One of my favourite lessons on graphs is when I use the floor of my classroom as the x–y plane. I fix an origin in the middle of the floor (in order to make sure negative coordinates are included). I use masking tape to represent the axes along the floor, with masking tape dashes marked on the axes at appropriate points. A little bit of movement of chairs can ensure that students are seated in rows and columns on the coordinate plane. I ask a few questions and then allow students to come up with some questions of their own. In my experience, things can advance at quite a rapid pace, and even expand into graphing inequality regions and quadratics. Below, you will see a mixture of my questions and some of the questions my students have come up with. I also use Geogebra (if you have not used it, this is one of my favourite free resources available to download at https://www.geogebra.org/) to represent some of the information simultaneously on the whiteboard. There is great scope for discussion about what is graphed on the board and this often results in student-led conclusions. For example, the students can see how the equation y = x + 2 is the same as, or shorthand for, ‘your y-coordinate is 2 more than your x-coordinate’.

Stand up if:

• you are the point (1, 2), (–1, 0), (–2, –1) etc.
• you are the origin
• your y-coordinate is 2 more than your x-coordinate
• your y-coordinate is 1
• your x-coordinate is 0
• you are on the line y = 2
• you are on the line x = –1
• you are on the line y = x
• you are on the line y = –x
• your x-coordinate is less than 2
• your y-coordinate is greater than –2
• you are a reflection of the point (2, 1) in the x-axis/line y = 2
• you are a translation of the point (0, –2) right 2 and ‘up’ 3 (with some discussion as to what up and down means)
• you are on the line y = x + 1
• you are on the line x + y = 2
• you are in the region y > x
• you are in the region y ≤ 1
• you are on the line y = 2x
• you are on the line y = 2x – 1
• the gradient of your line is 2 (this was a student’s suggestion and created a great deal of interesting debate along with ‘stand up if you are on a line parallel to y = 1’)
• you are on the curve y = x²
• you are the point where the line y = 1 crosses y = x + 2

Debbie Barton is a teacher, examiner and maths consultant with over 20 years’ experience. She’s written a number of books including Complete Mathematics for Cambridge Secondary 1. She also worked as a Gifted and Talented trainer and is passionate about ensuring able students are challenged with exciting stimulus.