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June 15, 2014

It begins again :)

The 5th - 7th grade I worked with at Isai Ambalam has become the 6th - 8th grade this year. The 8th graders will join another school after the first term and I decided use their presence to to continue the gains of a multi-grade classroom.

We had done a few things the previous week, but the admissions had happened that week and it was only this week that we had the full strength in the class with many new students. My goal was to provide a context to mathematics and get the children to start engaging in class.

We had started an EBD (Education By Design) project the previous week that would demonstrate what the most common mistake in addition of fractions of adding the numerators and the denominators together meant in real life. The 8th graders had an handle on programming through the summer camp and we decided to take up this project in scratch.
As part of EBD we derived the quality criteria and formed groups centered around the 8th graders so the children could quickly learn from each other.

The children found it easy to create 1/2 and 1/4 based fractions, but difficult to do for 1/8, 1/6 etc. One group created one 1/8 unit and rotated it by 45 degree to complete the circle.

I had been hoping to find something they knew that would connect what we were doing now (some 6th graders didn't know fraction addition) and I found this in the circle.

We started talking about what we knew about circles. The children knew that a circle is created by keeping the center at one place taking a certain length (with a thread) and moving it around. I asked what would happen if we were spinning an object in a circle and the thread snapped at the highest point. The children gave interesting answers - still along the circle, going down because of gravity and even one that went up before it went down. I then switched the question to something that was spinning horizontally and this really confused children as they knew that something was happening in two dimensions. It didn't help even when I talked about spinning on a table or on the floor where the vertical dimension is not important.

At this point they really wanted to know what happens and I introduced tangents and how small tangents (90' with the line from center to the point) when rotated by appropriate angles can give rise to regular polygons. We also saw that as the angle of rotation becomes really small the number of sides becomes really large and looks like a circle. This is the easiest way to build a circle that doesn't use trigonometry (it will come later).

A tree that had fallen in a recent storm was pulled out by a tractor and it twisted and broke another tree it had fallen on. We talked about why the second tree had broken and them more interesting how it had broken. After taking out the first guesses, the weight had increased - had it really? One student remembered that the second tree had in fact twisted, not snapped. We put two chalks on top of each other and noticed that as top one is moved away (tangentially) over the lower the lower chalk twists. Now the kids started to recall tangents and one example was that motor cars stuck in the dirt throw back dirt when they rotate.

We spent some time on angles as the younger children didn't seem to quite have a handle of it. What is an angle? The (guess) history of 360 degrees being a full angle and what different angles of objects in class including the door would be. We also looked at the number of angles in a shape and differentiated between internal and external angles.

We wrapped the week with a class where the younger children were learning scratch from the older kids and we talking about why we learn mathematics and how we can see and apply it in real life. This conversation took us to estimations like how much water does the school use and how math can help us find the volume of a cylindrical tank on campus or help us find out how much water overflows from the tank if the motor is switched off 5 minutes after the tank filled up.

We of course continued with putting the bigshot cameras together. This time the students who had participated in building it the first time took lead and others helped them. Us teachers also made a camera and the game was afoot. The first person to finish the camera would take pics of the others who were still working on their cameras. Here are the pics of the other two groups at work (what did you expect :)).


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