Transformations

It has been a long time since I've written a post that I hope I still have readers?  I have so many posts to write to wrap up last school year. Hopefully I can get them all done in the next week or two, because I have so many exciting new things about THIS school year to report on! (We just finished week 3 of the 2013-2014 school year)

Mid year last year we did transformations in Geometry, but since I know it's a huge portion of CCSS for Geometry this year, I thought I would write about what we did since many are starting this school year off with it.

This page of our Geometry ISN covered Reflections, Rotations, and Translations.  The left page went over what each of them meant and had an example.

The right side had the definitions along with a practice problem for each type.

The students easily caught on to Reflections and Translations, but had a more difficult time with Rotations.  To get students to understand how rotations work and why a shape ends in the position it does took some time.

To help them see how shapes rotate I gave them the graph paper in the pictures and we drew different shapes on each graph.  I then gave them each a blank transparency and Vis-A-Vis marker.  Students placed the transparency over their graph paper, and traced the shape with the Vis-A-Vis marker. They would put their finger on the point of rotation and then rotate the transparency the correct number of degrees and in the correct direction.  The outline on the transparency shows the students where the shape will end up.  Then they would draw the shape on the graph paper.  After doing the four on the page, they felt a lot more comfortable with rotations.  Some no longer needed the transparency to do the work, while others relied on it a little longer.  By the end they were doing rotations without any problems.

Station Activities

At the end of each year I like to think about what worked and what didn't work for my students so I can improve for next year.  Since I'm the only Special Education Math and Science teacher for my building/district, I have the same kids for 3-4 years.  So reflecting back really helps because I can see the improvement in my students and myself from one year to the next.

So what I have found out about this past school year is that my students absolutely LOVE their ISN and Station Activities.  There are many things they enjoyed about this year but those are their most favorite, and are the most effective.  

Here is how I create my station activities.  At the end of each day I give my students an exit ticket, and the exit tickets are based on the current unit objectives.  Sometimes if I know my students will need to use a previously taught skills I will incorporate that into the exit tickets as well.  These formative assessments allow me to see where each of my students are at; what they know and what they don't know.  Based off of that information I create my station activities.  

For this example we were just starting to work on writing equations in slope intercept form and some of objectives were:

I can calculate the slope given a graph, table, or two points.  

I can determine the slope and y-intercept of a line given the graph of a line.

I can write an equation in slope intercept form given the slope and y-intercept.

My students were given the exit ticket after we went over the ISN pages and did some whole group practice.  When they were finished I checked them to see which problems they got right/wrong.  For this class I had students who got problems incorrect from each objective, so I created stations based on each objective.  

This time I assigned them specific stations they had to complete based on the problems they got wrong from the exit ticket.  If there was time they could go back and do the other stations for practice.  Other times I have had stations for a test review and each table had an activity based on each of the unit objectives.  When I do this they are expected to finish all of the stations.

The main reasons why I like stations is because they get the students up and moving around the room, it allows me to work with individual students, and lastly they get excited because it isn't just a boring worksheet.

**I used Expo Neon Dry Erase Markers on my black lab tables, they wipe away easily with a wet rag. If you don't have black tables you can use regular colored Expo Dry Erase Markers on tables or student desks.**  

Angle Sum Theorem

I've taught Angle Sum Theorem in the past but I felt as though my students didn't truly understand what it means or how it actually works.  They can tell you that all angles in a triangle add up to 180 degrees, but if you ask them how do you know it's true they couldn't give you a good reason.  I usually get the response of "because you told us it does".  UGH!  Not the response I'm looking for.

This year I was determined to find a way that would help them understand just how it worked, and I came across these two different methods.  I used BOTH.

The first method is where you give students three different triangles: Equilateral, Scalene, and Isosceles.  They color each of the angles in the triangle a different color and rip off the angles.  Then they have to join all three angles, and in the end they form a straight line which they know measures 180 degrees.

The second method we used is where each student again is given three different triangles: Equilateral, Scalene, and Isosceles.  They again color each of the angles in the triangle a different color.  They start off by folding the triangle to create an altitude. Then the top angle is folded down to the point where the altitude and base meet.  The two other angles fold in, showing all three angles lined up creating a straight line.

They liked the folding method because when they glued them into their ISN they were able to fold and unfold the triangle as many times as they want.  The ones that were ripped could only be done the one time.

Here are the left pages when they are finished.  

Unfolded Triangles

Folded Triangles

On the right side of their notebook we worked out several different types of problems involving the angle sum theorem.  We also revisited supplementary angles, vertical angles, as well as the different types of triangles and their characteristics.

Overall this page so far has probably been their favorite.  I succeeded in getting them to understand why the angles in a triangle add up to 180 degrees, and I no longer get answers of "because that's what you said".

Angle Sum Theorem(1)

Angle Sum Theorem Practice Problems Sheet

Naming Triangles

We moved into Triangles in Geometry class and we began by naming them, using both the name based on their sides as well as the name based on their angle measures.

The students were given a sheet that contained all 9 triangles.  They had to cut them out and then sort them into groups based on their similarities.  At this time they were not given any of the names.  Students had to explain why they grouped certain triangles together.  They were also told that one triangle could not fit into more than one group.  This proved to be a challenge for some of them, but after awhile they were able to figure it out.

Everyone came up with that we could group them based on their sides, or by the types of angles.  We decided as a whole class to glue them into our ISN by groups based on their sides.

We went through the six different names for triangles and what the characteristics were for each of them.  After that they were asked to go back and name each yellow triangle using two names.

When they were done they were given this half sheet of practice and asked to go through it.  I had them start off on their own, only working through the first three at the top.  After that we went over them and I had them work in pairs for the bottom section.

Many of my students used different colored highlighters to make each of the triangles in questions #1-5 stand out so they knew which ones to focus on.

Under this page is where my students wrote down the six different triangles: acute, right, obtuse, equilateral, isosceles, and scalene.  They also were asked to summarize the characteristics of each one.

Triangles

Triangles Practice Page

Characteristics of Trapezoids

When we covered characteristics of trapezoids I wanted to make our ISN page different than the rest that we have done.  I looked around at other teacher's blogs to see what kind of cool ideas they were doing and I saw a post that had a page with a pocket on it.  I LOVE the pocket idea!

<~This is what our page looked like when it was completed.  We covered the three different kinds of trapezoids: Isosceles, Right and Scalene.

To make the pocket I gave students a regular size index card that we taped on three sides.  To make the cards the students cut out the green boxes and glued those onto the regular size index cards as well.

Each type of trapezoid got their own card, which we colored equal angles the same color and identified characteristics about their sides.

I had the students use protractors to measure each of the angles in the trapezoids to determine which ones were equal to each other and then color them.  After that we wrote the characteristics of the angles down under the characteristics section. We then began talking about the sides, some students needed to use rulers to measure the lengths because visually they weren't sure which ones were equal.

We then started discussing what equations that we could come up with for each of the trapezoids.   What we came up with we wrote under the equations section.

They then were given a green sheet that had problems involving trapezoids on them.  Students had to cut them out, then decide which problem belonged with which type of trapezoid.

Once they match up the problem with the type of trapezoid they glued them onto the back of the card.   Using the characteristics and equations they discovered on the front, they had to solve the problems on the back.

When they were finished we went through them together and they were given their practice for the right page.


Here is their practice page on the right. ~>

Trapezoid Cards

Trapezoid Problems