Day 6: It's a WRAP!

The last day of lesson was no different from other sessions. We were exposed to more interesting problems that never failed to set us thinking.

Dr Yeap started out with the basics like doing division. Guess what? I never knew the method that i have used all this while were wrong! yes, again Dr Yeap has pointed out incorrect practices that were happening around us that never came across in our mind. Our mentality was set to "If the method works, use it" even though we did not know the basis of it all.

The incorrect, normal practices that even I was taught of this method

How it should be done

After that we were given a piece of paper. The instructions given were to use as much of the paper given to make a 3-dimensional geometry. All i could think of was a rectangular cuboid. however I witnessed some interesting shapes from my peers. Some came up with a pyramid, a sphere,etc.

Here's my rectangular cuboid

We summed up the lesson by playing another card game. This time round the game exercise alot on our mental calculation skills. This game is called, 'Salute', where there will be 2 roles, one is the one who would count the sum of all the cards and the rest would have to guess the number on their individual card. The one that could shout out their answer first is the winner. We had lots of fun playing this game. As a matter of fact, i had fun throughout the 6 days course. Math is actually fun if you could appreciate and understand the concept behind it. Also, Dr Yeap has successfully influence at least half the class to not hate math anymore.Well, i'm one of them. The activities that he had planned for us were eye-openers, revision for our rusty mind and definitely a different approach to what was drilled in our mind when we were learning math years ago. 

Day 5: Trip to museum, Geometry, Tangrams

Visit to the different museums

We were given an hour to explore the art pieces in the different museums near our campus. First, we have decided to visit the Singapore Art Museum (SAM) however we did not find anything that we could relate much to Math. So we decided to visit the Peranakan Museum after much thought. We found something that we like that we could relate to counting in sets, patterning and addition! It is amazing at how we could craft an art piece into a math problem. So here it goes!

SingaporeArt Museum

Peranakan Museum 

Our chosen artefact

Back in school

We explored once again with tangrams. This time round on the different ways to make a square.

 Apparently, there are ALOT of ways to form a square! and here is our findings!

Day 4: Multiplication, Addition, Subtraction, Fractions, Area, Length, Geometry

Learning multiplication is not about memorizing the time table.I remember when I was in primary school, i was encouraged to memorize the time table. It was the most dreadful thing ever. The initial weeks, my teacher would paste a tiny piece of paper reflecting the time table 3 to 9 on each table so that we could refer to it and in hope that someday it will glue to our dear brains as well.

children need to conceptualize what multiplication is about by introducing them using the CPA approach

multiplication of 3
Concrete: show real objects of same noun. Get children to group the bottles in 3s.

Pictorials: use pictures and let the children explore grouping the pictures in 3. One way is by circling them.

Abstract: Getting children understand that 

3                + 3                   + 3

or

3 boxes of 3

or

3 x 2 = 6

Doubling Strategy

2 x 7 = 14

                            +7

3 x 7 = 21

                           +7

4 x 7 = 28

                          +7

5 x 7 =35

                         +7

6 x 7 = 42

Notice that 4 x 7 is the same as double of 2 rows

6 x 7 = 42 as it is double of 3 x 7 

So, with the doubling method in mind, we could say that,

 7 x 7= (4 x 7) + (3 x 7)

7 x 7= 28 + 21

7 x 7= 49

For 9 x 7 for instance,

we can take 9 x 10, which is easier to see and then just subtract 7 from the answer 90.

so with that,

9 x 7 = 63

                                                      

Day 3:Quiz Day

Ordinal

This problem is so common even during my time (not so long ago by the way), but did i noticed the error behind this ordinal question? The usual question that will be asked is " Who is the first in the race?" Can you spot what was wrong with that statement? Well, I thought that question was perfectly fine until Professor said otherwise. He set us thinking just by questioning us back, " How do you know who is the first when the race has not ended? Unless, the question is rephrased as "Who is the first from the finishing line?" Something to ponder..

Question on Patterns- Find the 2013th letter in your name

The different patterning types

What is enrichment and acceleration?
Enrichment: Practising more in depth within the same topic
Acceleration: A different topic that will be covered in a different lesson

like for example,

ABC-ABC-ABC patterning is the acceleration of AB-AB-AB patterning

Fraction

In fraction,avoid phrases like, "three out of four" unless we are talking about ratios or probability. Use "three fourths" instead.

Dividing Chocolate bar into 4 equal pieces

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Day 2: Whole Numbers - Rational Counting

Problem 5: How many going to St. Ives?

