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The grid below represents a city laid out in "blocks" with all the roads running north-south, or east-west.
Imagine two friends live where the red and blue dots are on the grid.
The animation shows three paths that one friend could choose if he wanted to visit the other. He likes to find the shortest routes possible, so he always travels north or east, never south or west.
What interesting mathematical questions could you explore on a city grid like this one?
Click below for some ideas.
Getting Round the City
This resource is part of "Dotty Grids - Exploring Distance"
The grid below represents a city laid out in "blocks" with all the roads running north-south, or east-west.
Imagine two friends live where the red and blue dots are on the grid.
The animation shows three paths that one friend could choose if he wanted to visit the other. He likes to find the shortest routes possible, so he always travels north or east, never south or west.
What interesting mathematical questions could you explore on a city grid like this one?
Click below for some ideas.
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What's Possible?
Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?
Why 24?
Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.