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Exploring dotty grids at upper secondary

The problems below are all taken from our recent dotty grids resources for Lower Secondary students. We've chosen to feature them on the Upper Secondary page because they all have scope for some interesting mathematical investigation at a higher level. We invite you to explore the problems and then send in your thoughts via Advanced Mathematics on Dotty Grids.
An Appearing Act link

An Appearing Act 

Stage: 3 and 4

Cut out and reassemble the pieces. Can you explain what happens?

Areas from Vectors link

Areas from Vectors 

Stage: 3 and 4

Use the applet to explore the area of a parallelogram and how it relates to vectors.

Find the Metagiff link

Find the Metagiff 

Stage: 3 and 4 Challenge Level: Challenge Level:1

Play the game. How many guesses do you need to find the Metagiff?

Getting Round the City link

Getting Round the City 

Stage: 3 and 4

In a city with a grid system of roads, how do you get from A to B?

Advanced Mathematics on Dotty Grids link

Advanced Mathematics on Dotty Grids live

Stage: 4 and 5 Challenge Level: Challenge Level:1

A dotty grid is a very simple mathematical structure that offers potential for very deep thought...