Introduction by Jo Boaler

It seems taxis have been part of my life for years. When I was a teacher and academic in London, I would see the iconic black cabs driving through the city streets, and every now and then I'd ride in one. Years later, these black cabs became important again, as some of the first evidence of brain plasticity, even in adults, came from studying the brains of London's black cab drivers. Researchers found that, after their intense spatial training, the brains of black cab drivers strengthened and grew. Years after that, I was teaching my first-year class when I met Tessa, who proposed this taxi activity for youcubed.

Instructions

How many different paths are there to get the taxi from point A to point B? You may only move directly to the right or downward. You cannot move left, upward, or diagonally.

Task

What do you notice and wonder? Can you find how many paths there are on grids of different sizes? What about a 2×2? A 3×3? A 4×4? A 4×6? Can you find a pattern for an m x n grid? Can you create a visual proof?

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