Teacher Notes

The three big advantages of this activity over others that I have used for teaching equations of lines is that it is:

• Social and Collaborative
• Very Visual
• Instant feedback and sharing of best practice

What to Expect?

Understanding why an equation can be used/is the best, current, definition we have of a line is one of those topics that I find a genuine milestone in mathematical knowledge. Some students really struggle to get any kind of grasp on how defining the relationship between a horizontal and a vertical position, and then expressing this in algebra, is any help or accurate depiction of a line. Others accept it quickly and can use and apply it effectively.

Many students, particularly the former (those struggling to grasp defining positions through horizontal & vertical displacements, and then expressing this in algebra), are often reluctant to draw attention to their difficulties and will struggle away unproductively until I get round to seeing them and realise. This activity ensures that I know how each pair of students is getting on, at a glance, instantly, thanks to the size of the board and the size, and colour, of the counters.

It allows those that have happily accepted the equation of a line definition to share their expertise with others in the class. This, in turn, helps them to better elucidate their own understanding of why/how the equation describes the steepness and position of the line as they find themselves having to explain it clearly and succinctly to others.

Expect a lot of discussion, questions and inter-personal interactions as pairs share their understandings and difficulties.

Examples of Students work

The video is a summary of three student's approaches to this activity. I originally had the videos themselves, but regrettably lost two hard drives recently [thanks Google Drive for slashing your cloud storage prices, now my files are safe(r)] so have re-produced their explanations below. Taking videos of students explaining how to plot the line from its equation makes great revision resources for the whole class to take home to help with their homework/revision (you can use the students words to explain and film if the student is too shy/doesn't want to have their voice explanation distributed to the whole class).