### Archive

Archive for the ‘Geometry’ Category

## Trigonometry and Clinometers

I know Clinometers are a pretty classic geometry activity to teach Trigonometry and Angles of Elevation, but I was really excited when the activity became relevant to my students.  I planned the activity and taught the necessary lessons.  We built clinometers using straws and protectors and practiced using them in the classroom.  The day finally came for us to go outside and measure items around the school that could not be measured with direct measurement.  I was in the main office that morning checking my mailbox and one of the Assistant Principals was showing off the new banners my school ordered to hang on the light posts  that line our school drive.  My high school is celebrating our 10th anniversary.  I asked the Assistant Principal who was going to hang the banners and if they had put any thought into it yet.  To my relief he said no.  I told him my class would be more than happy to help him.

I practically skipped to my classroom and couldn’t wait for Geometry to start.  I explained the new assignment to my class.  We needed to figure out how high to hang the banners and how long of a ladder we needed.  That was all the instruction they needed.  We spent the next 30 minutes outside seeing who could get the most precise measurements using our handcrafted devices.  I did not have to explain why someone would need to know how tall some random tree is or the height of our building.  They were hooked.  I convinced them we needed to let the janitor know by the end of the day so he could make sure we had a ladder at school that could work.  The students did a really good job calculating the height of the light poles, but the real discussion happened when we tried to decide the necessary height of the ladder.  The students wanted to know what would be a safe angle for the ladder to lean and the height of our janitor.  The more we discussed it, the more ideas and questions the students had, and I was ok with that.  We ended the lesson by turning in our discoveries to the janitorial staff.  I’m not sure if they used it or not (don’t tell my students), but my students felt a sense of pride in contributing to our campus.  The real reward came the next day when the students arrived at school and saw the banners hanging from the light poles.

Categories: Algebra 2, Geometry

## NCTM Review #NCTM11

April 21, 2011 2 comments

I had the pleasure of attending the NCTM conference in Indianapolis this year.  This was my first time attending any NCTM sponsored event.  Overall, I had a good time.  I wanted to dedicate this blog post to some of the highlights of the event.

• NCTM Android App:  NCTM released an application for cell phones that had the complete schedule and allowed the user to build their own schedule.  This was amazing.  It is nice to see conference utilizing the technology that is available.  I enjoyed not having to carry the large book around.  The application also notified the user when a session was canceled.  There was a twitter feed on the app as well as a map of the conference center.
• Loring Coes did an excellent job presenting on how to make movies in the mathematics classroom.  He addressed the benefits of LoggerPro and Fathom as software packages that make building graphs and gathering data from videos very accessible.  I was sad to hear the Flip Camera is no longer going to be manufactured.  I am going to have to try to get my hands on some before they are no longer made.  Some ideas that I walked away with were tossing a hacky sack to create a parabolic curve and spinning a hacky sack on a string to create a sinusoidal curve.  Fathom was nice in that it allowed the user to build an equation to match the video and create sliders for the coefficients to discover the equation.  I think this is beneficial to the students over just running a regression in LoggerPro and having no idea how the software created the curve of best fit.
• Angie Morgan and Gordon Wells from Ohio Valley University had a good session on Quantitative Reasoning or Quantitative Literacy.  For years the push has been reading and writing across the curriculum.  It is nice to see a push towards Numeracy across the curriculum.  They talked about getting other disciplines in our school to utilize their disciplines and bring mathematics into their classroom.  This can be as simple as analyzing data in science class and comparing local and regional global warming and looking for instances of ‘cherry picked’ data.  I know personally, I have been looking for opportunities to team up with our history department.  The study of government lends itself to incorporating numeracy.  They cited the Mathematical Association of America and their work on Mathematical Literacy.
• Sherrie Wisdom conducted a session on Applied Physics in the Mathematics Classroom.  I did walk away with a good activity for my Geometry Students that could be modified for different levels of students.  She suggested that we have students trace their shoes on graph paper and find the surface area of the bottom of the shoe.  They could do this by counting squares or grouping the drawing into Geometric shapes that they know.  Students then use the equation Pressure = Weight / Area to find the amount of pressure.  The students need to take their weight and divide it by the area of two shoes.  If you have students do this with multiple pairs of shoes, they can then determine which pair of shoes should be the most comfortable.  Hopefully, students will discover that as the shoes surface are increases (slippers) the pressure decreases (as compared to heels).

## Construction Week

If your classroom is anything like mine, then the week before spring break is a nightmare.  The kids are antsy and several parents pull their students out early to get a jump-start on their vacations.  My first year teaching I gave a major test on the day before spring break:  Big Mistake.  It was awful trying to get students to make it up when they returned and of course, they didn’t remember anything.

So, for the last few years I have taken a new approach to the week before spring break, at least in my Geometry classes.  I make it construction week.  No, not building, but compass and straightedge constructions.  I decided years ago not to teach them as I went because the students can’t remember to bring their compasses to class and I’ve never invested in a classroom set.  So I put all the basic constructions in one week.

