This type of activity is known as Demonstration. Please read the guidance notes here, where you will find useful information for running these types of activities with your students.

1. Demonstration

• I begin by displaying the Desmos page with none of the equations selected (just click on the coloured squiggle to the left of their equation to revel or hide the line)
• I ask my students to consider what the first equation will look like when plotted. I ask them to visualise this first and then sketch it on one of their blank girds (see below) marking on any points of intersection with the axes
• I then reveal this equation and ask students to reflect on their visualisation and sketch
• I then ask them to predict (and then sketch) what the second equation will look like, asking them to consider what has changed and what has stayed the same
• I then revel the second equation, and ask them to reflect on their prediction.
• I then hide the first line and ask students to predict what the third equation will look like
• I continue this process, always having two lines drawn at any one time
• When appropriate I will ask “what other equation had a graph that looked exactly like this?”, and reveal earlier equations as and when needed
• At the end I ask students to discuss the rule with their partners, and then we have a class discussion

This is the sequence of lines that I use:

Here are some blank axes for students to make their sketches on:

2. Possible variations

• Vary the coefficient of x
• Make all the x’s negative
• Change x to x²

Click here to access the Desmos file