My take away for this problem is that this video is not rational counting as we cannot count things that have different nouns. For example,

UNLESS

 we count count it with a common name like 'fruits'

Rational Counting

Subitize

Now, can you subitize all the pictures in this clip?

Why some children cannot count?

1. Unable to classify

2. unable to rote count

3. inability to understand counting in one-to-one correspondence

4. does not appreciate that the last number uttered represents the size of set.

5. no conceptualize idea in rational counting

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Day 1: Introduction to the Module!

Guess the 99th Letter in your Name!

It was an interesting introduction to Dr Yeap's Math module. He introduced himself with a problem that involved his name! How interesting! We were asked to guess the 99th letter in his name using a certain counting pattern and came up with different strategies used to derive the answer. I could not think of any other easier way to solve the problem except for finding the answer using rote counting method.Yes, counting it from 1-99!I was thankful that he did not ask us to guess the letter position that goes beyond 100s. However, he mentioned that even if it exceeded way beyond 100s, it could be easily solved if we could understand the pattern. At this point, I was a little motivated in finding out how to do it myself.
So, after much discussion among peers in class, here are the strategies that they came up with.
1. Look out numbers by 10s
2. Look at consistent repetitive numbers that were '1' or '9'
3.From either method 1 or 2, count up or down till you have reached the 99th letter

I've decided to try it out using my own name.
I have realized that there were no consistent repeated numbers found in any rows.
So, I looked for the number patterns in a row. I have realized that  each row ( only for 2nd -7th row) has an unique alternating differences in between numbers. Like in 'A'(2nd row) the difference from 2 to 14 is 12, 14 to 16 is 2, then it repeated itself by adding 12 to the next number followed by adding 2 for the subsequent number.I can repeat this pattern until I have reached the nearest number to my 99th letter.

Another way is to look at the 1st and 8th (last) row.
The difference between numbers are 14.
As per picture below, i have counted using the 8th row till I have reached the closest number to my 99th letter which is 92. Then I counted forward till 99. Thus, the 99th letter in my name would be, 'M'!

Magic Card Tricks: Spell out the number and the number shall appear
The next problem was a card trick. I have seen this trick a few times before and I remembered a friend sharing how the trick was conducted. He taught me a story similar to the video below and I was not that impressed as I still do not understand how the story was derived and what was the actual 'trick' behind it before 'somebody' came up with stories to make the trick easier to remember.
I was motivated by the idea of solving the trick on my own. It took me quite some time to actually solve it. With the help of friends I somehow manage to grasp a little on the pattern that i have to look out for. I could say that till now i'm still only 90% into perfecting this trick.

Entry 1:How does Math differs now and then?

Learning Math in the 21st century highlights the importance of understanding the different processes of thinking skills like problem solving, and conceptual understanding in solving a math problem.Children will realize after they have gained understanding of the concept, multiple approaches may be derived from even the simplest sum. For instance, we were taught borrowing techniques in subtraction. Back then, did we really understood that in fact it was due to the place value and not simply because 'there is nothing left to borrow from the next number'? Mathematics is everywhere and we need it in our daily lives as well. Let's look at how these processes could also affect children's day to day.
According to Principles and Standards for School Mathematics that was released by National Council of Teachers of Mathematics (NCTM), there are 5 process standards that refers to " mathematical processes through which children should acquire and use mathematical knowledge." (NCTM, 2000)

1. Problem Solving Standard

Problem solving standard is the process of applying the various possibilities in solving a problem. For instance, a child may ask, how can I share 7 cookies among 3 children? They will have to brainstorm ways to distribute it evenly among each other.





2. Reasoning and Proof Standard.
It is to support and making sense to answers provided. Children might portray this standard best when collecting and collating data using charts like, graphs through surveys.




3. Communication Standard.
Communication standard is the process of  being able to communicate ideas by talking and writing about it. Older children are able to document and record their findings in skills like estimation table and reading of a chart. A cooking activity can be a communication standard where children are to write and follow a set of measuring instructions.



4. Connection Standard.
Children may find relations in every concept to another. Like for example, a line graph can be represented by numbers or a pie chart in which it can also be converted to fractions!



5. Representation Standard
The use of symbolism to express mathematical ideas and relationship. As mentioned, children use different types of charts to document their findings.Another way would be using manipulative items like connecting blocks to represent non-standard measurement, or as a counting tool.