Patterns in coordinates GM3.3 Core Starter This pattern of triangles continues. a Find the coordinates of the vertices of these triangles: i the 6th triangle ii the 16th triangle iii the 25th triangle iv the 26th triangle Be prepared to explain how you worked out your answers. b Are any of these points on triangle vertices? i (4 , 200) ii (200, 0) iii (601, 4) Preamble This fairly straightforward activity is intended to recap the use of coordinates and practise mental imagery and pattern-spotting. It should be carried out in pairs, but with justifications presented to the whole class. Depending on circumstances, pupils may be given the opportunity to set similar questions based on their own patterns of shapes (these may make use of all 4 quadrants). Pupils should be challenged to explain how they arrived at their answers. Possible content Using coordinates of points to investigate number patterns. Resources None, pupils should not need a coordinate grid to answer the questions, but may need to draw coordinate grids in order to make up their own patterns. Solution/Notes a i (12, 0), (12, 4), (10, 0) ii (32, 0), (32, 4), (30, 0) iii (50, 0), (50, 4), (48, 0) iv (52, 0), (52, 4), (50, 0) b i (4, 200) – no ii (200, 0) – yes iii (191, 0) – no Original Material © Cambridge University Press 2009 Original Material © Cambridge University Press 2009