A snail slithers around on a coordinate grid. At what position does he finish?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
This problem offers a good opportunity for students to discuss patterns and find convincing arguments for their solutions.
Reuben Hersh has written that:
"In the classroom, convincing is no problem. Students are too easily convinced. Two special cases will do it."
This problem offers an opportunity to ensure that students are justified in generalising from the particular cases that they have selected.
Find a general symbolic expression for the coordinates of the vertices of the $n$th square or triangle.
Before working on this problem students could develop fluency in using coordinates by working on Cops and Robbers and fluency with linear sequences by taking a look at Shifting Times Tables.