High ground, low ground
What is the quickest route from Start to Finish across two types of ground where different speeds are possible?
Pythagoras' Theorem and speed-distance-time calculations are involved in finding the best route from the start at point A to the finish at point B across high/low ground travelling at different speeds on each type of ground.
Page 1.3 of the TI-Nspire document presents a simple map that allows students to experiment with different crossing points of the stream separating the two types of ground. As they move the white dot to change the crossing point, the calculated time varies and they can see that a straight line route from A to B is not the best answer.
On page 1.6 students are presented with a similar situation with different starting and finishing points and different speeds. This time students are asked to do a series of manual calculations of distance walked and time taken and so find the best place to cross the stream.
Teachers notes and extra worksheet examples are included for classroom use.