It's not very often something I teach turns out better than expected--but this is it! This year, for the 1st time ever, I successfully taught transformations to Algebra 1 students. Yes, that's right--Algebra 1.
I bit the bullet and spent more time than normal designing a unit which forces me to take my classes to the computer lab. I hate the computer lab--mostly because of the sheer amount of time lost to travel and transitions. Maybe someday my students will have computers with them at all times, or I won't be out in the portable trailer park where it takes me just short of forever to go get a chromebook cart.
I designed the task for a two-day intensive. On day 1, students use Desmos to match graphs to the paths of skiers and snowboarders.
By the end of the period, students mostly understand the vertex form of a quadratic equation: y=a(x-h)^2+k. They are able to describe what the a-value does and how to find 'h' and 'k' without sliders. I made a handout for the students to use during the class period that also includes some practice problems.
| 10i_quad_transformations_-_worksheet.docx |
Day 2 is about modeling a situation using the vertex form of the quadratic without using sliders. This means students look at real data, estimate the vertex, then calculate the a-value. They do this in two different situations.
Situation 1:
Rather than using another projectile example, I used the simple situation of rolling a can up and down a ramp. Below left is a student response on how they fit an equation to the data. Below right is an example of how well the curve fits the data.
Rather than using another projectile example, I used the simple situation of rolling a can up and down a ramp. Below left is a student response on how they fit an equation to the data. Below right is an example of how well the curve fits the data.
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Situation 2:
I use a basketball example here for two reasons: 1) the students dig it, and 2) I didn't do the greatest job tracking the data. Messy data forces student discussions about why the graph of their equation only works for the middle part of the graph but not the edges.
I use a basketball example here for two reasons: 1) the students dig it, and 2) I didn't do the greatest job tracking the data. Messy data forces student discussions about why the graph of their equation only works for the middle part of the graph but not the edges.
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| 10i_day2_quad_transformations_-_worksheet.docx |
Here's an example of some student work on the practice problems.
A huge thanks to John Stevens and Matt Vaudrey for responding to my cry for help on Twitter with insightful comments. Once again the #MTBoS math community demonstrates the benefits of online collaboration.
If you decide to give it a whirl I would love to know how it goes. If you change it up, I'd love to know how so I can tweak it with my students as well.
If you decide to give it a whirl I would love to know how it goes. If you change it up, I'd love to know how so I can tweak it with my students as well.
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