iPad Apps - Singapore Math, Bar Models Grade 2

Date:  Mar 1, 2014

Time flies.  Today is first day of March of 2014.  Already.

Today going to introduce one of the app I like and I think Jay Jay not so fond of it, but he has no choice but must learn to like it.

His father say so.  Muahahahahaha.

Oh ya, I do let my kids play iPad from time to time, only before bed time.

And some times I will say “Education Games” for 15 mins, and after education games, you can play any of your game for 10 mins.

This actually works!

The kids actually will get the chance to learn more things from the iPads, before they play the games.

Kay Kay will play his “Sight Words” games.  Very awesome games.

Jay Jay will play this Singapore Math game.  Actually is not a game, it is more like an assessment app.  HaHaHa.

Anyway, the title is called “Singapore Math, Bar Models Grade 2”.  It’s free for few questions, to unlock all questions, you need to pay US$9.99.

A bit pricy, but I think it is a very well done App for kids in P2.

 

By the way, if want to know more about other math apps that is suitable for Singaporean kids, go to below link.

http://singaporemathsource.com/resources/singapore-math-ipad-apps/

If you want to know more about this “Singapore Math, Bar Models Grade 2” app, click on below link.  It is quite cool.  And you may have guess, there are Grade 3, Grade 4, and so on.  I am very sure the person who wrote this will be rich.  I got to spent some time to write apps too.

https://itunes.apple.com/us/app/singapore-math-bar-models/id461707896?mt=8

In primary 2, Jay Jay started to learn bar model diagram to solve addition and subtraction problems.

This is what they called “Word Problems” in school.

What I found is Jay spent a lot of time in “drawing” “perfection” rectangle in the word problem instead of trying to figure out what is the problem.  So, it actually “slow” them down in that sense.  As they need to use ruler to draw perfect rectangle and so on.

So, this app helps in the sense that he does not need to draw perfect rectangle as it will always become a perfect rectangle.  So, he can focus in is workings.  And understanding the question.

On Singapore Math app, you are given a problem, and you simply need to solve it using a bar model diagram.

The process involves drawing two rectangle, size it, add a text in each block, and then add a bracket and show the total, and mark down the question mark for things you need to solve.

Then, pull up the working area to write your equations and do your workings.

Then, you fill in the answer.  If you get it right the first time, it will be 3 stars.  If you get it wrong, each time, 1 star will be deducted.

Cool, isn’t it?

Here is the video of me trying to solve the word problem.  Quite fun!  Easy to learn.

And most important thing is the concept.  The more question he does, the more bar model diagram he drew, the more better he grasp the concept.

Also, running the app on iPad serve as an incentive for him.  After doing 2 questions per day, he gets to play iPad games such as Minecraft, fieldrunner, monopoly, and so on.

Check out the tutorial, it also teach them how to solve each type of the problems.

When you go to harder questions, it has the necessary tutorials too.

This is the introduction video about this Singapore Math Bar Model Grade 3 app.  Take a look and you get what I mean.

Not only you can play the game in order, they also shuffle the questions so that each time you get a group of different questions.

So, you have comparison model, you have part-whole model, and all these are according to MOE P2 syllabus.  Which is a very cool app.

Later part, there will be money and measurement question too.

Multiplication and division will reintroduce slowly too.

So, with this app, not only the child will be happy using it, by giving a little incentives after each lesson, it also encourage them to learn.

Try it!

Really Don't Know What Is He Doing... HaHa

Date:  Jan 18, 2014

Once a while, it is fun to watch what Jay Jay is doing.

He is doing his CMA homework.  Let’s check out how he come up with answers.

CMA has both Mental Arithmetics and Abacus Arithmetics. 

Seems like very easy questions.

I watched from behind how he does the abacus calculations.  

And I am totally lost.  Wahahahahahaha

But to him, he seems to know how to visualise (-8 = -10 + 2) or (-7 = -10 +3 = -10 + 5 - 2)

I was completely lost there.  But I am glad that Jay Jay knew the basic concepts.

I did not get the chance to learn Abacus when I was young.  But I do see quite impressive improvement from Jay benefited from this class.  Although it is not MOE syllabus, but it helps Jay Jay to learn that there are many ways of dong computations.  

And only last week that I learned that parents (we) need to help mark their homework as teacher will not mark it for us.  So, that is why I need to take a look at what he is doing so that I can mark his work at the same time.  For 1 whole year, I thought that Jay Jay did the homework and the teacher will correct it when he go to the class.  But I was wrong unfortunately.  Wahahahaha

But it is fun!

