The Left Angle Mystery - Does Such an Angle Exist?

Geometry is probably my favorite part of math to teach because it is so visual; plus the subject lends itself to doing many hands-on activities, even with my college students.  When our unit on points, lines and angles is finished, it is time for the unit test.  Almost every year I ask the following question:  What is a left angle?   Much to my chagrin, here are some of the responses I have received over the years NONE of which are true!

1)   A left angle is the opposite of a right angle.

2)  On a clock, 3:00 o'clock is a right angle, but 9:00 o'clock is a left angle.

3)  A left angle is when the base ray is pointing left instead of right.

    4)      A left angle is 1/2 of a straight angle, like when it is cut into two pieces, only it is the part on the left, not the part on the right.

5)      A left angle is 1/4 of a circle, but just certain parts. Here is what I mean.

Now you know why math teachers, at times, want to pull their hair out!  Just to set the record straight, in case any of my students are reading this, there is no such thing as a left angle!  No matter which way the base ray is pointing, any angle that contains 90^○ is called a right angle.

$3.50

If you would like some different hands-on ways to teach angles, you might look at the resource entitled, Angles: Hands-on Activities.  This resource explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.

                                      

You are invited to the Inlinkz link party!

Click here to enter

Using Glyphs to Gather Information, Interpret Data and Follow Directions

What is a Glyph?

A glyph is a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and necessitates a legend/key to understand the glyph and require problem solving, communication, and data organization.

Remember coloring pages where you had to color in each of the numbers or letters using a key to color certain areas? Or how about coloring books that were filled with color-by-numbers? These color-by-number pages are a type of glyph. Some other activities we can call glyphs would be the paint-by-number kits, the water paints by color coded paint books, and in some cases, even model cars. Some of the model cars had numbers or letters attached to each piece that had to be glued together. These days, this could be considered a type of glyph.

What is the Purpose of a Glyph?

A glyph is a symbol that conveys information nonverbally. Glyphs may be used in many ways to get to know more about students and are extremely useful for students who do not possess the skill to write long, complex explanations. Reading a glyph and interpreting the information represented is a skill that requires deeper thinking. Students must be able to analyze the information presented in visual form. In other words, a glyph is a way to collect, display and analyze data. They are very appropriate to use in the CCSS data management strand (see standards below) of math.  Glyphs actually a type of graph as well as a getting-to- know-you type of activity.

CCSS.Math.Content.1.MD.C.4  Organize, represent, and interpret data with up to three categories;

ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 

CCSS.Math.Content.2.MD.D.10  Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. 

For example, if the number of buttons on a gingerbread man tells how many people are in a family, the student might be asked to “Count how many people are in your family. Draw that many buttons on the gingerbread man." Since each child is different, the glyphs won't all look the same which causes the students to really look at the data contained in them and decide what the glyphs are showing.

$3.00

Holiday glyphs can be a fun way to gather information about your students. You can find several in my Teachers Pay Teachers store.  My newest one is for Thanksgiving and involves reading and following directions while at the same time requiring problem solving, communication and data organization. The students color or put different items on a turkey based on information about themselves. Students finish the turkey glyph using the seven categories listed below. 

1) Draw a hat on the turkey (girl or a boy?)
2) Creating a color pattern for pets or no pets.
3) Coloring the wings based on whether or not they wear glasses.
4) Writing a Thanksgiving greeting based on how many live in their house.
5) Do you like reading or watching TV the best?
6) How do they get to school. (ride or walk?)
7) Pumpkins (number of letters in first name)

THE O-H-I-O State and the Math Polygon - Octagon

An octagon is any eight sided polygon.  We often use a stop sign as an example of an octagon in real life.  But in a actuality, a stop sign is a regular octagon meaning that all of the angles are equal in measure (equiangular) and all of the sides have the same length (equilateral).  For an eight sided shape to be classified as an octagon, it needs to have only eight sides.

I got to thinking about this since fall is just around the corner, and our family are BIG Ohio State football fans.  Being raised in Ohio and having relatives who taught at Ohio State have fueled this obsession, but so has doing graduate work there.  If you aren't familiar with the Ohio State Buckeyes, here is your opportunity to learn something new.

On the right you will see one of the many symbols for THE Ohio State University.  The red "O" is geometric because it is an octagon (just count the sides). Even the beginning of the word Ohio is an octagon. (I just adore mathematics in real life!)

The Ohio Stadium, a unique double-deck horseshoe design, is one of the most recognizable landmarks in all of college athletics. It has a seating capacity of 102,780 and is the third largest on-campus facility in the nation. Attending football games in the Ohio Stadium or watching the game on television is a Saturday afternoon ritual for most Ohio State fans.  The stadium is even listed in the National Registry of Historic Places. Anyone (and we have) who has been to a game in the giant horseshoe understands why. There are few experiences more fun or exciting!  In the middle of the football field is the octagonal O as seen in the picture below. (Another example of math in real life!)

Before I continue this posting, I must answer the age old question, "What is a buckeye?"  Since I grew up in Ohio, this question is easy for me to answer, but for everyone else, a buckeye is a nut. (I bet many of you thought it was candy.) Buckeye trees grow in many places in Ohio. The trees drop a "fruit" that comes in a spiked ball with a seam that runs around it. If you crack the seeds open, you can remove the "buckeye." When the nut dries, it is mostly brown in color but it has a light color similar to an over-sized black-eyed pea on one end. This coloration bears a vague resemblance to an eye hence the name, buckeye. 

Then there is Brutus Buckeye, (a student dressed in a costume) the official mascot of THE Ohio State University; so, you might say, since I was born and raised in Ohio, I am a nut!  Brutus (as seen on the left) wears a headpiece resembling a buckeye nut, a block O hat, (another octagon), a scarlet and gray shirt inscribed with the word "Brutus" on the front and the numbers "00" on the back.  Brutus also wears red pants with an Ohio State towel hanging over the front, and high white socks with black shoes. Both male and female students may carry out the duties of Brutus Buckeye as long as they are a committed Ohio State fan.

O-H-I-O

Finally, if you ever are lucky enough to see four people with their hands in the air, forming letters of the alphabet, it is most likely four Ohio state fans spelling out O-H-I-O!  That's how our grandchildren learned how to spell it! (The picture on the right is of our youngest son with his four groomsmen on the day of his wedding.)

And it is so-o-o easy to remember.  Just use this riddle:  What is round on the ends and high in the middle?  You guessed it - OHIO!