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*= 2*x* - you are on the line
*y*= 2*x*– 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*=*x*^{2} - 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. *

I really like your idea of teaching graphs to students by setting up an axis on the classroom floor. I believe that this allows the students to actively participate in the content which, I think, is very important in allowing students to understand key graphing concepts. I will have to remember to try this the next time I am teaching a graphing lesson.