Abacus

Date:  Dec 4, 2013

In School, they will teach our kids to do addition and subtraction from RIGHT to LEFT.  So, they will have to learn how to do the math operations from RIGHT to LEFT.  The correct way.

I aslo sent Jay to CMA so that he can learn how to use Abacus as well as doing mental calculations in his head.  For Abacus, one will need to compute calculations from LEFT to RIGHT.

So, in order to combine and blend this skill into his day to day life properly, I let him do some Math assessment book without the Abacus.  And then, made him correct his own work by checking the answer using the Abacus.

He likes it.  As he gets to use the red pen to mark his own homework.  When there is something that is wrong?  Then, he gets to see why he got it wrong and try to get the answers correct.

Studying for Math Test

Date:  Sep 17, 2013

Hey, I have to be careful using the word "Test" or "Exam" for Primary One students.  Ha Ha Ha Ha.

P1 & P2 not suppose to have "Test" or "Exam".  They have what they so called "Holistic Assessment".

Aiya, MOE is really… really…. "Holistic Assessment" has to be tested under a "Test" or "Exam" format.  So, it is still a "Test" or "Exam" la.

After we been thru Term 2 and Term 3, although they did not say when exactly, we know the "Test" is going to be on the first or second week.

There is nothing much I can do about Chinese and English.  So, my job is to make sure Jay Jay understand the concept of Multiplications and Divisions.

The other day, I shared how I train Mr. Jay to do Multiplication by self creating a Multiplication Table.

Pls see:  http://miniliew.blogspot.sg/2013/09/kids-math-multiplications.html?utm_source=BP_recent

Also, I blogged about how a Geeky dad trained his son on Divisions Concept & Prime Numbers.

Pls see:  http://miniliew.blogspot.sg/2013/09/p1-math-divisions-geek-dad-way.html 

Let's put all these concepts into test.  My test.

HaHaHa

It is just the same as what every parents would do, buy some extra assessment book for him to do.  Then correct it and teach him the taught process. 

So, let's start from the book from the left and one by one he finished the Multiplication and Divisions chapter in a few days.

 

Initially on the first book.  It is a assessment on how they think, and what they know from the class.

Seldom you get 100% right.  Given that this is the first time, parent steps in to teach him.

Like Question #9, I have to teach him that, always use the correct operations based on information given.  If there are two piece of info given, he has to put the information in the left side of the equation, Instead of putting it anywhere.

For Example, here you know you got total of 25 balloons, and he bought three packets of 8 balloons which total to 24.  So, He must know and learned how to put 25 and 24 on the left side and make use of "Subtraction" to find answer.

Instead, he simply any how write 24+1=25 instead of 25-24=1

(Ignore Question #10, I think the question itself is in question).  My son answer correctly, because she is short of 3 pencil, and how many does see need, which is 3.  What kind of questions is this?  

So, sometimes assessment book also got lousy questions or wrong question.  Must be careful and explain to them.

He really hates this kind of question.  Because it is like writing a English journal, he said.  He sure kalang kaput when answer this kind of question, and like daddy, his English need a lot of polishing.

Sometimes you get a few of challenging questions.  But it is fun, and that is how he learned, by having fun!

OK.  Now, we come to the main topic of this blog entry.

1.  When you see questions like this where it has space between questions, that means he has to do the working and find the answers.

2.  Although he is P1, but you know that MOE promotes Model drawings.  So, you can start teaching him Model.

3.  Let him visualise the problem by drawings, and then, at the side produce the working.

4.  If you do not know what is Model, I suggest you can go learn it in some talks, or tutorial session.  I actually paid to attend a parent tuition on Model drawings.  I learned a great deal.  Those questions previously I thought need to use Algebra to solve, can all be solved by simple Model drawings and visualising the Model.

5.  In primary schools, they are going to use a lot of Model drawings to solve their problems.

For example.  This questions here.

Andrew collected 9 stamps.

Danny collected "TWICE" as many stamps as Andrew.

How many stamps did they collected all together.

So, for Andrew, you draw a rectangular of 9.  Then, on the below of the first rectangular, you draw two equal size rectangular, as Danny collected twice.  Fill in the "9".

So, you know you need to solve 3 x 9 = 27.

The other questions is ...

Edward has 2 stamps at first.

So each week, he doubles his collection.

So, 1st week, you draw two rectangular of the same size.

2nd week, you draw the same rectangular of the same size than the week before.

In this case, you add up the 2+2=4, and fill in 4 in both rectangular.

And do the same for last week.  You fill in 8's in both rectangular.

