I have been working on Speed Distance Time and Distance/Time Graphs with year 10. They have been looking at Gradients of a line with their other Maths teacher so I thought i’d spend a lesson looking at SDT then move on to the graphs.
Students were having difficulty using proportional reasoning to find the speed. They understood that Speed was a measure of distance travelled over a period of time, usually 1 hour. They also knew mph and km/h as units but i felt they didnt seem to grasp that if the speed was constant and you travelled at 12mph then you would move 6miles in 30 minutes and all the proportion work we looked at on Percentages seemed lost. I did remind them that when we found 10% of a number we could find 20% so if we moved 40mph then finding the distance in 2 hours was also easy to find. I suspect from talking to students they have mostly dealt with SDT using a formula which has its uses but not thinking in a proportional sense.
I created a few activities to get students thinking about speed proportionally
I wanted students to be able to then move on to looking at speed on a distance time graph. It was important to me they used the proportional reasoning again or extend the lines to make the time 1 hour if they prefer.
UPDATE!
I hope students can see that some questions could be solved by scaling up the time and some by looking at the relationship between time and distance
MathsHKO 
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