On Monday, I introduce the idea of constructions and let them play with the compass to get used to it.  I’m always amazed with how much practice it takes to get a smooth circle.  I let the students be creative and I teach them how to make a flower with the compass.  They love it.

On Tuesday, I introduce them to this Math Open Reference Website.  I print off copies of the worksheets that accompany the website and hand them out to each student.  The students are put in groups of 2 or 3 and given one laptop per group.  They use the website to complete each construction.  There is a java applet that shows them how to do each construction step by step.  There is also a list of the steps with pictures below the applet.  This allows students to go back and repeat the steps as often as they need to so they can master the constructions.  I assign 8 different basic constructions involving line segments and angles.  At the end of the week, I give them a quiz on constructions.

For the students that are absent during construction week, I assign them a project when they return.  They have to use the website to create a book explaining the constructions and provide step by step directions.  I also allow them to use YouTube for this assignment.

At the end of the week with the laptops, I was surprised and a little disturbed with the number of students that had a difficult time following written, step by step directions.  I explained to them that this is not just a math skill, but a real life skill.  There have been and will be many Christmas Eves’ spent in tears and frustration trying to interpret directions on how to assemble a bike or toy for my children.  And don’t get me started on Ikea’s picture directions…

Categories: General, Geometry

## We Built This City

March 14, 2011 2 comments

I know it has been a while since my last post.  I am teaching without textbooks this semester, and it is more work than I imagined.  In class, we don’t seem to have a problem.  I never assigned a lot of homework in the past and I very seldom referenced the book in class.  My real problem is the logistics of absent students and students who don’t pay attention in class and all of a sudden realize they want to master the past three weeks of Geometry at home on weekend, so of course they need resources.  I would send a book home, but our school has no extra books, thus the teaching without books this semester.  I have posted a ton of online resources on my class webpage, but I still have several students without internet access.  I’m learning being textfree is liberating for my classroom and limiting to students who need to work alone.

On another topic, my Geometry class completed their city projects.  Every semester, I let my students choose groups and design a city based upon the idea of parallel lines and transversals.  Several groups get very creative and develop 3D monstrosities.  Most groups of students stick to a drawing on poster board.  Either way, the ideas behind the cities are always fun.  I’ve had students design Candyland, Legoland, Classic Rock City, and even Afghanistan.

This is not an orginal project and I need to give credit.  I use a rubric based upon this one I found on the internet.  The rubric and instructions do a great job of reinforcing the relationships of angles using parallel lines and transversals.  I normally give the students two class days (we are on a block schedule) to complete the project.  I am always pleased when they realize our city, Cleveland, is based upon parallel streets and they identify important buildings in town and their angle relationships.

Categories: General, Geometry

## First Day Geometry

January 6, 2011 1 comment

Like most teachers, I struggle with what to do on the first day of class.  This year in my Geometry classes, I started with ‘Me by the Numbers’.  It worked well and the students seemed to like it, but even this activity only takes 15 minutes of my 90 minute class.  I decided to try something new.  I broke the  students into groups of 2 or 3.  I gave each group a net for a cube.  I masked each group to design a cube.  They had access to colored pencils, scissors, and tape.  Some cubes were basic and others were quite ornate.

When all the groups were finished, I collected the cubes.  I then redistributed the cubes to different groups.  Each group now had a cube that they did not design.  I handed out another blank net and asked them to copy the cube that was given to them.  Some groups had a more difficult time than others depending on the complexity of the cube assigned to them.  The students had a good time and it gave me a chance to walk around the room and get to know them.  My goal with this activity was to get my students to realize that taking a 3 dimensional object and trying to reconstruct it using a 2 dimensional template is difficult.  Some students really excel at this and others really struggle.  I feel like Geometry is often the math for those students who aren’t as good at solving equations.  I wanted to take the fear of math and the unknown away as we started Geometry.

Categories: Geometry

## Fringe Geometry

October 24, 2010 2 comments

I spent this summer catching up on Fringe and it is now my favorite TV show.  I was watching this episode the other night and was so excited :with the math involved.  I always have a difficult time teaching students the relevance of constructions.  Well, here it is.  I decided (in classic Dan Meyer style) to try to make a lesson out of it.  I am not teaching Geometry this semester, but next semester, here are my plans:

1.  Show clip and stop at 2:05.  Hand out maps of Boston.  Assign each student two major land marks on map and have them complete what Peter is doing with his map of Boston.  (The addresses used in the Fringe episode are not accurate.)

2.  The students must first take the two points assigned to them (for example, Boston Univ. and the Convention Center) and label two possibilities for equilateral triangles.

3.  The students must find the center of the triangles.  If the students seem stuck, I will show them how Peter discovers his centers.  We can then discuss that Peter actually uses the incenter and not the circumcenter.  Does it really matter in this case?  Why or why not?

I can’t wait for next semester.  (I apologize for the watermark on the video.  I’m using a free trial right now to cut out clips from DVD’s.)

Categories: Geometry