So, you know to find total stamps he has for 3rd week, he has to do 2 x 8 = 16.

I love doing his math together with him.  

I never learned Model drawing before.  Before that, I solve everything using Algebra.

But now, since I have some prior knowledge of drawing the Models, I am using it to solve the question.

And I love it because it is also a challenge for me to see how to draw the CORRECT MODEL and the child can take a look and find out what is the answer quickly.

HaHaHaHaHa.

So, for teachers/adults, I drew 5 squares.  And I know each square is $3 each.

Immediately, under the teacher squares, I drew a rectangular which equal to 5x square.  That will be my 5 students.  So, I drew 3 big rectangular, which equal to 15 students.

Each rectangular, I marked 5x$2 to represent a group of 5 students.

So, for each group of 5 students, I SHADED one square in the teacher/adult square.  Because, every 5 children get a free adult ticket.  

So, you got 3 groups of 5, then, you SHADED 3 squares.

Fill in the dollar value $3.

And now, you can solve the total admission fee needed which is total to $36.  

Jay did this wrong.  But after he saw the Model drawing, he immediately understood.

Jay Jay is very lazy.  When he did the last book on Sunday.  He did not do any workings at all and straight away write the answers.

For both chapter in this suppose to be hardest book, he score all correct.

Well, after the training from his school homework, and the previous two books, he becomes better.

And he felt very proud of completing the last book with flying colours.  HaHaHaHaHa.

Another one.  I love this sort of question as this is the typical solving Math using Model drawing question.

So, for this question.  

Because Box A has 4 more than box B.

1.  So, you draw the rectangular of A which is longer than B.

2.  Both rectangular has to draw side by side vertically.

3.  Then, you EQUATE THE PARTS.  Mean, you draw a line so that the rectangular A has equal parts same as rectangular B.

4.  Fill in "4" in the smaller rectangular there.

5.  Next clues is Box B has 6 FEWER than Box C.  So, you know Box C going to be longer than Box A and B.

6.  So, you draw a longest box there.  Then, you EQUATE THE PARTS AGAIN.

7.  You can fill in 6 or further equate the parts as Box A, so that you can fill in 4 and 2 in separate equate parts.

8.  How many marbles in Box C?  

9.  So, you take 25 subtract those extra one, which is 25 - 4 - 6 = 15

10.  Then, you know the for P1, their division is merely draw all the 15 objects there and CIRCLE equally.

11.  So, the answer of the missing square for A, B and C (which is all equal) is "5".

12.  So, Box C has 5 + 6 = 11.

I love the Model drawings, as it really helps to constructs your math concept and your thought process in a very organised manner.

All the divisions you can simply draw the total objects and figure out how to circle the groups.

This is the last questions.  And it seems that he has read the questions very carefully and that is why he can score 100 in both Multiplications and Divisions in this book.

Good job Jay.

No wonder when we go Garden by the Bay yesterday, he wrote this on his wishing card.

He is such a confident kid.  Now, only his carelessness can stop him from getting full marks.  hahahahaha

Good luck my son.  You can do it.  Even you don't get full marks, I know you has learned well in both the multiplication and division concepts.  Your foundation has been fixed. 

加油！

Kids Math: Multiplications

Date:  Sep 14, 2013

I made this for Jay Jay.  And I told him, memorising multiplication is very easy.  You only need to memorise the colour one.  

Jay: Huh?  We need to learn ONLY 9x9=81 for 9 multiplication?  

Dad:  Yes!  You have learn 9x8, 9x7, etc before.  

Jay: Huh?  Puzzled.

Dad:  9x8 is 8x9, 9x7 is 7x9, so, you learned those in 8 multiplication table, so no need to learn twice.

Jay: Oh really. Ya!  

Dad:  So, you do not need to learn twice.

Jay:  Happy.

Of course, I have another one that has the answer on it.

You can do this using Excel.  And then print it out.

So, every morning, let him take a look at the table and try to memorise.

I sent him to CMA class.  And there is a nice little multiplication songs that he has to learned since few weeks ago.

So, here he bring up his iPod to learn the song.  The challenge is when you use a song, he has to sing the song from 9x1, 9x2 to 9x8 to get the answer of 9x8.  HaHaHaHa.  But that is the easiest way to do it.

After that, let's put this on test.  Give him some assessment book.  And when he can do all these, then, it is OK.  

So, do this every day, and his multiplication will be improve.

Make it a fun thing for him to learn.

I caught him "trying" to read my book one day.

And the next thing you know, he has mastered the multiplication of 11 with any two digit number.

Dad: 43 x 11 =?

