It was an exciting class period recently in my Geometry Honors class. We switched to having our Honors Students buy TI-Nspire CX calculator this year. There was some grumbling from parents - like what is this expensive new calculator going to be able to do better than the tried and true TI-83 or TI-84. I patiently explained what I thought would be the advantages - like we can use the Geometry App, I can send the students documents using the TI-Navigator, and my personal favorite - there is color.

I have been working with the students recently on altitudes and medians. We talked about the centroid and the orthocenter. For some reason I like talking about the Euler line - it's just cool! I usually have the students draw a triangle and we draw the medians. I have them cut out the triangle and balance it on their pencil at the centroid. They think that part is neat, but the measuring and drawing in the medians - it's painstaking...as embarrassing as it is is, there is always someone - even in honors math that doesn't use the ruler correctly, etc.

This year I decided - hey we have this cool new piece of technology, let's try doing this activity on the Nspire. Needless to say, it took about 1/4 of the time. The kids loved it. They showed me some new ways to do things, and I was able to fill in lots of other information at the same time. For example, I could show them how the medians ALWAYS intersect in the centroid by having them drag the vertices of the triangles. And, I could convince them that sometimes the altitudes DO go outside the triangle - they could tell me when that happens (when the triangle is obtuse) instead of me having to draw several examples and hope they believed me.

Also, I used a great activity from Teachers Pay Teachers from Emily Allman. She designed it as a performance task. I really enjoyed using it. Check it out Triangle Centers Performance Task.

## Saturday, October 27, 2012

## Thursday, October 25, 2012

### Thinking About Geometry Proofs - Do They Get It?

Another year and another chance to teach students about Geometric Proofs...however, they are all starting to seem the same to me - how can the students not see another another set of vertical angles - another line that is shared by two triangles - JUST WRITE DOWN REFLEXIVE ALREADY!

I often wonder if the students really understand what we are doing here - or are the students that are successful at proofs the ones that are super good at copying what I am doing? Do students honestly understand that SSA can't be used to prove triangles congruent, or do they think that I just don't want them to use those combination of letters because they spell a bad word if you look at it backwards???

No matter that I have explained until I am blue in the face...

I have honors students, so I think they should be able to understand, but do they...

I think that when I show students later in the year a "proof" of the Pythagorean Theorem - note: no two columns involved...that they appreciate a teenie tiny bit of the beauty of mathematics.

But, back to these congruent triangle proofs...I am open to suggestions on making them more exciting and fun - do you have any suggestions??

I often wonder if the students really understand what we are doing here - or are the students that are successful at proofs the ones that are super good at copying what I am doing? Do students honestly understand that SSA can't be used to prove triangles congruent, or do they think that I just don't want them to use those combination of letters because they spell a bad word if you look at it backwards???

No matter that I have explained until I am blue in the face...

I have honors students, so I think they should be able to understand, but do they...

I think that when I show students later in the year a "proof" of the Pythagorean Theorem - note: no two columns involved...that they appreciate a teenie tiny bit of the beauty of mathematics.

But, back to these congruent triangle proofs...I am open to suggestions on making them more exciting and fun - do you have any suggestions??

## Sunday, October 7, 2012

### High School Math Competency Test

One thing that I think is very important in high school math is that students master certain basic skills. However, it is very frustrating as time after time, students don't master them!

For example, I actually had a student in my Geometry Honors class tell me the other day "I don't know how to do this one - I don't do percents." Hmmm...how to respond??? Other examples could follow...students in AP Calculus who say - I know I need to find the equation of the tangent line, but I don't know how to do that (even though I've done about 5000 examples!)

So, I thought about it for a long time and decided that there are some skill based things that students absolutely HAVE to be able to do...how are they supposed to solve harder problems without being able to do basic things? So I decided to start using the idea of a competency test in my classroom.

Here's the idea. I have 5 different competency tests each quarter. Each one is worth 10 points, so a total of 50 points. Students have to keep taking the competency test until they achieve a score of 10/10. This quarter I used the idea in my calculus class for the first time. The 5 competency tests were: 1) Factoring, (2) Writing Equations of Lines, (3) Trigonometric Convenient Values, (4) Right and Left Hand Limits, (5) Basic Derivatives.

I think this helped the students in two ways. First, it forced them to learn topics that they previously didn't focus on enough to master. Second, it gave them 50 points that they easily could get if they put their mind to it : )

If you'd like to see a couple of my competency tests, visit my store on www.teacherspayteachers.com

http://www.teacherspayteachers.com/Product/Basic-Factoring-Competency-Test

http://www.teacherspayteachers.com/Product/Competency-Test-Basic-Derivatives

See you soon!

For example, I actually had a student in my Geometry Honors class tell me the other day "I don't know how to do this one - I don't do percents." Hmmm...how to respond??? Other examples could follow...students in AP Calculus who say - I know I need to find the equation of the tangent line, but I don't know how to do that (even though I've done about 5000 examples!)

So, I thought about it for a long time and decided that there are some skill based things that students absolutely HAVE to be able to do...how are they supposed to solve harder problems without being able to do basic things? So I decided to start using the idea of a competency test in my classroom.

Here's the idea. I have 5 different competency tests each quarter. Each one is worth 10 points, so a total of 50 points. Students have to keep taking the competency test until they achieve a score of 10/10. This quarter I used the idea in my calculus class for the first time. The 5 competency tests were: 1) Factoring, (2) Writing Equations of Lines, (3) Trigonometric Convenient Values, (4) Right and Left Hand Limits, (5) Basic Derivatives.

I think this helped the students in two ways. First, it forced them to learn topics that they previously didn't focus on enough to master. Second, it gave them 50 points that they easily could get if they put their mind to it : )

If you'd like to see a couple of my competency tests, visit my store on www.teacherspayteachers.com

http://www.teacherspayteachers.com/Product/Basic-Factoring-Competency-Test

http://www.teacherspayteachers.com/Product/Competency-Test-Basic-Derivatives

See you soon!

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