Engaging students: Defining the words acute, right, and obtuse

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Johnny Aviles. His topic: how to engage geometry students when defining the words acute, right, and obtuse.

green line

A1.) How could you as a teacher create an activity or project that involves your topic?

To have the students get engaged with the topic of Defining the terms acute, right, and obtuse, I will begin with having the classroom set up into groups of 4-5. Within their group they will create 10 examples of where each acute, right, and obtuse angles or triangles can be found in the classroom or in the real world in general. For example, the letter Y, end of a sharpened pencil, and the angle under a ladder can be used. They will be given about 10-15 minutes depending on how fast they can all finish. This is a great activity as the students can work together to try to come up with these examples and can familiarize themselves with amount of ways these terms are used in life. I will tell them before I begin the activity that the group that comes up with the most examples will be given extra credit in the next exam or quiz. This will give them extra incentive to stay on task as I am well aware that some groups may finish earlier than the rest and may take that extra time to cause disruptions.

 

 

green line

B1.) How can this topic be used in your students’ future courses in mathematics or science?

In previous courses, students have learned had some exposure to these types of angles. Most students have been familiar with the use of right triangles and have learned methods like the Pythagorean theorem. When we extend the terms acute, right, and obtuse in geometry, it begins to be more intensified. These angles then extend in terms of triangle that will then have many uses. Students will then be expected to not only find missing side lengths but also angles. Students will then be exposed to methods later like, law of sines and cosines, special right triangles, triangle inequality theorem and triangle congruency in. This topic essentially is the stepping stone for a large part of what is soon to be learned. Other courses will use a variety of other was to incorporate the terms acute, right, and obtuse. Geometry, precalculus and trigonometry will essentially have a great deal of uses for these terms for starters and can then also be extended in many higher-level math courses in universities.

 

green line

E1.) How can technology be used to effectively engage students with this topic?

An effective way to teach this topic using technology and the terms acute, right, and obtuse would be games. There is a magnitude of game that involve angles and be beneficial in the understanding of these angles. I have found this one game called Alien Angles. In this game, you are given the angle of where the friendly alien at and you have to launch your rocket to rescue them. the purpose of the game is for students to be familiar with angles and how to find them. after you launch the rocket, you are given a protractor that shows the angles and I believe this is beneficial for students as they can also be more familiar with the application of protractors. I can post this on the promethean board and have students identify what the angle I need to rescue the aliens. I can then call for volunteers to go on the board and try to find the correct angle to launch the rocket.

https://www.mathplayground.com/alienangles.html

 

Engaging students: Defining the words acute, right, and obtuse

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Katelyn Kutch. Her topic: how to engage geometry students when defining the words acute, right, and obtuse.

green line

How could you as a teacher create an activity or project that involves your topic?

As a teacher I think that a fun activity that is not too difficult but will need the students to be up and around the room is kind of like a mix and match game. I will give a bunch a students, a multiple of three, different angles. And then I will give the rest of the students cards with acute, obtuse, and right triangle listed on them. The students with the angles will then have to get in groups of three to form one of the three triangles. Once the students are in groups of three, they will then find another student with the type of triangle and pair with them. They will then present and explain to rest of the class why they paired up the way that they did. I think that it would be a good way for the students to be up and around and decide for themselves what angles for what triangles and then to show their knowledge by explaining it to the class.

 

green line

How does this topic extend what your students should have learned in previous courses?

The topic of defining acute, right, and obtuse triangles extend what my students should already know about the different types, acute, right, and obtuse, angles. The students should already know the different types of angles and their properties. We can use their previous knowledge to build towards defining the different types of triangles. I will explain to the students that defining the triangles is like defining the angles. If they can tell me what angles are in the triangle and then tell me the properties of the triangles then they can reason with it and discover which triangle it is by looking at the angles.

green line

How has this topic appeared in pop culture (movies, TV, current music, theatre, etc.)?

I found an article that I like that was written about a soccer club, FC Harlem. FC Harlem was getting a new soccer field as part of an initiative known as Operation Community Cup, which revitalizes soccer fields in Columbus and Los Angeles. This particular field, when it was opened, had different triangles and angles spray painted on the field in order to show the kids how soccer players use them in games. Time Warner Cable was the big corporation in on this project.

 

References:

http://www.twcableuntangled.com/2010/10/great-day-for-soccer-in-harlem/

Engaging students: Defining the words acute, right, and obtuse

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Lisa Sun. Her topic: how to engage geometry students when defining the words acute, right, and obtuse.

green line

How could you as a teacher create an activity or project that involves your topic?

I believe a scavenger hunt will be a great activity for the students to help concrete their knowledge of acute, right, and obtuse angles. It will be a take home activity rather than an activity that they’ll complete in school. I’ve created this scavenger hunt to take place outside of the classroom so students will understand that what we learn in math class takes place in our everyday lives outside of the walls of school.

