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August 04, 2013

Math for 7th Graders (1)

I decided to take up Math education at Isai Ambalam for the 7th Grade (5 and 1 in 6th Grade). I got myself a block of 1-1/2 hr in the afternoon to give enough time to actually do something.

I started with trying to connect Math to real life. The question was what in real life!

While helping teachers with learning gaps they had they brought up that they had trouble connecting volume in Litres (L) to measurements e.g. how much water in L (or a fraction of it) can you put in a rectangular box of 
5 cm x 5 cm x 10 cm. 

The only gap for the teachers was that 1 cubic cm (cc) = 1 ml, but it got me thinking about what the children think of volume, estimates of volume and measurements.

In my first class, we started with very simple question - how much water does the school consume in a day.

The first thing that came to the children's mind was of course drinking water. One child said that he drank 3 glasses of water in a day. There was some debate on how much water was there in one glass of water. One said 250 ml another 500 ml. One kid went off to get a glass and another pulled out the measuring jars that the school has. Soon we found out that the glass he was referring to was only 200 ml. Then I initiated a discussion as to whether everyone only drink 2 glasses of water in a day. This started a short survey with the people around and they found different children and adults were drinking different amounts of water going up to 6 glasses in a day.

I wondered if it was a good place to bring up averages, but my limitation in Tamil came forward and I could not explain this. I went on to getting an estimate of the water of the whole school with around 100 kids (actually 109+teachers, but ballpark) if they just drank 2 glasses of water. With some difficulty, prodding the conversion from ml to L finally happened and we got to 40 L. I asked them to picture 40 L of water and if this really was the only water used in the school.

One kid bashfully mentioned that the bathrooms use some water. I asked how much water is there in the buckets used. I will skip the guesses and the measurement process, but we finally arrived at 8 L of water in one small bucket. Well, and how many buckets of water do you use? The kids had enough of this step by step calculation of water and started asking for short cuts. I asked them to ask around. They asked a few and finally figured that the coordinator will know and asked her, she estimated 1500-2000 L in a day. I think it left the children more confused than when they started, but given the popular concept among children of 'finished' they said they were done.

I told them that they need to figure out if and how this number makes sense. They came back with a gem the large tank on the school premises from where the water goes to everyone. Perfect, my opening to Math! We were going to measure some dimensions of the tank and find its capacity.
I brought my measuring tape and we tried using it a few times to make sure that the boys going up the tank knew what they were doing.

Measuring the tank that is placed 4 m high turned out to be much more of a challenge than I had estimated and involved some acrobatics that made me a little uncomfortable, but the children seemed very comfortable and confident with what they were doing. We got done with the outer perimeter of 6 m, hieght of 170 cm and an approximate diameter (the top is not flat) of 190 cm. Can you figure out the volume of our tank? :). 

I realized that children love activity, but not to process what was learnt from the activity. 
The next day was a shocker, some kids (there are only 5 in the class) had not bothered to write what they found and when they did they still wrote the the glass could hold 200 L of water and the tank perimeter was 6 cm...Needless to say my idea of giving them a sense of what they are doing was looking like an uphill task. 

When I tried to analyze the data with them I realized that the students were yet to encounter area and perimeter of a circle. I attempted to save the class by giving them the 'formula', but I realized that had difficulty understanding the formula and applying it. I mean, of course I arm twisted pi and made it '3'  and got them to find the diameter, but it seemed like getting an 'answer' rather than learning anything from it and I dropped it...

The next day we took measurements of various circular objects perimeter (with a rope) and their diameter for half a class and tried to analyze the data. We found measurement inaccuracies and once I color coded the xls they decided that they were going to remeasure the outliers like 2.2 and 5.5. We fixed the table below. Can you guess which measurements were 2.3 and 5.33 (Hint, they had a scale that was 60 cm long)?

S.No Things Perimeter (P) cm Diameter(D) cm Ratio (P/D) Area
1 Shifu Tire 61 19.6 3.112244898 301.84
2 Iron Rod 15 4.6 3.260869565 16.62571429
3 Tree Trunk 2 114.5 39 2.935897436 1195.071429
4 Bangle 19 5.9 3.220338983 27.35071429
5 Van Tire 232.5 74 3.141891892 4302.571429
6 Tree Trunk 1 25.5 8 3.1875 50.28571429
7 Pillar 49 15 3.266666667 176.7857143
8 Bike Light 50.7 15.4 3.292207792 186.34
9 Ring 6 2 3 3.142857143
10 Tank 6 1.9 3.157894737 2.836428571
11 Handle 8 2.5 3.2 4.910714286

When measuring the van tire they had missed out one set of 60 cm giving a low ratio and when measuring the handle they had erred with the decimal and written 2.5 cm as 1.5 cm.

At this point I would like to introduce (anyone who is not familiar with) Marvin (the depressd robot from the Hickhiker's Guide to the Galaxy) to the following:

Marvin: I think you ought to know I'm feeling very depressed.
Trillian: Well, we have something that may take your mind off it.
Marvin: [depressed] It won't work, I have an exceptionally large mind.
Zaphod: Its all part of life you know...
Marvin: [even more depressed] Life? Don't talk to me about life!
Marvin: The first ten million years were the worst. And the second ten million: they were the worst, too. The third ten million I didn't enjoy at all. After that, I went into a bit of a decline.

From then on, as Marvin would say, things went a bit on the decline. I tried to get the kids to analyze the data themselves and found that they could not do any calculations with fractions (22/7), decimals (3.14) and needed to approximate everything to an integer division. I gave up, got depressed, hit rock bottom, shook it off and decided to fix the fractions, decimals...

I told then that in order to do some experimental math they need to be comfortable with fractions and decimals and we will cover it well and quickly. In 3 days most of the kids really picked up on fractions, they could do calculations, but they still didn't have a 'feel for it'. I thought I could fix this in the following week. I had asked them to make their own problems, try the exercises in the book, but come Monday morning they came like a clean slate. They could not even follow what they had done on their own the previous week! 

The next 5 days they worked harder than they have worked ever before. We recovered (pun intended) fractions and calculations. I figured the issue each kid was having, but made them work in the class and at home. We plunged into mixed fractions, decimals, threw in the number line and negative numbers and then placing positive and negative fractions on the number line. I even threw in powers of 10 as it was the next topic in the textbook. I gave them textbook problems to do and a special problem set over the weekend.

But, as the weekend has come it has given some time to contemplate and look through what is to be covered by the sciences and how it can be related to Math.  I also need to reconsider what I am becoming :), a classical classroom teacher trying to cover the textbook! The kids have actually become much better, they can recognize a fraction and at least think for a second if it is proper (less than 1) or improper. Most of them are able to place them on the number line and tell a story about it...but then let's see Monday morning.

I will start working with a pendulum and see what we can learn from it about Math and the world around us (and maybe sometime when I am brave enough we can get back to the water audit of the school).

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