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.

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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.

 

 

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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.

 

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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.

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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.

 

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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.

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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.

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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.

 

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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

 

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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

 

A Review of WuzzitTrouble: an app for math education

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Most apps and computer games that claim to assist with the development of mathematical knowledge only focus on rote memorization. There’s certainly a place for rote memorization, but I’ve been very disappointed with the paucity of games that encourage mathematical creativity beyond, say, immediate recall of the times tables.

Enter WuzzitTrouble, a new app that was developed by Keith Devlin, a professor of mathematics at Stanford and one of the great popularizers of mathematics today. An introduction to WuzzitTrouble can be seen in this promotional video:

One minor complaint about WuzzitTrouble is that the first few levels are so easy that it’s easy for children to low-ball the game… in much the same way that the first few levels of Angry Birds are utterly easy. (My other complaints is that the game only assume one user, so that a parent can’t play the game without affecting a child’s settings.) However, the level of difficulty does eventually increase. Here’s another promotional video showing how to solve Level 1-25:

Here’s a sampling of some of the higher levels. Remember that the wheel has 65 steps along the circumference, as shown in the above picture and videos.

  • Level 2-5: Using cog wheels of size 5 and 9, pick up keys at 23 and 36 and prizes at 27, 45, and 55.
  • Level 2-15: Using cog wheels of size 5, 7, and 9, pick up keys at 11, 16, and 21 and prizes at 32 and 42.
  • Level 2-25: Using cog wheels of size 5, 9, and 16, pick up keys at 24, 48, and 59; prizes at 11 and 37; and avoid a penalty at 64.
  • Level 3-3: Using cog wheels of size 3, 4, and 5, pick up keys at 7, 17, and 27 and prizes at 12 and 22.

In the words of their promotional materials:

At InnerTube Games, we set out to design and build mobile casual video games and puzzles that can attract and engage a large number of players, yet are built on fundamental mathematical concepts and embed sound mathematics learning principles.

We start with one simple, yet powerful observation. A musical instrument won’t teach you about music. But when you pick up an instrument and start playing – badly at first – you cannot fail to learn about music. And the more you play, the more you learn. In fact, using that one instrument, you can go all the way from stumbling beginner to virtuoso concert performances. It’s the music that changes, not the instrument. In modern parlance, the instrument is a platform. And (well designed) platforms are good for learning because they make the learning meaningful and put the learner in charge.

InnerTube Games does not build video games to “teach mathematics.” Rather, we build instruments which you can play, and we design them so that when you play them, you cannot fail to learn about mathematics. Moreover, each single game can be used to deliver mathematical challenges of increasing sophistication.

Our vision for learning design is to build the game around core mathematical concepts and practice so it looks and plays like the familiar casual games on the market. As a result, you won’t be able to see the difference by playing the first few levels, or by watching someone else play. It’s the educational power under the hood that makes our games different.

We’re not making a secret of the fact that our games are math-based. It’s not “stealth learning;” it’s a form of learning through action that the brain finds natural, having much in common with what educational researchers call embodied learning.

Wuzzit Trouble is our first puzzle to reach the market. It is built around the important mathematical concepts of integer partitions–the expression of a whole number as a sum of other whole numbers–and Diophantine equations. At the easiest levels of the puzzle, these provide engaging practice in basic arithmetic, leading to arithmetical fluency.

But that’s just the start. Integer partitions and Diophantine equations are major areas of mathematics, still being worked on today by leading mathematicians.

Freeing the Wuzzits won’t take you into those dizzy realms—at least in the initial release, which comes loaded with puzzles aimed at the Elementary and Middle School levels. But as you progress, you will face challenges that increasingly require higher-order arithmetical thinking, algebraic thinking, strategy design and modification, optimization, and algorithm design, all crucial abilities in today’s world. Getting three stars can require considerable ingenuity.

As you attempt to free each Wuzzit and maximize your score, you will be developing and applying valuable conceptual, analytic thinking skills that sharpen your mind—all without lifting pencil to paper.

As educators and former educators, all of us at InnerTube are very aware of the importance of learners meeting agreed standards. In its initial release version Wuzzit Trouble provides natural learning in the following areas of the US Common Core Curriculum:

  • *Grade 2, Operations & Algebraic Thinking #2
  • *Grade 2, Number & Operations in Base Ten #2, #8
  • *Grade 3, Operations & Algebraic Thinking #1, #4
  • *Grade 4, Operations & Algebraic Thinking #5
  • *Grade 6, Number System #5, #6

But we don’t want anyone to play our game purely to hit those Common Core markers. We want you to play it because it’s fun and challenging. Improvement in those CC areas comes automatically. Just like learning music by playing a musical instrument!

The analogy that I prefer is playing basketball. When young children are first learning to play basketball, there’s a place for learning how to dribble, how to pass, how to shoot free throws, etc. (These are analogous to learning how to add, subtract, multiply, and divide.) But children don’t just learn skills: they also go out and play. That’s where the WuzzitTrouble app fits in: it offers children a chance to just play with mathematics and enjoy it.

More references:

http://profkeithdevlin.org/2013/09/03/the-wuzzits-free-at-last/

http://aperiodical.com/2013/09/review-wuzzit-trouble/

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.

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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

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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

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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/