GETTING STARTED You will be given a printed copy of the grid on a sheet that you may stick into your book.

1. Glue a copy of the grid into your journal/work-book (To download, right-click image and 'save-as')
2. Write the title 'Taxi Stand' and the date on a clean page in your journal (write your name at the top of the page if you are sharing or not using your own journal).
3. Carefully colour-in each of the three circles. The circles are use to show the passenger pick-up points.

Stephenie is a Manhattan Island (New York, USA) taxi driver. Unlinke Australia, where most roads are curvy and have unpredictable name, in Manhatten, most of the streets and avenues are arranged in a grid of streets and avenues. Most of the streets and avenues names are numbers, such as 1st Street or 42nd Street, and 3rd Avenue or 5th Avenue.

A taxi driver is responsible for all passenger pick-ups in one area of a town. That area is shown on the chart below.

• One night, the driver is called out three times.
• Each time she starts out from the taxi stand and picks up a passenger at one of the intersections (indicated by a coloured dot on the image below).

Later, when everything is quiet, she thought about all of the possible routes she could have taken to each pick-up point, and she wonders if she could have chosen a shorter route.

On the image below, imagine that the horizontal and vertical lines (the edges around each square) are roads. The taxi driver must stay on the lines at all times.

PROBLEM:

• The taxi driver must stay on the lines at all times and cannot cut across corners.
• Find the shortest route to each of the three passenger pick-up points (coloured dots) marked on the grid.
• Starting from the taxi-stand in the top left corner, work out if there is more than one shortest route to each of the passenger pick-up points.

All trips must start/originate at the taxi stand in the upper-left-hand corner of the grid (See: Image 1.)

1. Without cutting corners, what is the shortest route from the taxi stand to each of three different destination points?
2. How do you know it is the shortest route?
3. Is there more than one shortest route to each point?
   1. If not, why not?
   2. If so, how many?

Solve the problem for yourself and develop a way to convince others that you have found all of the shortest routes.

Write down and explain your solution in your book.

• Beebot activity (concrete thinking).
  • Create a grid on floor or on desk tops (using masking tape for example), to one or more locations. Each side of each square should be about one BeeBot long (approximately 150mm).
  • Students program their BeeBot using the smallest number of turns to follow the shortest route to one or more of the destinations.
  • Students vote for two team where their BeeBots travel to a designated grid location along the grid lines that represent Streets and Avenues. Taxis are not allowed to move diagonally over the areas inside a grid square:
    1. The team whose BeeBot travels the most accurate route
    2. The team whose BeeBot travels the most interesting route

The taxi company decides that they will run a trial of driverless taxi cabs

• The company (teacher) specifies two or more locations on the gride
• Each team must program their beebots to travel the designated route
• Each team must program their BeeBots at their desk, and are then invited to bring their BeeBot to a designated starting position on the grid.
• Students may not re-program their beebot once they leave the table. Any attempt to re-program or manually adjust the BeeBot will disqualify that team.
• Taxis (BeeBots) are not allowed to move diagonally over the areas inside a grid square:
• A team representative presses the BeeBot start button and the class vote for each of two winning groups
  1. The team whose BeeBot travels the most accurate route
  2. The team whose BeeBot travels the most interesting route

A dance teacher decides to create a dance for 10 or more Beebots

• Teacher chooses a 30 second music segment having a distinctive beat
• The class must work together to create a line-dance type series of dance moves using Beebots
• The class must program their Beebots to work together and perform the dance moves
• The teacher allows 10 to 15 minutes for the class to collaborate and program their Beebots
• Students must explain their dance moves and programming.
• Students should discuss/write down what they learned or would do differently.