#MTBoS30: Proving Parallelograms Pong

For the first time, in Geometry I taught a lesson about proving quadrilaterals on the coordinate plane are parallelograms.

We used three methods: slope, distance formula, and a combination of slope and distance formula. We never actually used a coordinate plane. I had students sketch the parallelogram and label the vertices in the order of the given ordered pairs.

I want to point out here that it's important to explain how to label quadrilaterals because for triangles, the order doesn't really matter. Now it does, and mixing up the letters can change a side to a diagonal and really throw them off.

Then I asked them, what two sides should be parallel or congruent to form a true parallelogram? This gave them a starting point to set up there problems and solve.

To practice, I made my go-to Pong powerpoint (see: all the pongs). It's not awesome because the answers are just yes and no and don't have worked out solutions. But considering that I could find nothing else on this topic, it's better than nothing, Literally.

My original thought was a Desmos activity but I couldn't figure anything out. I think seeing the ordered pairs on the coordinate plane would lead students to just guess yes or no based on it's looks and lose all the motivation to actually work the problem out.

Any ideas?


#MTBoS30 System of Equations: Elimination

I'm prepared to kill three birds with one stone:
  1. I'm shooting for a goal of 110 posts this calendar year to break my all time best record of 109 posts so 30 posts in 30 days will really help my count.
  2. I'm continuing an unintentional series about systems of equations from 2011 (how many solutionsgraphing and substitution)
  3. Answering @k8nowak's January call to share the unsexy, borderline boring basics.

My normal way of teaching is to do INB pages together as a class as notes and then some kind of worksheet/structure/activity to practice. Since January I've been working really hard at not giving worksheets. But this, for some reason, is just one of my golden worksheets that somehow works like a charm.

It starts with really simple vertical addition problems that lead into elimination where one variable automatically cancels out. It just keeps building from there up until you have to multiply both equations and change the sign. 

I give this out first before we ever do any notes. We do 1-5 together and then it's like you have unleashed the krakken and you can't get them to stop. Some of the problems have answer banks so they are not shown in the powerpoint. But honestly, I barely use the powerpoint anyway because they can't be bothered to look up from their papers to watch me.

It's love.

And I don't really even know why but this is probably the sixth year in a row that I've used it. After we finish this, I give them examples to put in their INBs (stolen from here) but it's more like an afterthought after all the time they've spent working these problems. (BTW this took about three full 47 minute class periods.)

It also seems to motivate them to rework problems when they mess up without me having to push for it. My guess is they like that it is answered with a nice and tidy ordered pair and they feel a sense of accomplishmeny when they finish.

But I'm just guessing.

It's definitely unsexy....and yet so satisfying!


Properties of Diagonals

This lesson comes straight up stolen from @pamjwilson. I used it last year for the first time as a full class period lesson. I used it again this year as an intro into properties of quadrilaterals.

She explains it way better than me so you can go read it. Seriously. Go. But I can share some photos from my class and the INB pages we did last year.

This is based off of an activity called The Kite Task but I couldn't find any more information on it other than what Pam posted about.

Here's the literal kite shape. The green and blue 'braces' are two different lengths. Each student gets a combination of three pieces so that they can build with congruent diagonals and without. A gold brad or fastener is used to hold them together and then they trace. Last year we used legal sized pink paper and this year they literally drew on the desk (with dry erase markers).

Next year I'm thinking chart paper and making them go to the board and switch writers each time so that there is more participation. Maybe even a competition to see which group can get the most unique combinations?

Not going to lie, the students struggled with creating different combinations besides the one example of the kite that I showed them to start with. I had a few students who I think had no idea what had just happened at the end of the activity.

A lot of students started by literally tracing the braces so we had to go over the fact that we were looking for four-sided figures.

Last year we did an entire set of INB pages just on diagonals. This year I incorporated it with our quadrilateral properties pages. Here are pictures of both.

What other suggestions do you have to make this activity better?


Graphing Tangent and Cotangent

So, thanks to Twitter, mainly @megcraig, I learned for the first time how to graph tangent and cotangent.

We just finished graphing secant and cosecant so this was a natural progression. It was also farther than I made it through trig last year (yay!) so I had to learn new math so I could teach new math.

I made this Desmos activity to introduce the tangent curve.

We summarized what they figured out with some example graphs on Desmos and then we went to these INB pages of actually graphing.

Those pesky negatives can get the best of anybody.

If you haven't noticed a theme here, I'm a really big fan of windowpane graphing. Also, it's the only way I know how to graph.

Here are the pages:

And a matching PowerPoint:



Earlier this year I introduced function transformations through absolute value functions. I always feel like this is such an obvious lesson but I didn't get that same feeling from my students. They could see it when they looked at graphs and equations but not just by looking at an equation.

I originally called this dry erase build-a-function because I was going to have students just write equations on their desk. Then I decided to actually make them pieces to literally build-a-function with their hands.

I think having pieces to choose from helped them make connections quicker because it didn't seem to materialize out of thin air. It narrowed their options.

The first half of the Powerpoint described a function and students created the equation. This focused on only absolute value functions. 

For example, the slide says:

Left 4
Down 5

And the students build this:

The second half of the powerpoint gives them equations and they have to identify the type (linear, quadratic, absolute value, exponential) and the transformations.

For example, the slide says:

y = -|x+4| - 5

And the students build this:

Another plus about this activity is that you don't need a fancy powerpoint. Just write it on the board or say it out loud and students go to work.

Low prep FTW.

Here are the pieces:

I printed each groups on different colors of paper and laminated.

Here is the powerpoint:

Good luck!