4 in a line further extended

the idea for this work comes from the very fine NRICH Diamond Collector task
in which students try to create straight lines that collect as many diamonds as possible:

there are three levels - increasingly complex


















the idea of the tasks below is that students try to find three straight lines
(none of which are vertical or horizontal)
passing through the 9 points

on each of the 3 lines, find a missing 4th coordinate pair to create 4-in-a-line

then find the equations of the 3 lines

(in the example there is more than one option; I hope that in the questions the three lines should each have 3 coordinates on them)

4 in a line extended

this work extends the introduction to coordinates and the equations of simple straight lines
(i.e lines that are: vertical, horizontal, parallel to y = x and parallel to y = -x)
into negative quadrants

this work can usefully introduce or reinforce the procedure for subtracting a negative (the 'geometrical/algebraic imperative' as Hans Freudenthal calls it)

students find a 4th coordinate to complete 4-in-a-line
and then try to find a rule for the lines

these rules only involve gradients of plus 1 and minus 1

the powerpoint is here

4 in a line steeper gradients

these lines have gradients that are plus 2 or minus 2

one way to more easily find the rules could be to find those coordinate pairs that are in the positive quadrant, by extending the coordinate sequence

the powerpoint is here

4 in a line and coordinates

the powerpoint is here