This scavenger hunt activity requires students to observe their surroundings everywhere they go. I want them to find 10 acute angles, 10 right angles, and 10 obtuse angles. Along with that, they must take a picture or sketch accordingly to which angle the image has. (For example, picture/sketch of a corner of book shelf – right angle). To spark some motivation and interest, I will announce to the students that if they are able to find 15 of each angle instead of 10, I will add 2 points to their next exam grade.

 

green line

What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?

Archimedes and Euclid are the mathematicians who have discovered and developed the idea of the types of angles that we have today. As a student, when my teachers related the topic with the brilliant minds who made such discoveries, I felt that the topics that I was learning were more relatable and I had gained a deeper understanding of the topic. I hope to do the same for my students with this topic. Here are the following interesting facts about Archimedes and Euclid to keep the students enlightened for geometry.

Interesting facts about Archimedes:

  • 1 of 3 most influential and important mathematician who ever lived (other two are Isaac Newton and Carl Gauss)
  • Rumors that he was considered to be of royalty because he was so respected by the King during his time
  • Invented the odometer

Interesting facts about Euclid:

  • “Father of Geometry”
  • His book “Elements” is one of the most powerful works in history of mathematics
  • His name means “Good Glory” in Greek

 

green line

How can technology be used to effectively engage students with this topic?

Above is a link that I would present, on replay, as students are walking into my classroom to set the tone of the classroom for the day. Once they are all seated, I will tell them to get out their interactive journal and write at least 5 facts that are new to them as I play the video for them once more. By doing so, we’re keeping the students engaged as they are reinforcing what they just heard in writing. Once students are done with this task, I will select students randomly to state one fact that they had just learned from the video. Guide the students to know and remember the “take home message” which are the following:

  • Definition of Angle: The amount of turn between two rays that have a common end point, the vertex
  • Angles are measured in degrees
  • Angles are seen everywhere
  • Acute angles: 0 – 89 degrees
  • Right angles: 90 degrees
  • Obtuse angles: 91-180

 

References:

https://www.mathsisfun.com/definitions/angle.html

http://www.yurtopic.com/society/people/archimedes-facts.html

http://www.10-facts-about.com/Euclid/id/382

 

Engaging students: Defining the words acute, right, and obtuse

In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.

I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).

This student submission again comes from my former student Jesse Faltys. Her topic: how to engage geometry students when defining the words acute, right, and obtuse.

green line

E. TECHNOLOGY: How can technology be used to effectively engage students with this topic?

ACUTE, OBTUSE, and RIGHT Angles Song

This is a great video for the end of the lesson when first introducing acute, right, and obtuse angles.  A little corny but it’s always helpful to link new knowledge to a song.  Music brings back memories or in this situation recognition.  By using creative things, you are helping the students reinforce new ideas.  Just hearing words will not help us retain the information, but adding the words to a song help reinforce the reminder for the information.  We can remember anything if we just put our minds to it.  The kids in the video are singing lyrics about right, obtuse and acute angles to the song Old McDonald Had a Farm.  The video helps the students to summarize their understanding of the three new terms and a way to retain it for future use.

http://www.watchknowlearn.org/Video.aspx?VideoID=2446

green line

D. HISTORY: How have different cultures throughout time used this topic in their society?

In Egypt as far back as 1500BC, measurements were taken of the Sun’s shadow against graduations marked on stone tables. These measurements are just different angles used to show time with some degree of accuracy.  Gromas were used for the purpose of construction in ancient Egypt.  Gromas were right-angle devices that the ancient Egyptians used when they began construction project by surveying an area. They could sketch out long lines at right angles.  The Romans will actually use the same tool to sketch out their roads.  1,713 years ago they were using right angles.  This might be important.

http://www.fig.net/pub/cairo/papers/wshs_01/wshs01_02_wallis.pdf

angles

green line

C. Culture: How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?

Angry-Birds: “Use the unique powers of the Angry Birds to destroy the greedy pigs’ fortresses!“ Angry-Birds is an app that is played by a large percentage of children on a daily basis.  Birds are positioned on a slingshot and launched at pigs that are resting on different structures.  We create a zero plane from the bird sitting in the slingshot, releasing the bird, and mark the maximum height reached. We now have an angle. The bird has created an angle with its path.  Can we classify the majority of these angles as acute, right or obtuse?

angrybirds

Bubble Shooter:  A Puzzle game that will help you stay busy for a while!

The point of the game is to remove all the spheres by matching like colors.  The “cannon” at the bottom of the page is your tool to directing the sphere were you want it to go.  You can directly shot the sphere or you can bounce off the edge of the wall.  Here is the trick, what kind of angle do you need to deliver your sphere.  One of the helpful hints from the website, “you can use the left and right border to bounce new balls in more advanced angles.” These advanced angles can be denoted as acute, right or obtuse.

http://www.shooter-bubble.com/