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

Quadrilaterals

So I thought over spring break I would catch up on all of my blogging, find cool new activities to do with my math students, and create some new ISN pages.  Well needless to say that never happened...

We covered Quadrilaterals in Geometry class, however we only went with regular quadrilaterals for the time being.

My students love charts, and when I say love I really mean LOVE!!  It's weird how excited they can get about a chart, but whatever will make them happy.  So to cover the characteristics of the different types of regular quadrilaterals I had my students fill in the following chart.

We started off drawing a picture of each shape and from there the students told me what to write in both the "Angles" and "Sides" boxes.  It turned into a whole class discussion where all I did was fill in my chart as they told me what to put in it.

My students will admit that they are not the best artists (frankly neither am I ), so made these shapes on the computer for them to cut out and tape into their notebooks.  Students used rulers and protractors to help them figure out what angles and sides were congruent. As they discovered characteristics of the quadrilaterals as a class we wrote the information below and to the side of each of the shapes.  We did go through in the beginning identifying each of the shapes by name, then color coding their different characteristics (color chart at the top) that they had discovered through their exploration of the 6 quadrilaterals.

**Update: Both pages have been change to reflect the correct information for Kite**

Quadrilaterals Characteristics Chart

Quadrilateral Shapes

Functions Continued...

I love my students and wouldn't change them for the world, but so often they have a hard time with math that has multiple steps.

We were working on function and they needed practice, but not just sit at their desks and work on a worksheet practice.  So I decided to make these huge posters, one poster for each of the three steps for graphing a function.  

This activity got my students up and moving around the room while still working on practice.  The few feet between each step made a big difference.  It gave them time to stop thinking about what they just did and focus on what they are to do next.  To them it made each problem seem like three easy tasks.

I had three sets of these posters and even though it was only three problems worth of practice they got each of them correct.

At the end of the hour I gave them an exit ticket over these types of problems and found that most of my students were ready to move on the next day.  I did have to work with one student who has been struggling all year, but this activity gave me the time to do just that.