While we learn factoring techniques we will keep examples and notes in our Factoring Foldable.
As we learn each new technique students will add those examples to the foldable.
Here are some samples.
Update [Oct 28 2014] – Students are loving this foldable……some even enough to keep it year after year. Here is one of my NOW returning grade 12 students who has kept her foldable for the last three years.
Other foldables:
[UPDATED – Sept. 25 2015]
We have just spent a week working with quadratics in MPM2D and today I had students create their own angry birds level.
The only real requirement was for them to create at least two flight paths and model them with quadratic equations.
I was hoping to see how they relate the equation to the graph. This worked out better than expected. Most students did not initially make their curves symmetric…..and that gave us a chance to discuss symmetry and these questions
Most students started creating their flight paths with placing the zeros on the graph….then picking a vertex. The best part of the day was discussing how students knew where their vertex was.
Most knew that the axis of symmetry had to be half way between the zeros and also knew the vertex was on the axis. The issues, and then real thinking came when they went to create the equation to match. For example if Alexis wanted her bird to take off from x = 0 and land when x = 24 …she also wanted her highest height to be 7.5 units high. She wrote the equation y = – (x)(x – 24) and assumed she was correct. This assumption gave us lots to discuss!
I asked her to show me how she knew the vertex is (12,7.5) and she had a hard time. “I knew the x value was 12 but I just picked that height”. So I asked her to use the equation and find which height does go with an x value of 12. She did and then we graphed….
Something clicked in her….”Aaah! The a-value must not just be -1″ and then that led us into discussing what the a-value should be and how we can get it more accurately! We did this…
I loved that we discovered and struggled to find the correct a-value instead of me just giving an example and them copying.
I floated from group to group having similar conversations. Some students created their equations first and then found the vertex from the equation and plotted that.
Extensions
Some students started to ask if they could use different birds!!
Pictures are from 2010….new pictures coming!!!
