The last week of algebra consists of an introduction to statistics. They start the whole process by reviewing (for most) how to interpret graphs. Normally, this isn’t a very exciting process but I found some fun graphs to spice things up.
First I put up a blank slate and them ’em guess what it could be:
Turned out to be something like grams of fat for ingredients of a sandwich.
After we went through all the different types of graphs, here are my favorite examples of each:
Gotta keep content interesting with the end of the year looming….
Algebra is getting into quadratics. They know a bit about vertex and how to determine what direction a parabola will open. To keep momentum after introducing quadratics, I pulled a great acitivty from Dan Meyer’s Blog again.
Last year I spent an entire day on guessing and tracing where the ball would end it. It was a bit of overkill. This year I spent about 20 minutes on it, which was a good amount.
Students came up and traced the path they thought the ball would follow.
I threw the pictures into desmos and fitted a curve to them.
We watched the end of the video.
After a couple, students picked up that the ball followed the same path on the way up as it did on the way down. They are pretty comfortable with quadratics now and finding the max,min,vertex, and axis of symmetry.
“Over two out two from the origin both ways, then go beneath the x-axis, over 5 down 5, then back above the x-axis above 10 and 10 over”
Any ideas what the graph this student was trying to describe looks like?
Algebra is starting quadratics and with that comes a mountain of vocab; upwards, downwards, vertex, maximum, minimum… ect. Instead of having students read/take notes or listen to a lecture on the important of all the vocab I have them do the following:
- Break into pairs
- Each pair needs a single whiteboard, marker, and eraser
- Move desks around so students are facing towards each other; one needs to be looking at the smartboard while the other has their back to it.
- Throw a graph up on the board (Thanks Desmos)
- Without drawing in the air, pointing, listing off ordered pairs or anything like that the student facing the smartboard describes the graph as best they can to their partner (who can’t see it).
- Students struggle.
- Students get it.
- Partners switch positions and repeat.
Some of the best conversations about math happened today. Listen to a student describe to another what an exponential curve looks like for the first time ever was priceless. Students developed strategies and realized which points were critical in their partners success. They also saw the need for some mathematical framework, which was laid in place only after they encountered some tough ones.
Here are a few other graphs I threw up
Can you guess which one the student was trying to describe?
As a disclosure I haven’t taught trig before. One of my colleagues shared how he introduces it, so I gave it a try and wanted to share out on here also.
Student created a right triangle with a 40º angle.
We talked for a second about how to label each side.
After they found all the different combinations of ratios and then we threw em up on the board to compare.
They were close… but not exactly the same.
Students agreed that all their triangles were similar by AA. And theoretically ratios should all be equal.
I told a great and ancient story of how I once heard that there used to be tables with all these values for each and almost every angle in the back of textbooks. We searched long and hard for said tables but could not find any.
We threw up some general ratios and I told em about how mathematicians named those.
At this point the bell rang… tomorrow we will talk a little more then move onto Soh Cah Toa action.
Let me know what you think/how you introduce trig. This is a year one of teaching geometry sort of intro and I am really interested in how other teachers approach and introduce trig.