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!

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Unit Two Logic Honors Geometry

I want to say first and foremost, many of my ideas and inspirations for this unit came from a couple fantastic blogs. First, Mrs. E Teaches Math, and also Meg Craig! Thank you for sharing what you do with all of us! Many of the pictures you see here are because of their creations. Teaching is a lot of inspiration from others. #MTBOS on Twitter is a great start if you haven’t found it yet!

First a little Inductive Reasoning

Then logic vocabulary.

Deductive Reasoning is next.

Here are my deductive reasoning notes.

Next we investigate about angle pairs and do a little introductory proofs. I am thinking of making these proofs a little simpler, as I have a lot of 8th graders in this class and they’re not always ready for this many steps.

The Linear Pair/ Vertical Angles investigation can be found here.

Finally, I wrap the chapter up with some Parallel Lines work and a little more proof.

There are many cut and paste proof activities out there. I find these best to get the students to think about a logical order. They are not going to be perfect at Geometric proof at first. It takes work!

Unit One Honors Geometry

It has been a while since I have blogged (at all), but specifically about Honors Geometry. Some have asked about my INB pages recently, so this is probably the most efficient way to share! I use so much from others helpful sites too. Hopefully I am able to link you to their sites as well, accurately!

Our first unit is the language of Geometry and getting the students to write definitions precisely. Some pages are similar to ones I have used in the past. We start with the basics…

Link here

I don’t have the link to the above notes right now. Sorry!

I also do an activity similar to the one here, except I laminated and students work together to complete.

Next, my students review some Algebra with segments on papers I got from Mrs. Newell’s site. And I made up a practice paper.

Here is the file.

We then move on to Angles. Again, I modified some ideas from Mrs. Newell (angle pairs) and made up some work myself.

Next, polygons and triangles.

The right side of triangles I found on Mrs. E’s site. The LHS is mine.

More definitions, this time polygons.

And finally, a lot of circle definitions from Mrs. Newell.

That’s unit one! Unit Two is another mix from many sources. Maybe I’ll get a chance to go through it soon!

AP Calculus MPACs

Nothing major to share tonight, but did create some classroom decorations I wanted to put out there. AP Calculus has Math Practices similar to the common core. I made some displays to remind me and my classes (AP and Honors Precalculus) why we do the things we do.


The first is a link to the actual MPAC banners. This second link is to the subtopics banners. These are editable PowerPoint files. I will try to edit this post with PDF files if I think of it later.


Enjoy!

#MTBoSBlogsplosion Round #3

Better late than never, right?! I read the prompt for this week’s Exploring the MathTwitterBlogosphere and thought…who is spying on me? Has the MTBoS found a way to get in my mind?! Next week, I will start teaching Honors Trigonometry for the first time in 2 years. I was looking over my old Interactive Notebook and realized I had only used the INB idea once for honors trigonometry, so some of the pages could use a makeover. Off to Pinterest I go! My colleague and I share a Trigonometry page so I wanted to see what was there.
A few minutes on Pinterest led me to Sarah’s Math = Love site and Shireen’s Math Teacher Mambo blog! Great blogs, if you have never been! They both have fabulous ideas for my beginning Trigonometry unit. The pages I used the first time teaching this course with an INB are not bad, but I like to spice things up with some fresh ideas.

The first unit in trig consists of a lot of angle basics necessary for the rest of trig. First, I saved an idea from the agony and dx/dt‘s page to explore what a radian is. I have done this activity before, or one similar…with string. How boring is string when you can use candy!!!!


Twizzler’s Pull and Peel to be exact. I love using food whenever I can, and don’t know why I didn’t think of that! I will probably do something like Sarah’s pipe cleaner idea when transferring the lesson to their notebooks, candy doesn’t last on paper.


Instead of my boring sketching angles pages, I am going to use the cool page Sarah created. I even get to use a fastener so the angle rotates in the notebook! Oh boy oh boy oh boy!


What drew me to Math=Love’s trig page was her Coterminal Angles Sort. So that will be next in my notebook.


The coolest thing ever in getting students to understand reference triangles and special angles though might be from Math Teacher Mambo, and I am so excited to give it a try and see if my students think as highly of it as I do! I love how colorful this all is…and I especially like doing something that helps with student’s understanding of fractions.


