## Saturday, December 22, 2012

### Speed, Ratios, Unit Conversion and a Scalextric track

I was chosen ("volunteered") to work with students transitioning from year 7 to year 8 this year and needed a hands on lesson to position kids into seeing math as interactive and engaging.  With 30 students of varying levels of engagement that I didn't know well, it can be a little daunting.  In previous years I have chosen algebra or working mathematically, but for a change I chose a measurement topic this year.

My daughter Kensie has a Scalextric track (a common 1/32 slotcar racing system) and I've wondered how fast the cars actually go around the track.  I also had 10m of string, a 1.6m lump of wood and some stopwatches.

First we discussed speed itself and how it is encountered in the real world.  We used the example of travelling on the freeway.  Travelling at 120km/hr, they knew was too fast.  They knew that the value and units (speed) described how fast I was travelling.  We then discussed distance and time.  Students stated that we moved 120km if we travelled for one hour.

We then thought about how it related to our Scalextric track.  I suggested that we build a track long enough that the cars could travel for an hour.  The students then said we could go round the same track for an hour if we knew how long a lap was and then multiply the distance by the number of laps.

I gave a 1.6m ruler to the yr 10 helpers and they tried to measure the track.  The yr 7's laughed and said use the string to determine the exact length of the track.  They lined up around the track and held it in place until the string was in the slot all the way round.  They then removed the string and measured it against the 1.6m ruler.  They tended to take the ruler to the string rather than the string to the ruler which made it a bit awkward (the 1.6m ruler is quite a heavy bit of wood with measurements manually marked on).

We started the cars around the track and discovered that we didn't have enough time for the cars to travel for an hour (it was a 40min lesson) and that it was hard to keep the cars on the track for the whole time.  At the board we then looked at the speed measurement again

Firstly we converted hours to seconds

120 km per hour = 120 km per 1 hr
= 120 km per 60 minutes
= 2 km per minute (divide the distance by 60 for the distance travelled in 1 min)
= 2 km per 60 seconds
= 1 km per 30 seconds

Then we converted km to m

= 1000 m per 30 seconds (multiply the distance by 1000 to convert km to metres)
= ~33 m/s (divide the distance by 30 for the no. of metres travelled in 1 second)

By doing the reverse process we could work out the speed of the cars.

We timed the cars around the track and had a range of answers from the stopwatches timing a lap around the track.  Students suggested averaging the results.  We also discussed doing more than one lap and finding the average lap time.

This left us with a speed of 6m per 4.3s

This became 1.39m /sec and about 5km /hr (repeating the process above in reverse).

.. and no mention of 3.6 anywhere (to all you Physics heads!).  There's another lesson here for another day.

Viola.

I'd like to continue this in our after school classes with my 11's and 12's for those that find related rates or kinematics difficult.

(This is the worst post for the year, drawing a lousy 3 visitors.. not sure if it is a poor idea or just the time of the year.  It's a shame as it is a good lesson.)