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Why do this problem?
emphasises to students that squares don't just exist in
their usual orientation. It goes well with the game Square
The context offers an ideal opportunity to challenge students
to visualise relationships between coordinates.
The interactivity could also be useful when introducing
Pythagoras' Theorem and when working on the gradients of
Display the interactivity. Ask for volunteers to move the
corners to make a different square.
Fix a couple of corners and challenge students to complete the
Offer them a chance to see the coordinates.
Choose two points where all the coordinates are either all
even or all odd. Challenge students to complete the square with
these as opposite vertices.
Set students to work in pairs (ideally at computers)
practising making squares until they can answer the key questions
below. Suggest they make a variety of squares of different sizes
and note down the sets of coordinates of their completed
This could lead to a plenary discussion or, when appropriate,
challenge students to work away from the computer on the final
questions in the problem. This sheet
practice with tilted squares, but without reference to their
How can we construct a square when we are given two adjacent
How can we construct a square when we are given two opposite
How can we construct a square when we are given the centre and
If we are given four points, how can we tell if they will make
a square or not?
Can we do all this without plotting the points?
How does this extend to rectangles?
If you are given three coordinates, work out how to determine
if they will define a right angle.
Draw squares with as many different areas (under 50) as is
possible. Which areas are possible and which aren't?
Provide students with a handout of some tilted squares drawn
on squared paper and ask them to box each one in with a non-tilted
square. Students can look at the four right angled triangles which
result around the edge and will see that these triangles are
Students can answer the last four questions by plotting the
points provided and boxing them in to decide whether they make a