Jay:  473 (1 second calculate in his head)

Dad:  54 x 11 =?

Jay:  594

Dad:  how about 65 x 11 =?

Jay:  (he took 4 seconds) 615, no 715.

Yes, if you add up the two numbers is more than 10, you need carry over the 10 to the first digit.  So, you add 1 to 6.  

Good luck in teaching your kid multiplication ya!

Jay & Sudoku

Date:  May 1, 2013

Jay's school suddenly give out a Sudoku exercise which in my opinion quite hard for their level.  They are only P1 leh!

Don't worry.  兵来将挡，水来土掩!

Luckily, all these while, I downloaded the "Sudoku School" app for him on his iPod.  

And we also have bought a few Sudoku board game for him.  I got that feeling that the school will teach them Sudoku some day, I just did not expect it to be so fast.

Another Sudoku board game we have.

Doing Sudoku can be bored and dry.  

But if you run a TIMER while Jay doing the sudoku, it is a different story.  After you have finished it, you write down your timing below the puzzle.  And then, you compare with your last timing and try to beat it.  

Instantly, Sudoku become lively again!  Also, for the first few exercises, you will need to see how they solve it, and then teach them the correct strategies.  There are repetitive actions needed to be done in a certain order so that you do not miss out any obvious solving steps.  

And there you go, Jay Jay did the "Challenging" 4x4 Sudoku Puzzle within 2m 08s on his own.  I am proud of you Jay!

Learning Math & Understanding Math

Date: Mar 18, 2013

Today, I sat beside Jay Jay and see him doing his term break math homework.

In school the teachers taught him a lot of method. Count up, count fingers, number bonding, etc. But he seems to be struggling in a certain type of math questions...

Jay: "it's very hard..."
Me: "Which one?"
Jay:"2 plus something equal to 20. What is that something?"

And I saw him count up from 2. And he added 18 using his fingers.




So, I told him. Didn't you learn the Good Friend song? He learned that from the CMA class.

"One nine two eight three seven, four six five five makes a ten..."

Why don't you use that to solve the math number bonding of

2 + __ = 20

At first, he was a bit puzzle what I meant...

Later I explain to him that the 2 have to add to a number bigger than 10. So, he needs only to find the single digit of the missing bond. And to do so, because it is a good friend (10) song, the answer is eight (8) in the single digit.

So the answer is

2 + 18 = 20

Instead of using finger to count, he can use the song to remember and do the mental arithmetic fast.

He understood what I said and then, he finished the whole page at much faster pace. Instead of using the finger to count.




So, for question such as

__ + 14 = 20

I taught him that since 14 has a ten in there, you need only to find the best friend of single digit "4". Which is six (6). So he got it and be able to solve the math fast by covering the (1) in the tenth digit and figure out which good friend is missing.

For questions such as

7 + 8 + 4 = __

It would be easier to draw a line below 7+8 and write the partial answer of 15 and then proceed with finger counting 15+4 which equal to 19.

At first he was struggling on how to find a three way addition answer.




Tips...

1. For the beginning, you really need to sit beside your kid and watch how he solve the math. What he learned from school does not necessary mean that he understand math. Watch him, observe him and if he struggle, ask him how he trying to get the answer, and figure the best way to make him understand in layman.

2. Sometimes if he says he knows and understand, that does not mean that he really understands. You will need to give a few more drills from time to time to see if he remembers and he understands.

3. Most of the time if he has got it. He will skip a lot of steps. But since he is P1 at learning stage, make or force him follow the steps. Such as regardless how easy is the question, must always under line the first part of the equation to show work. And write the answer below. And proceed to solve the rest of the equation.

4. You are the parent and don't always think that teaching is not your job. Most if the parents will tends to check the answer at the end of the exercise but not sit thru and observe how your kid complete the exercise. In my opinion, even the answer is correct but you may not know how he got the answer and whether it not he got the answer using the better method. So some kids will need this sort of help during their growing times. As a parent if you can afford the time, always stay beside them and watch over them. Don't have to be with them 100% all the time but at least 20% to see the process.

I also learn a lot of new stuffs when I was doing the home work with him. Like that hope that Jay Jay's thinking process can be trained so that next time it will be easier on the parents role.




- Posted using BlogPress from my iPhone

The Singapore Model Method for Learning Mathematics

Date:  Mar 4, 2013

Call me a Kia-su Parent, I don't care!  But what I care is, when your kid bring a simple math question (or is it an English question about math) to you and you are not able to solve it using the correct Singapore way.  What will you do?  Will it be too late to learn the correct math?

