#myfavfriday

What a long week…every Friday I feel it. There were some great moments this week though.

On Tuesday, the 9th graders in my Honors Geometry were at an assembly. Just enough kids that would make it a pain to move on with the remaining 8th graders (they come up from the 3 middle schools to take the course a year early). I was at first struggling with the thought of what to do…and then MTBOS! Of course we would spend some time with WODB and counting dots! This group of kids got into it! They were all geeking out over it, not worrying about others thinking they weren’t cool. Love that these kids have a place to enjoy math!

In AP, we were working with the definition of the derivative. Since it’s BC, chances of them seeing this on their test are low. They do need to recognize the functions and the difference between average and instantaneous rate of change. On Facebook someone posted a picture of an activity that looked intriguing to me as an opener. Rather than rewriting the cards every year, I typed the expressions on “cards” and I plan to laminate them when I get a chance. It turned out to be an ok activity 2nd hour…but so much better 3rd as usual after an hour of experience!!

Cards

Yesterday, as part of my basic derivatives lesson we worked on this Desmos activity to “discover” the derivative of sine and cosine. The kids found it very useful to remember how those derivatives happen!

Sine Cosine

I forget where I found the links but I know it was in the #mtbos.

And to top the week off…Math with Bad Drawings came in the mail today! I had a stack of papers to check, but not sure I’m going to get to them now!!

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Honors Geometry Unit 5-Polygon Properties

Another #MTBoSBlaugustpost!!!

I created a lot of items for this unit last year. Strange because of how busy I was with my AP Calc class, but nonetheless, here you go!

Polygon Angle Conjectures are first up. We begin with an investigation and sum this up with some conjectures. Students have different shapes on the back of the chart. They answer the row according to their shape and walk around to find others who have different shapes.

Kites and Trapezoids are the first quadrilaterals we talk about. Within the notes there is some investigation work we do to complete the conjectures. I do this on patty paper. I made these flip book notes last year.

And the LHS of each is a short reinforcement worksheet. Kite Trapezoid

We first discusses midsegments in the construction unit. Here we continue the discussion with a few conjectures. I don’t have anything exciting for this topic. The students are usually amazed at the triangle conjectures. Yeah, my students are a little nerdy! Most are 8th graders that come to the high school from the middle schools to take the class.

And then there are parallelograms. I made up most of the items, though I got some ideas and worksheets from Mrs. E’s blog. Especially when teaching AP Calc for the first time this year, like I did, other teacher’s ideas and work is so much appreciated!!

I do some coordinate proofs, again some things from Mrs. E. I made this up:

I then do some quadrilateral proofs, mostly for the thinking exercise. I used to do so much more and I think they are great for reinforcing the ideas in the unit but it usually comes at the end of the term. Exams come up and ruin all the fun.

Polar Graphing Activities

Happy #mtbosblaugust once again!! I was thinking about some of the activities I did in Honors Precalculus and AP Calc last year to reinforce some new or tough ideas, thinking about what worked and what to use again this year. I’ll briefly try to describe something I learned last summer at an APSI from Dr. Joe Brandell, our AP Calc guru!

Graphing polars is a topic discussed in my honors Precalculus class since we now have a majority students who move onto AP Calculus BC. I do everything from plotting points by hand, plotting on graphing calculators and on Desmos. All seem abstract to my students but they are fun to play with, especially with sliders on Desmos. I don’t want to even think of a time before Desmos existed!

Back to the activity from Dr. Joe. He introduced our group to human polar graphing!! You will need a long rope and a lot of space, oh, and a class of students! Depending on how new or quick students are at computing the radius from given theta, you may want to give them an equation or two to create a table. Pick a point to be the pole (origin in polar) and how far out a radius of 1 or 2, etc. will be.

The first student will hold onto the end of the rope and find their first point in the polar space you created. Then the next volunteer will hold onto the rope at the point of the second coordinate, etc. Eventually, a circle or a cardioid or a rose…will be in the space with kids as the coordinates and the rope as the curve! Human Polar Graph!!

Another polar graphing activity that I do thanks to Infinite Sums can be found here. Now, his goes on and on and I strive to do that with my group! We started small this year.

It was very fun, and who doesn’t love to create with sidewalk chalk?! This is a great activity to get the students to practice plotting points and graphs. It usually shows up at a nice time of year where we need to get out of the class.

Honors Geometry Unit 4…Triangle Properties

Day 2 of #MTBoSBlaugust!!!

This unit will focus again on what’s in my Interactive Notebook, but there is a proof activity I found from All Things Algebra. Other class activities are done depending on the needs of my students. I’m always chainring things, so who knows if theirs is how my unit will look this year!

The unit begins with a triangle sum activity I found on Math by Tori‘s site. Here are pictures including a proof.

