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From A Different Angle

Here is a riddle for you.  What did the little acorn say when he grew up?  Give up?  It's Gee-I'm-A-Tree or Ge-om-e-try. This is what my students are beginning to study.  I absolutely love teaching this part of math, and it is interesting how the students respond. Those that are visual, love it, but usually, those who do better with the abstract aren't so fond of it.

I have a beautiful, talented daughter who loves languages.  She is fluent in Spanish and loves to write, write, and write.  To my chagrin, she always struggled in math, especially in high school, until she got to Geometry.  Her math grade changed from a disappointing (let's just say she passed Algebra) to an A.  She thought Geometry was wonderful!!

I enjoy teaching Geometry because there are so many concrete ways to show the students what you mean. For instance, when introducing angles, (before using protractors) I use my fingers, coffee filters (when ironed, they make a perfect circle), interlocking plastic plates, the clock, etc. to demonstrate what the various angles look like. Here is an example of what I mean.

To introduce right angle, I have the students fold a coffee filter (which is ironed flat) into fourths, and we use that angle to locate right angles all around the room.  We discuss the importance of a right angle in architecture, and what would happen if a right angle didn’t exist. 
We then use an analog clock to discover what time represents a right angle. Right away, they respond with 3:00 or 9:00. Some will say 3:30, but when I display 3:30 on a Judy clock (comes in handy even on the college level), they see that the hour hand is not directly on the three which means it is not a 90 degree angle.
I also demonstrate a right angle by using my fingers.  What is great about fingers is that they are always with you.  I call the finger position you see on the right, Right on, Right angle.
So are you ready for another geometry riddle?  (I have many!)  What is Orville and Wilbur's favorite angle? That’s right; it is a right (Wright) angle.

Angle Resource
Want more geometry riddles? Check out Geometry Parodies by clicking here. Also, if you are interested in many different concrete ways to teach angles, take a look at my product entitled: Angles: Geometry Hands-On Activities.





A Perfect Ten

Don't you love tests where you ask a question which you believe everyone will get correct, and then find out it just isn't so?  I gave my algebra college students a pretest to see what they knew and didn't know.  One of the first questions was:  Why is our number system called Base Ten?  This is an extremely important concept as it reveals what they know about place value.  Below are some of the answers I received.

1)  It is called Base Ten because we have ten fingers.  (Yikes! If that is so, should we include our toes as well?)

2)  It is called Base Ten because I think you multiply by ten when you move past the decimal sign.  (Well, sort of.  You do multiply by ten when you move to the left of the decimal sign, going from the ones place, to the tens place, to the hundreds place, etc.)

3)  I think it is called Base Ten because it's something we use everyday.  (Really????)

Enough!  It is called Base Ten because we use ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to write all of the other numbers.  Each digit can have one of ten values: any number from 0 through 9. When the value reaches 9, just before 10, it starts over at zero again.  (Notice the pattern below.)

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, etc.


In addition, each place is worth ten times more than the last. Ten is worth ten times more than 1, and 1,000 is ten times more than 100. The pattern continues infinitely both ways on a number line.

The decimal point allows for the place value to continue in a consistent pattern with numbers smaller than one. As we move to the right of the decimal point, each place is divided by ten to get to the next place value. One hundredth is one tenth divided by ten, and one thousandth is one hundredth divided by ten. The pattern goes on infinitely.

100's, 10's, 1's . 0.1, 0.01, 0.001, 0.0001, 0.00001, etc.

Since all mathematics is based on patterns, this should not be a new revelation. Perhaps on the post-test, my students will omit the fingers and instead rely on patterns to answer the questions!

A Go Figure Debut for a Cavalier Who Is New!

You are probably wondering how "cavalier" got into today's title. Well, in the "small" world of Teachers Pay Teachers, (it has over 89,000 sellers!) I met someone who grew up in the same little town I did, and even graduated from the same high school (our town only has one).  She graduated five years after I did; so, we really never knew each other; however, we were both Cavaliers; so, hence the title of today's article.
Diane Vogel

Diane is a retired teacher of 40 years. She has taught in a resource as well as a self-contained learning disabilities classroom. In addition she has taught 2nd and 3rd graders in a regular education classroom. Towards the end of her teaching career, she taught in a psychiatric hospital, and concluded her final years with teaching 4th-6th grade gifted students.

Her Teachers Pay Teachers store contains 24 resources, three of which are free.  They include items from many disciplines, including special education and gifted. Her resources for grades K-10 reflect her multi-disciplinary hands-on approach to teaching which incorporates all modalities. 

Free Item
One of Diane's free resources is called Just Ducky and is appropriate for grades 1-3. She claims that most workbooks never contain enough measurement activities; so, this resource can serve as a supplement. In it, students count ducks and measure the length of duck calls. In addition, students are encouraged to write about how measuring with ducks is different than measuring with a ruler.

Only $4.00
Diane's featured resource is entitled Periodic Table Activities which is appropriate for grades 6-10. It is a review activity using the Periodic Table. It consists of seven spelling units, each with an answer key. As an alternative, it might be assigned as homework or as an activity suitable for a substitute teacher. Usually, each activity takes 20-40 minutes to complete depending on the level of your students. Diane has used it with gifted students whom she said were very motivated to see who could spell the longest word using the Periodic Table.


Diane also owns and operates a school supply store, which is up-to-date with the latest trends in education. She attends two buying trips a year which provide her with an exclusive and unique opportunity to interact with all of the educational vendors and to view the newest materials for teachers and their classrooms. GA School Supply (GA stands for Georgia/Alabama) offers a full line of educational materials, teaching supplies, classroom decorations and teaching tools to help your students' learning experience.

If you are having trouble finding a specific item for your classroom, you might check it out. Also take a minute to visit her store and at least download one of her three free resources. While you are there, take the time to rate the resource and maybe even become one of her followers.

See You Later Alligator

I originally posted this article back on May of 2011, but as I view products on Pinterest, I feel a need to revisit it. I have seen alligators, fish, movable Popsicle sticks, etc. as ways to teach greater than or less than. Even though these may be good visual tools, to be honest, there are no alligators or even fish in mathematics.
Because many students still fail to understand which way the symbol is placed, here is a different method which you might wish to try. First of all, every child knows how to connect dots; so, let’s use that approach.

Suppose we have two numbers 8 and 3. Ask the students, “Which number is greater?" Yes, 8 is greater. Let’s put two dots beside that number. 8 : Now ask, “Which number is smaller or represents the least amount?" You are right again. Three is smaller. Let’s put one dot beside (in front of) that number. Now have the students connect the dots.....

8 > 3    

It will work every time! When two numbers are equal, put two dots beside each number and connect the dots to make an equal sign. What makes this method a little different is that the students can visually see which number is greater because it has the most dots beside it; so when reading the number sentence, most of the time it is read correctly.

Free Resource

In a free handout, entitled Number Tiles - Activities for the Primary Grades, is a greater than and less than activity which can be used over and over again. Just click on the title to download your free copy.