand what affect the answers.

Another activity that I enjoyed both was the card tricks where we are able to spell and show the correct sequence of playing cards. Click on the link to see Jenny sorting the card in sequence. So that the cards will be in order of the number and spelling.

This activity is great to interest children in learning about numbers, counting and number words.

With these activity, I am looking forward enthusiastically to the next lesson!

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Setting the right attitude for you & your child in learning Mathematics


Ever wonder how you can teach your child Mathematics?

Before teaching your child, set the right attitude for you and your child first.

1. Being Persistence 
Mathematics is about trying and investigating to find out the answers. Just like what Stigler and Hiebert (2009) had mentioned, it is important to create challenges for children to solve as it is part of learning. Celebrate their success with them when they find the answers. Do not neglect the process which they try to find out the answers too. That is part of problem solving too!

2. Positive Attitude Before guiding your child in Mathematics, you must have positive mindset towards Mathematics. Try new ways to solve challenges. Explore with your child together the possible ways of problem solving. Build up their confidence and again, celebrate small little success with them, creating a positive mindset in them.
3. Be ready to accept changes Be brave to open up to your child if they managed to solve the problem differently. Mathematics concept can be acquired in different ways. By accepting the differences the children will learn that there is no one way method to problem solve and thus opening their mindset.
4. Be reflective Always update yourself with new knowledge by upgrading yourself. To learn more yourseDlf, Is to bring benefit to you and your child. If there are workshops, u may like to attend to upgrade or refresh your learning. Share what you have learnt with your child as we'll to empower them further.

Remember, treat every errors that your child has done as an opportunity for his learning. Give him the space and time to solve the problem. Productive struggle is essential for your child to catch the "aha" moment when he can finally find the pattern in solving the problem. Scaffold your child with concrete materials to assist him in solving problems, from simple to complex. And as mentioned above, there are no one way in solving problems. Be open and encourage your child to try multiple approaches. Finally, give your child the opportunity to talk about mathematics too. Get him to verbalise and share his findings or thoughts. It will help him in his thinking and problem solving process.

With the above, let's try it out today and see the difference it makes to you as a teacher and your child as a learner. Do drop me comments to discuss further or to share your experiences! Till then, have fun with Maths!

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