They practice this with a worksheet from Mrs. Newell‘s page and one I created.

This is followed up by Exterior Angle Theorem which uses similar activities from the same sites.

Is it a triangle and Triangle Inequality activities are next. Students use snap together sticks (AngLegs) and this worksheet I think I found on Misscalcul8’s page a while ago to investigate what makes a triangle and I sum the activities up in notes from Mrs. Newell.

Finally, we get to congruent triangles, starting with a review of how we know things are congruent… the spacing may need to be adjusted.

Many activities to reinforce the shortcuts. Notes from Mrs. Newell

A cut and paste activity from TpT

And practice

Finally, proofs! Mrs. E and Mrs. Newell have a lot of proof tips for students on their sites.

And CPCTC

Thanks for reading!

I’m Dishing it Up…

This post is intended to take part in the Virtual Conference of Mathematical Flavors.

Are the students taking it?!

As a teacher, you always wonder this. There is a lot of work that goes into my lessons. Creation, modification, connection, copies, practice, etc. We all know what it takes in our own classroom to effective (hopefully) get mathematical ideas through to teens in an ever-illogical world. But do the students see that??

2017-2018 was my first year of teaching AP Calculus, and BC nonetheless. A perfectly stressful agonizing year full of planning and homework and learning (and that’s just me!). Would my students learn what’s necessary? Would they see the work I did to try to help them get through this crazy course? The answer of course is yes. I didn’t always know that, but as long as I show my students each day that I care if they are successful, they will do their best to work at being successful. They won’t always show it in an obvious way. They won’t yell it from the back of the class. They will slack and have senioritis. As long as I don’t give up on them and bring it every day…they will get it. They will also appreciate it in the end. Just keep showing you’re willing to put in the work for them and they will put in the work for you. Let’s be honest…we didn’t go into this gig for fame fortune and fandom!!

Honors Geometry Unit 3- Tools of Geometry

Today is August 1st…and a girl from work posted on FB “August 1st is the worst”. It can mean thinking about work again, and working is worse than playing! But August 1st also means #Blaugust!

Unit 3 in Geometry means Constructions! I love constructions, though not all kids tend to feel that same love. It seems that less and less emphasis is put on constructions since no standardized tests ask students about them, but I think a lot of learning and investigating can be done with just the basics.

The first page in my notebook is a Basic Constructions instruction booklet I found from Crazy Math Teacher Lady.

I use this throughout the first few days of the unit, introducing each separately and giving the students practice time.

I use compasses and patty paper.

Segment/perpendicular bisectors lead to a couple of conjectures (Theorems the students discover) and some other vocabulary.

I’ll try to remember to post some links to these when I get into school. I don’t have them in my Dropbox right now.

Altitude is another use for perpendicular lines. (The link is .docx, so the font and spacing may be a little off. Sorry!)

This gives us skills to construct squares and rectangles too.

The last construction skill that is important to me is angle bisectors.

I did constructing parallel lines by duplicating angles last year, but am struggling with the necessity. It does reinforce what we learned last chapter. I still have to give that more thought.

I wrap the unit up with Points of Concurrency. This is my page from last year…

I read a post today that may have me rethink the end to my unit. Give Me a Sine has an awesome PBL project I’m thinking of adapting to my class. Students need to answer the question “where should the grocery store be built?” to help people in “food deserts” (watch the video).

I want to find some constructions activities for classroom practice. Homework didn’t work well this chapter especially if the students did not fully understand what they were supposed to do at first.

Unit One – Limits, AP Calc

I made it through a year of AP! Well, pretty much. My students were successful, but time to change up a few things for next year.

I started to go through my INB to see what kind of changes could better help my students. Also, I’m considering how I could incorporate other activities to reinforce what I’m teaching. This is how my unit starts:

I typed up a table of contents for them to show the Learning Objectives from the AP curriculum. I’ll take a picture of the next couple of pages, but I’m changing them up a bit.

Here is a link to the modified file for limits graphically and numerically. The delta-epsilon definition is not something I spend a lot of time on but I do talk about with my class. I’m putting that on its own page this year.

Last year I used a lot of the notes I already had from regular Calculus.

I’m changing it up a bit…making it more about content than a cute note sheet.

And properties.

Next, continuity. I found some good notes on Teachers Pay Teachers.

Onto Intermediate Value Theorem. This is important, but not too big of a challenge for my group as we talk about it in Precalculus.

This google site has been helpful to me in organizing my thoughts after a year.

Limits at Infinity wrap the chapter up.

This year, I’m hoping to give my students more opportunities to see AP questions (or AP-like). I want not knowing how to start right away to become no big deal by May. That’s tough for these kids because they’re so used to knowing, or feeling like they should know!