Graphing a Picture - PreCalculus Review Edition

It's the end of the year (well, it was over a month ago), we've completed the curriculum to the extent we're going to and it's time to review. We didn't get to include systems as much as I would have liked, I need students to recall how to graph and analyze the variety of equations, but I really hate review packets. Enter this awesome project:

Link to word doc

You’re going to draw a picture! Here’s your chance to be creative! You’ll make a design on Desmos and then make a poster presentation of your final product as well as the process. 

You will use at least five of the types of graphs we have studied this year.

Sine Cosine Tangent Parabola Ellipse Circle Hyperbola Polynomial (with degree >2) Exponential Logarithmic Rational Linear 

Each equation should have a domain and/or range indicating how much of the curve should be drawn. Desmos allows you to do that by using brackets. As you work you’ll need to make sure that your equations intersect at the correct point, or solve to find the point where two equations do intersect. On your poster, show the algebra to find where three different pairs of equations intersect. Write a description of how you wrote one equation that you wanted to place on your image (how did you make it pass through a certain point or intersect something).

I had grand projects in mind and they did not disappoint:

 

 

 
 

Their choices are so classically Salem. Pumpkin, bat, spider, ghost... Halloween themes infiltrate the entire year, despite my examples being Taylor Swift and a clown fish! Earlier in the year we did a graphing conics project where we took photos and fit curves to them, so most students started with an image inserted into the graph and then wrote equations to match it. Others started with an idea and made up equations to draw it. We found that the systems were often challenging, I forgot that when you don't make up problems to work out nicely they can be tricky! I pushed students toward solving one challenging system and the rest an intersection with a line.

For the final products I took screen shots of the graph and equations and printed them for each student. Then they added in their calculations.

The posters look awesome and I can't wait to hang them up before school starts this year. What a great way to show kids what they'll be able to do if they stick with their math studies! (I have mostly 9th graders and one class of precalc.)