This project directs students to create the Canada flag using linear functions. The program Autograph is used and descriptions for software use are included, but any graphing software could be used. I have also done this project by hand, without any use of the graphing software and have also completed it only on graphing calculators. All work fine, but this is my preferred method as Autograph allows students to enter functions without explicitly solving for y. This allows them to enter linear equations in any form, not just y = mx+b, but also (y-y1)=m(x-x1) or other forms.
There is also a requirement for students to restrict the domain of the functions so they are only showing the linear function for a specific domain. For example, they need to know the function y = 3x+45 may represent a part of the Canadian flag, but only if they use a domain of x values belonging to an interval of [-5,0]. This allows me to work on both linear functions, function notation and domain and range within one document.
I complete this project after their unit on linear functions, and can be a reasonably evaluation of their understanding of the unit.
Marking is quick and easy - if the linear functions used line up directly on the maple leaf, they get full value for that line. Slopes, intercepts or points used that are not exact will result in shapes that are not as accurate and result in a loss of the value of the line itself.
The results of the project can be added to bulletin boards.
Students get a strong reminder of slope during this activity as they are forced to work on positive and negative slopes. Also, some lines are more easily completed using slope-intercept forms of the linear functions and they are required to determine when each method is most efficient.