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.

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!

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.

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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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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180 – Day 50

I was out today. I went to my county ISD for a PD session on Formative Assessment. It was interesting, but since finding The Global Math Department, leading me to tweeps and the MTBoS, formal PD seems to be lacking something. But it was still informative, and left me with a lesson to try with my class.

While I was out, I left my Honors Precalculus class a notes sheet on ellipses.

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This should be review for them, though they have not worked with them in a while. I love that Desmos does conic sections so easily! It makes my notes look so much better! We shall see how they did with this tomorrow!

180 – Day 14

I know, I missed day 13…but I was out sick yesterday for an appointment. Stress fracture In my leg. It’s keeping me from running, was supposed to run in a half marathon next weekend. Guess I’m out of that. The doctor told me to stay off my feet. I looked at him like he’s nuts. He obviously has no idea what it takes to run a classroom, and sitting isn’t going to cut it! So now I’m stuck with this for a few weeks.

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Today in Calculus, we talked about where limits exist, and the ways limits don’t exist. This has been brought up several times this week with some practice and homework problems, but we formalized it for our notebook today:

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Then we ended with turning places where limits don’t exist to intervals where they do exist. I love turning the “negative” into a positive statement!

In Honors Precalculus, my students rocked their first test yesterday!  A few students who were struggling through a lot of the chapter even turned it up and did awesomely! Today, a review of quadratics before we get into everything they never wanted to know about Polynomials and their graphs! I got this foldable idea from High Heels in High School’s blog.

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The students enjoyed a different kind of foldable, and it was great to use as a quadratic review. We also reviewed completing the square relatively quickly and did a little practice with that on the LHS of their INB. I love it when I find exactly what I needed on someone else’s blog, and it works out exactly as I intended it to!

 

180 – Day 10

We made it to double-digits! Honors Precalculus was once again on the graphing kick…working more with piecewise functions, which we started on Friday. I used notes I found on Sam Shah’s site, and they worked great! Today we reviewed a bit of piecewise, and applied the transformations with (a, b). When you put everything in one problem…it really gets the student’s brain churning!

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We then moved onto Operations on Functions, the last topic for this function chapter. I made a foldable to use for their notes. We got part-way through it in my block today. This too is review, but I’m really stressing the domains with students because there is less of an emphasis on that in Honors Advanced Algebra.

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