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!


My First Desmos Activity

For once I was actually planning ahead and thinking about how to introduce transformations of trig functions.

I wanted to use Desmos so I outsourced to Twitter.

Here's one from Tina Cardone and one from Christie Bradshaw. As usual, my mind had created something else, I just had to figure out how to get it to the students.

So I decided to teach myself how to use activity builder and make my own Desmos.

You guys.

It is sooooo simple. And elegant. And easy to learn. I had to google how to make a slider but other than it was very intuitive.

When I used it in class I was SO proud. I walked around with an iPad watching my students move slide to slide and answer questions. Every student was engaged and the classroom was totally silent. But they could see each other's answers so there was still some sort of communication.

I literally had to turn away because I was smiling so huge for no reason.

Here it is.

The next day we followed up with these INB pages:

Here are the files:


Creating the Sine and Cosine Curve

While some people are not fans of this lesson, it's my second year doing it and I like it well enough. Here is the link to the actual Illuminations lesson.

You need butcher paper, yarn, spaghetti/fettucinni, yard sticks, measuring tape, and Sharpies.

I break the project into parts. First I send students on a 'mission' to get the butcher paper. When they come back, I have supplies laid out for them. They follow the directions to create a unit circle and function graph.

They then move on to the second sheet of directions. In this section they are using a giant protractor (printed on transparencies) and a yardstick to measure increments of 15 degrees around the unit circle.

Next they wrap the yarn around the circle and mark the angles with Sharpie on the yarn. This is so they can stretch the yarn out on the function graph and transfer the angles. They then label the function graph with degrees. The fettucini is used to measure the vertical distance on the unit circle from the each angle to the x-axis. Then it is placed on the function graph where students make dots and then eventually connect into the sine curve (remind them where sine should be positive and negative, above or below the x-axis). Last they will label the x-axis with radians.

One of my favorite parts of this is printing each question separately on a post-it (each pair gets a different color).

I give them questions #1-6 on post-its. They write the answers on the post-it and tape it to their paper. I do this by first printing on regular paper. Then place post-its over each box. When you print the second time, remove the outline of the boxes to print words only on each post-it. I think it helps students not be overwhelmed by focusing on one question at a time.

After #1-6 (this also gets printed on a post-it) it's time to measure the horizontal lengths from each angle to the y-axis and create the cosine curve (they will need some prompting with this idea).

And the last four questions printed on post-its.

As each pair finishes, I give them reflection questions. I'm really proud of these. They have to analyze their graph and compare it to exact values from the unit circle and the calculator. My goal was for them to realize where the curves come from and think about what the numbers mean and I think I accomplished that.

We follow this up in our INBs with these two pages.

Here are the files:

And here are some 'live action' pictures from my class.

The final product


Algebra II Unit 4: Quadratics Interactive Notebook

Unit 4: Quadratics

Page 33-34 LHP Wax paper parabolas stolen from Sarah Carter. Interesting to do but we never came back to directrix again. RHP I loved this super cute envelope and the idea of these flash cards- color coded even- but it's just sooo much information. It's really hard for students to keep all of these separate.

Page 35-36 All my factoring stuff comes from Sarah Carter. And the Zero Product Property came from Google.

Page 37-38 Giant plus or minus sign again comes from Sarah Carter.

Page 38-39 I think I created this myself but I'm not sure. I liked having students decide what form on the RHP before solving but again, this is a lot of information to cover and keep straight.

Page 41-42 I will always and forever teach completing the square geometrically, thanks to Mimi!

Page 43-44 I've been doing a discriminant sort for a couple years where students find the discriminant and then sort into three groups. This was the first year of me realizing the magic of having students find the discriminant first, then plug in their answer under the square root and do the rest of the quadratic formula. Somehow, there are way less arithmetic mistakes this way.

Here are the files: