# Linear Graphs

I have been working through linear sequences and the next topic is graphs. It was perfect next step and it allows students to see the sequence increases on a graph. I have often used Boat Hire when first looking at graphs. It’s a fantastic lesson taken from a sequences of lesson featured in ICCAMS Students make sense of the information, rather than plotting an arbitrary equation. Two options of hiring a boat are posed; one is a lower hourly cost but higher initial cost and the other boat company is the opposite way round (higher hourly cost, lower initial cost) Students look at the situation where two choices are posed and are invited to decide which is better. There isn’t a definitive answer because the “better” options is dependant on how many hours you hire the boat for. so this lends itself well to plotting the information on a graph.

The group I’m teaching linear graphs at the moment is in year 11 and we’ve just looked at linear sequences, looked at Boat Hire and now seem comfortable with plotting equations. My next step is for the class to spot parallel and perpendicular lines and what that means for the gradient. I want them to see what happens to the line when the gradient is a larger value and also link it back to linear sequences.

A really interesting lesson with year 11. We were looking at direct proportion and discussing an EG involving buying pens. We had sketched a graph (number of pens and cost) and one student said “what if you have a discount when you are paying?”. So we discussed how we couldn’t just multiply the number of pens by a constant value and that we had a second step of subtracting the discount. We then thought of a scenario where we would add a constant amount (buying one bag) It reminded us of our last topics work on sequences. if we looked at a linear sequence of say 3n We could multiply the term number by 3 but if the sequence increased by 3 and there was a subtraction/addition (shift) after we would need to apply that after.