1.  Design your neighbourhood or school

• This could be done as a group activity with students sharing ideas and cooperating to decide on a final design.
• You could change the number of squares given (the area) to make it harder.
• Students could be encouraged to have two grids, one to be cut up and colour coded in individual sections to be arranged and rearranged on the second grid. This would incorporate the idea of design as well as the number aspect, and might fully engage the more creative students.
• There is a similar interactive digital learning object that you could refer to on the teacher website here: http://nzmaths.co.nz/digital-learning-objects. This is conceptually close and it would provide a good introduction to this task.
  You could also encourage more capable students to do this in 3D with Lego or other software such as Sketch up or Minecraft.

2.  Loopy cards

• You could give this task to a group or several groups. If more than one group does the task they could test their set on another group.
• You can vary the number of cards that the students are required to make.
• It is easy to make a mistake so stress the importance of checking that the cards can follow only one pathway to make the loop.

3.  How many ways?

• Encourage students to be creative and find as many different representations as they can. For example, they could put a hat on one out of four students or close five windows out of twenty.