Montessori at our home - 8 - Geometry stick box

Finally, found some time to post our prized possessions.

The Geometry Stick Box and Board

We used the stick board and got some of the concepts cleared

• Convergent Lines
• Divergent Lines
• Parallel Lines
• Equilateral Triangle
• Isoceles Triangle
• Scalene Triangle
• Different polygons, quadrilaterals

 Here is the other material I got -

Power of 2 Cubes

Binomial Cube

There are a number of presentations available online for the binomial cube, much less for the power of 2 cube - I am yet to successfully figure it out.  Binomial cube is a visual representation of

(a+b)³

The cube lays the foundation to the formula.

Binomial Squares

We can also use the squares to get to (a+b)² .  While I wanted to get the squares for all numbers - 2 - 10 from http://montessorisupplyindia.com, I got the stock only for one  hundred square.

The technique for introducing binomial square is very simple - Use two rubber bands and ask the child to make 2 smaller squares from the bigger square. My guru is the online video series from EdVid on youtube.

Ed-Vid : Binomial Square Video

So, since we have the decanomial material made from "maths notebook" - We are going to be doing this using the paper decanomial material.  This will also be fun - children can "cut" the individual pieces and then put them together.  I am sure this is going to be an interesting activity.

Montessori at our home - 7 - Fractions - Part I

There are a lot of materials online on Fractions and Fraction Insets.  However, I was really looking for albums on how to move towards Fraction related basic operations

For that, we needed to do some work prior to these operations by themselves, such as -

• Knowing LCM in case of complex Fraction addition where denominator is not the same
• Reducing Fractions

This led me to multiples, factors, HCF, LCM, proper, improper fractions, mixed fractions etc

So much - so finally, we made a humble beginning by making the cutouts.

We made the fraction cut-outs at home - after taking printouts of Fraction Circles from Montessori Mom.

Here is our fraction box and a fraction practice activity gift from his Aunt.

We have since then moved on to describing the numerator, denominator, proper fraction, improper fraction. He is right now doing conversion of an improper fraction into Mixed form.

We also deviated a bit and did multiples and factors.  My source primarily has been Montessori Commons for this activity.  We haven't yet reached Prime Numbers. But, he has already got a hang that there are numbers that have only 2 factors, 1 & the number itself. 

We have also got the Fraction Tower activity set.


We still need to go through some activities before we get to the Tower. That includes Decimal, Decimal operations, Centesimal Frame. 
 

Montessori at our home - 6 : Division Stamp Game

I meant to post this long time back, but due to lack of pictures, could not.  We did a DIY of stamps using coloured chart/A4 size paper/Card stock from phoenix days.  The Kellogs corn flakes boxes were used for giving some firmness to the stamps.  Coloured paper was stuck on both the sides as right below.

For the skittles, we took the ludo pieces for the ten lakh, one lakh, ten thousand.  For the thousands, hundreds, etc, I just rolled paper so that it could stand like a skittle.  We just need 9 pieces for each place. Also, I  made sure that the decimal chart had the same colours.  The decimal board and decimal checkerboard have also been DIYs and will be in an upcoming post.

Here is the problem being worked out 425/25.  I thought it would be difficult for him to grasp that if we give 10 to the group of 10, we need to give 1 to the unit.  But, he understood it quite easily - that was a big bonus for me.

Phew...that has indeed saved me few thousand bucks that I used in buying the solid material that we are just better off buying.

Montessori at our home - 5 Square of Pythogoras (Decanomial)

The cricket fever is not over yet.  In fact, in the coaching excesses that are all over, I am constantly hearing that my son wants to play for the Indian cricket team!!!

I discussed this with one of my uncles and he just said that allow him to explore "most" of the "classes" and withdraw from those that he is not actively interested at a later point.  Guess I will have to do that.  Few weeks back it was Chess mania and now cricket.  Most likely the next is going to be Tennis with Wimbledon matches coming up.

Back to our Montessori that we have not been able to pursue so vigorously since the school reopened.

Finally, oh yes, finally I completed the Square of Pythogoras.

In India, we have neat Mathematics square notebook 1cmX1cm squares.  We pasted a sheet on to cardstock and then cut them for the various dimensions.  Since the squares were all 1cmX1cm, this is probably the easiest material to make.  However, we did not stick it on different coloured card stock for instance

1 - Red
2 - Green
3 - Pink (Orange for our beads)
4 - Yellow
5 - Light blue
6 - Purple (Ours is violet)
7 - White
8 - Brown
9 - Dark Blue
10 - Golden Yellow

I am however planning to ask my son to colour the "white square side" of the decanomial with the above colours.  So, then, it becomes easy to show that

2x3 Green is same as 3x2 Orange.

and so on...

My son had his friend over at our place and we all arranged this.   Here is the work in progress....

And, phew it is complete (the blue Dupatta of mine was enough to spread the whole thing across)

Here is the close up

And, we did end up doing the multiplication fact practice by -
1) Placing the Golden bead bars - essentially telling that the bead bar and this is pretty similar
2) By doing 6x7 by "counting the total number of squares inside the 6x7 rectangle
3) We also started doing the "Square of Pythogoras" but haven't been able to complete it

The kids found it quite tiring after just the above.  Hmmm....may be it is an age thing that they want to grab the "content" faster than before.

We need to use the squares a lot more so I would prefer to use the decanomial or something similar.  In fact, in my mind I am already planning on using this instead of the beaded square for the Binomial presentation.  But, for now, lets get the rest of the square related facts, and sum of 1 to 10 numbers etc in place.