That is as far as my thoughts have gone considering I am not yet done with this semester and have some planning yet to do with my current classes. The MTBoS is so helpful and I love that these teachers have provided links to the handouts. Things I create will too be uploaded here…as the unit goes. It is so tough to choose just one thing to write about as far as the usefulness of this community, I utilize so many great ideas every day and try to make them my own. Please know I appreciate all of your blogs so much for inspiring me. Thank you for sharing your ideas!!

Honors vs Non-Honors

There are many instances in my classes where I tell my students “This is where you earn your honors points.” At our school, students earn an extra half point for taking a class with honors in the title and an extra point for an AP class. This is to reward/encourage students to take the more challenging version of the courses, or just the challenging course if there is no other non-honors counterpart.

This year I taught both Honors Geometry and Geometry (skinny version). The skinny version of Geometry is slightly different from the Block Geometry we have and from the Honors Geometry class. Some of the time, Geometry is Geometry, and there are things we need to do regardless of the class. Sometimes students “earn” their points in Honors, whether it is through tougher problems on assignments and assessments, the speed at which we work on topics or through the level of notes we take together in class. Here is an example of Honors Geometry note for Special Parallelograms…

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hon geom special parallelograms notes

Pretty basic and right to the point. Students have to spend some time sorting through what makes something a square versus a rectangle versus a rhombus on their own after we talk about what determines each special parallelogram. Then students summarize their thinking by completing a table, checking the quadrilaterals and their properties.

As far as Skinny Geometry goes, a little more time and instruction is necessary for students to completely grasp the concept and we spend more time sorting through the differences together. Here are some pictures from our interactive notebook:

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Then we get into the coordinate proofs:

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We do additional work in class, including a coordinate proof maze I made up in both classes. we complete them a little differently in each class…both being partner work though. In skinny, time is also spent on the properties with a card sort. We did not have time to play the card sort as a game (spoons or go fish) but that is something I would like to make time for in the future.

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Avoiding Worksheets

In my spare time, I love to peruse Pinterest. You can follow me here. I think it’s relaxing…even if I don’t particularly need new activities for the topics I’m teaching at the moment. I may find something useful, or something to store for later. Most of the time I get ideas…not anything I use as is. But there are so many creative teachers out there who give me great ideas for my own class. Today was one of those days I used a lot of what I found on Pinterest, with my own spin.

In Honors Precalculus, we worked on a Maze Review for Polynomials. This activity was intended as an in class review, to get students familiar with the skills they still need to fine-tune when they go home to study. This is an example of a time where it is better to pay a fellow teacher on Teachers Pay Teachers for an activity then try to recreate the wheel. The activity was perfect for what I wanted my students to do in class.

I was particularly proud of the MathLib I did in Calculus though. We are beginning our chapter on Derivatives and the power rule, but I know that half the trouble (or more) that students have with this rule is their understanding of exponent properties. Sometimes they haven’t even thought of this since Algebra One. So we did a quick graphic organizer on the Exponent Properties and tried a few tougher examples together. Then students paired up to tackle the MathLib. I got the idea from Pinterest, using All Things Algebra‘s Similar Triangles MathLib in my Honors Geometry class last semester. The students enjoyed it, and I like that these types of activities give students a chance to practice the math and know if what they chose is correct almost immediately. They serve the purpose of a worksheet, without the bore of a worksheet. Plus, working on it in class gives students the opportunity to ask questions of each other and me. Here is a shot of one of my slides…and I’ve linked my dropbox file here.

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I used some fonts I found on Pinterest, mostly Kimberly Geswein fonts. The students had fun with the nonsensical MadLib and were able to fix any mistakes they might have made by the end of class because all I had to do was check the answers they chose:

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If there was anything wrong…they went back and tried again, something students do not do too often on a typical worksheet.

My final Pinterest inspiration for today was in Geometry. We are working on our Area unit, and in need of breaks from the typical area problems in the book. We spent Thursday and Friday talking about the basic area formulas (parallelograms, trapezoids…) and today we took some time to start their banner problems. We only had time to do 4 of the problems, but it was a good start since we haven’t spent too much time in this unit yet. Screen Shot 2016-03-07 at 7.06.13 PM.png

I got the idea from Scaffolded Math and Science. She has a ton of great ideas on her site, including her own area banner activity. The problems on hers would not have completely been right for my group of students, so I created my own. I appreciate the inspirations, they really get my mind working.