Welcome to the world of "Model Method" for learning Mathematics.  :)

From time to time, my ex-colleagues will pass me some math questions for their primary kids and hope that I, "the Engineer" can solve it.  Well, the truth is, when I see the question, it is very simple question.  But when you try to solve it, by nature, from what we learned 30 years ago… we used Algebra to solve it. In fact, most of the questions took me more than 10 minutes to solve.

Wait now, we are talking about primary school children, so, how on earth that they know about Algebra in Primary school?  

Well, Singapore's answer is the "Model Method".  A very powerful visual method to help solve complicated math question for Primary School students.

I know Jay Jay is only Primary 1 this year.  And they only learn about Model method in P3 onwards.  But you know me, I have strong interest to learn and explore "Model Method" and there I go...

To sign on a one day short seminar about Model Method.  From http://OnSponge.com

(Note:  You don't really have to pay money to go for this seminar, some school do provide this free or as low as $2 with free food.)

The reason I went is because one of my friend went there, and she think it is good. 

Also, these are the people who write math books for schools here in Singapore.  Only sell it in school's book store I heard.  So, can't be wrong right?

I bought this book after the lesson so that I can practise 3 questions a week.  So, by the time Jay Jay reached P3, his daddy will be or should be able to solve any kind of math questions using the Model method. kekeke

OK.  Let's do one simple question so that we can have a quick peep on what is Model Method.

Question:  There were 320 more red marbles than blue marbles in a bag.  If 30 red marbles were removed and 80 blue marbles were added, there were thrice as many red marbles as blue marbles in the bag.  How many marbles were there in the bag???

To solve this question, one has to be GOOD in ENGLISH.

Also, one has to be able to brackets or highlights the different condition.

Once you have understand the question.  It is time to draw the model.  

So, there are 320 more red marbles than the blue one.  So, you draw two blocks, one for red and the other for blue.

Stacks both blocks together.  And then, the red one should have 320 more marbles.  So, you indicate "320" in the additional block for red.  At this stage, you don't know how many blue marbles, or whether it is more than 320 or lesser.  So the SIZE of block is not important.  So, don't worry about the proportion of the blocks.

Now, some thing has happened.  So, you drew the same model diagram below and call it "IF (this happen)".

So, what has happened?  IF 30 red one were removed…. So, you SHADE the small block and label it 30.  Whenever you SHADE the block, that means, you have remove that number of block from the red one.  In our example, 30 red one is removed.

Very important tip is to use pencil to draw the model.  Because from time to time, you will need to erase the block and redraw so that it is nicer and easy to understand.

Next, 80 blue marbles are added.  So, you draw a small incremental block beside the blue block.  In our case, label "80" on it.  This is to indicate that you added 80 blue marbles.

Next step.  "EQUAL PARTS".  So, if you add 80 down at the blue block.  You EXTEND a line in the red block.  Then, fill in "80".  This is call to EQUAL the PARTS.

Now, you now that the additional block beside the red original unlabelled block has a TOTAL of 320.  So, that makes the remaining parts to be 210.  i.e. 320 - 30 - 80 = 210.

Lastly, "There are thrice as many red marbles as blue marbles at the end.  So, the total red block represents 3 UNITS compare to 1 UNIT of blue block.  

So, the remaining 2 units is actually 210.  Can you see it?  The original 1u blue + 80 = 1 unit of blue.  So, the total red now becomes three times of this 1 unit of blue.  So, that makes 210 equal to 2 unit of blue.  So, solving the 2 unit of blue will tell you what is a single unit.

As you can see … the confusing part is the size of the block of 210 is almost equal to size of 80.  And the 1u size is greater than these 80 and 210 blocks.  So, that is why proportions are not important.  The key important concept is that you know how to visualise the model diagram and solve the puzzle.

Once you can see 2 units of blue equal 210.  You can easily solve the math question.

The truth is, when I first read the questions, I got stuck there for almost 2-3 minutes with my mind blank.  But after the trainer explain how you solve it, I am like understand a bit here and there.

Then, when I continue the next 15 questions in different categories, again, each question is like a new question to me.  So, it is not easy.  And I am glad that I went to course to learn this.

At least, it gives me an idea what I am facing in next two years.  And it also gives me the preparation I need to teach my Jay Jay the correct math.  So, it is important to teach them to think how to solve it using model diagram.  No longer you need to memorise formulas or solve complicated algebra.  By using some block diagrams, you are able to solve these math questions.

It is a big WOW for me, but I enjoyed every single questions and every single challenge.

This is another good book where the trainer heard it is good.  This is for P1.