TBD
1) Complete Pythogoras square
2) Complete Square presentation and repeat
3) Sum of first n numbers - lets see if he can get some simple facts in place

Thats it for now!

Montessori at our home - 4 - Great Lessons Hindu Vedic Style

After a successful homemade checkerboard, my son now is looking for challenges and I am honestly not able to cope up. 

My other struggle right now is to "wean" my son from "cricket mania". Like every other Indian, my son has taken now to cricket. It has tremendously improved his mental addition and subtraction, but at a cost of being close to not wanting to do anything else at all - either play matches or watch matches. Just hoping that all this would stop or at least slow down next week as his school reopens.

Meanwhile, I downloaded some of the Great Lessons from Monteaco.  

Here is the first one Great Lesson 1 - God with no hands (Universe and creation)

In my case, I was aware of "Purusha Suktam" that says that all that emanates is from "Purusha" -

पुरुषं एवेशकं सर्वं
यत भूतं यत च भव्यं

and in fact, found a beautiful similarity with the above explanation and "Mantrapushpam" in the Vedas.

योपां पुष्पं वेद पुष्पवान प्रजावान पशुमान भवति
चन्द्रमावा अपां पुष्पं पुष्पवान प्रजावान पशुमान भवति

अग्निर्वा अपां आयतनम्  ...

वायुर्वा अपां आयतनं ...

चन्द्रमा , पर्जन्यो , नक्षत्राणि, संवत्सरो
 

Where everything seems to be derived from the "Cosmic Waters". These have got denser and denser to give rise to air, fire, as a result the stars and the elements. There is an interesting presentation on the meaning of Mantrapushpam here Mantrapushpam explained in English.

But to my surprise some things were already on his mind - for instance - how do you think the clouds and the sun came. "God made them", prompt was his reply. Well, over the last 6 years he has had tremendous opportunities to hear the word God. But, such a casual answer made me wonder whether he was even ready for the "Big Bang". 

Still, we went ahead and we have now kind of come to a common point called "Purusha". The enormous space that condenses. We also got terms such as Prakriti introduced, rest of the story was very much similar to what Maria Montessori has explained.

My son would not recite Vedas right now - not until we go through the Upanayanam process that will happen in due course.

Back to the lessons, I guess, I am more confused about the timelines since, like many practising Sanatana Dharmis, I find it difficult to cope up with the eons and eons explained in the Puranas and transposing them and making it appeal to the child in a way in which he is able to get

1) A hold on the original Vedic pronouncements

2) Being able to manage it with the practical reality of theories abounding our world such as big bang and steady state

3) Being able to verify it with literature available on carbon dating etc

I would not yet like to reveal anomalies that are abounding in our times of interpreted, mis-interpreted history, archeology etc. Not for a 6 year old yet. I just would like to show some connections, rest is upto him to tie some of these anomalous loose ends later in his life!  

Montessori at our home - 3 Homemade Checkerboard

Homemade Multiplication Checkerboard

We did use the Checkerboard online. However, I could sense that my son had difficulty in dragging and dropping the bead bars using the mouse. It was quite disappointing for me. But then, that turned out to be a blessing in disguise. I had scouted for beads in Pune, but here in Chennai, everything needed for the board just fell in place.

Thankfully, we got some beads and golden wires at the local Lucky Stores and made the golden beads ourselves. There was a cute box with 12 compartments just about right to put the different sized beads.



For the board, we took empty cardboard laptop boxes and stuck green, blue and red shiny paper(Each square is 5cm X 5cm). With some cardstock stuck on the remaining cardboard, we got the number stamps. I haven't yet completed the board, but, he has started working. The entire effort has taken about 2 1/2 days (of course with other activities thrown in). Cost - Rs. 300 ($6). Had it not been for my son himself helping me out and pushing me to complete it, I might not have finished this so soon.

Some more pics -





Our thanks to all the people who have put up the Montessori videos and all those useful posts. I do feel far more satisfied at taking some effort for this. Hmm....may be there is an invisible hand at making some small dreams come true! :)

Montessori at our home - 2 Hunting for Checkerboard

I am glad to have finally purchased the following from Flipkart.com

The Secret of Childhood

And, Montessori Today

The second book was primarily for what to introduce to the elementary years.

To be honest, I am unable to keep my eyes wide open - am hardly reading 2-3 pages and then it is zzzzz.....

Meanwhile -

We have moved on from division on unit division board that have zero remainder to equations that do contain remainders.
And, a lot of mental math activity has been going on. Our friend's son who is a chess pro has been doing some minor coaching for our son on how to do different types of checkmates.

Thanks to our friends visiting over this summer we have also learnt about Vedic Mathematics. It is quite appealing and I have gone through some of the tips. But, for now, I feel, the child needs to learn concrete concepts - in a visual sense. And, seeing a square as a square rather than a number has tremendous benefits of later integration.

Finally, the surprise and the biggest discovery today -

The Checkerboard

OMG! OMG! I am pinching myself - unable to believe this. Yippeee Yahoo! And, thanks a trillion, zillion times to Free Montessori

I had just posted to another person asking advice on what next to invest on, for frankly Checker board for Large Numbers as well as Decimal numbers was on the expensive end to buy. Yes, yes, I myself am a person who likes kids to work hands on - sensorial and no laptops or TV etc. But, then, I either wish I could afford all of the material or make them myself at the speed with which I could outpace my kids' interest or learning pace.

I could of course try to make the complete bead material or just buy the bead material and make a laminated checkerboard myself....but, this one serves the purpose for now! Amen!