Table of Contents

Mathematical Thinking Banner

TAXI-STAND

Date: __.__.__

Title: Taxi-stand


GETTING STARTED right-click to save copy 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.

13.1.1 The Task

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.

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:

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.

EXTENSION 1

Beebot


Image 1. Taxi Stand Grid Map

Taxi-stand problem


EXTENSION 2

Beebot activity (abstract thinking)

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

EXTENSION 3

Beebot activity (blend art and technology)

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