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!

Calculus INB – Optimization and Integration

Seniors leave early due to graduation every year in May. With the seniors, we made it through Optimization…and then spent some time on a project optimizing boxes and cans. Maybe I’ll have some time later to post about that. With three juniors, we finished up the year learning about differentials, linearization and integration. The topics don’t necessarily lend themselves to being a unit…but hey, it’s the end of the year!

Optimization was pretty much done like I did first semester, so I won’t bore you too much with those details. Integration was done in a similar fashion as that post too, though I had some time to use rectangular approximation to introduce the topic, which I did not have time for first semester due to the crazy amount of snow days we had.

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Newton’s Method: File-25-06-2014-10-39-20 A neat topic to spend a short amount of time on, relating how these numbers were approximated before the advent of graphing calculators and computers. It’s really amazing how close these approximations were so long ago!

Optimization Files

Differentials Files

Integration Files

Calculus INB – Extreme Values

This chapter is more uses for the derivatives, and how we can graph without being dependent on the graphing calculator. It seems to be an obsolete topic nowadays, but I think it offers a lot of thinking opportunities for students. They have to organize a lot of information for themselves, what each derivative tells them about the graph, how to apply the intervals and turn them into graphs. Even with the graphing calculators and apps and computer programs, it is definitely necessary. The other part of this unit I find important is the use of the theorems. These theorems really force the students to think about the hypotheses and whether they’re applicable to each problem. I think it is one of the first times since geometry that students really have to consider the hypotheses and what they are telling them. By calculus, students are definitely more mature math students, so it is nice to come back to this. Special shout out to Math=Love for the vocabulary sheets! They have been working out awesomely this semester, usually as an introduction to the chapter. I have to find a way to get my students to do this more independently next year.

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Dropbox files

Calculus INB – More Derivatives

It seems like Derivatives go on forever in this class. As I’ve mentioned before, it’s non-AP, so there is more time to spend on topics that AP goes over more quickly because we do not have to be at a certain place for the AP test at the end of the semester. Plus, these students need more time processing the Algebra involved. I always tell my students they should ace the college algebra placement test by the end of this class because we actually use all of the algebra they have learned since 9th grade, or whenever they took algebra!

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A couple of the pages were hand-written and you can see the scanned pages here: File-25-06-2014-09-47-45

I also talked about related rates applications in this chapter, but my notes were not different from the notes I posted in my post from first semester. There are several related rates posts…this is just one link.

Dropbox files.

Calculus INB – Derivatives

I really tried to focus on the use of color, especially at the beginning of this chapter, graphs of derivatives and the power rule. There were some students who continued this on throughout the quizzes and tests we took over the material. This helped those students a lot, I think. My students are mostly seniors though, and they were a little on the lazier side this semester, or they never really used this learning technique before, so were not as open to trying this.

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I also had a few pages that I scanned in since they were hand-written pages and not handouts: File-25-06-2014-09-23-35

My INB files for this chapter can be found here.

Calculus INB – Limits

I made a few changes to my INB for the winter/spring semester. I get a chance to modify some things being on 4×4 block scheduling, but didn’t seem to have any time to write about it here! Now that I’m on summer break, let’s see what I can share.

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They aren’t too different from the pages in my first INB for this chapter. I modified the discontinuities pages slightly. This semester I tried to put less information per page, knowing that I had plenty of room in the notebook to spread things out, but there is still quite a bit of information in there. I also have a link to some of the files I used. I hope it works!

Limits INB folder

Hon Precalc – Solving Systems and Partial Fractions

We’re in a rough part of the year. No breaks to look forward to…except summer, but our school year has been extended due to snow days in the worst winter on record for the Metro Detroit area. In honors precalculus, we are clicking along though. We are currently working on Conic Sections…a post I hope to complete when we finish the unit. Just after spring break, my class worked on Solving Systems of Equations and Partial Fraction Decomposition…and it was as exciting as it sounds! Here are a few pictures of my Interactive Notebook pages for the unit.

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There are a few pages different from the first notebook I did…first semester. Going through a full INB showed me there was plenty of room to expand upon some of the pages I made. There was a lot of information on one page, and not as useful as it could be…There are not too many exciting activities I have found to do with PFD, but if you have anything half way fun to do with this dry topic, I would love to hear from you!