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How Many Sides Does A Circle Have?

Believe it or not, this was a question asked by a primary teacher.  I guess I shouldn't be surprised, but in retrospect, I was stunned. Therefore, I decided this topic would make a great blog post.

The answer is not as easy as it may seem. A circle could have one curved side depending on the definition of "side!"  It could have two sides - inside and outside; however this is mathematically irrelevant. Could a circle have infinite sides? Yes, if each side were very tiny. Finally, a circle could have no sides if a side is defined as a straight line. So which one should a teacher use?

By definition a circle is a perfectly round 2-dimensional shape that has all of its points the same distance from the center. If asked then how many sides does it have, the question itself simply does not apply if "sides" has the same meaning as in a rectangle or square.

I believe the word "side" should be restricted to polygons (two dimensional shapes). A good but straight forward definition of a polygon is a many sided shape.  A side is formed when two lines meet at a polygon vertex. Using this definition then allows us to say:
  1.  A circle is not a polygon.
  2.  A circle has no sides.
One way a primary teacher can help students learn some of the correct terminology of a circle is to use concrete ways.  For instance,  the perimeter of a circle is called the circumference.  It is the line that forms the outside edge of a circle or any closed curve. If you have a circle rug in your classroom, ask the students is to come and sit on the circumference of the circle. If you use this often, they will know, but better yet understand circumference.


For older students, you might want to try drawing a circle by putting a pin in a board. Then put a loop of string around the pin, and insert a pencil into the loop. Keeping the string stretched, the students can draw a circle!

And just because I knew you wanted to know, when we divide the circumference by the diameter we get 3.141592654... which is the number π (Pi)!  How cool is that?


A Go Figure Debut for a Mathematician Who Is New!

Secondary Math Solutions
Julie has taught high school math for 22 years, having taught everything from Pre-Algebra concepts to Honor Pre-Calculus. The past four years she has been teaching Algebra 1 to 9th graders. Most of her students would be considered on-level or below-level. (This sounds like my remedial math college students.) She loves the challenge of figuring out a way to teach them so they can understand the concept, practice it in class, and feel successful while not getting frustrated and giving up.

Currently, her TPT store (Secondary Math Solutions) contains over 200 resources and many are Algebra 1 products she has created and used in her own classroom. A large number of the concepts are broken down into scaffolded steps or prior knowledge skills. There are also pages and activities that go over and over the same concept because that is what her students need. Julie’s products do not contain "difficult numbers" because she doesn’t want her students getting bogged down with trying to remember how to add fractions, when all she really wants them to be able to do is solve an equation or find the slope of a line. She tends to make notes and practice sheets that are very focused on a specific skill or skills (sometimes prerequisite) that need to be developed so that her students can be successful. Her TPT math products reflect this.

Julie endeavors to make her math classes as interactive and hands-on as possible. Her "4 Types of Slope Activity" allows the student to create their own diagram which helps them to remember the four types of slope. Educators recognize that the student will have a greater chance of recalling what they create rather than what they are told. This is a great activity that can be glued into an interactive notebook when finished.

Speaking of interactive notebooks, Julie uses foldables as well. Her "Writing Equations of Lines Foldable" reviews all the ways the student might be asked to write the equation of a line. They fill it in themselves after they have been taught all of the material. This allows them to gauge what they do and do not remember. After it is filled in correctly, the students can go back and use it as a study tool before a quiz or test.

If you are a math teacher, I hope you will check out Julie’s store and consider her focused resources created just for the high school math student!

Is Zero Even or Odd?

Is the number zero even or odd?  This was a question asked on the Forum page of Teachers Pay Teachers by an elementary teacher. She stated that Wikipedia had a long page about the parity of zero and that some of the explanation went a little over her head, but basically the gist was that zero is even because it has the properties of an even number. She further stated that before reading this definition, she probably would have said that zero was neither even nor odd.

Here was my reply. Zero is classified as an even number. An integer n is called *even* if there exists an integer m such that n = 2m,  and *odd* if 2m + 1. From this, it is clear that 0 = (2)(0) is even. The reason for this definition is so that we have the property that every integer is either even or odd.

In a simpler format, an even number is a number that is exactly divisible by 2. That means when you divide by two the remainder is zero. You may want your students to review the multiplication facts for 2 and/or other numbers to look for patterns.

2 x 0 =               3 x 0 =
2 x 1 =               3 x 1 =
2 x 2 =               3 x 2 =
2 x 3 =               3 x 3 =

There is always a pattern of the products. Let the students discover these patterns - Even x Even = Even, Even x Odd = Even and vice versa and Odd x Odd = Odd. Since ALL math is based on patterns, seeing patterns in math helps students to understand and remember. Now ask yourself, "Does zero fit this pattern?"

The students can also divide several numbers by 2 (including 0), allowing them to see a second way to conclude that a number is even. (The remainder of the evens is 0, and the remainder of the odds is 1).  Again, "Does zero fit this pattern?"

To demonstrate odds and evens, I like using my hands and fingers since they are always with me. Let's begin with the number two.  I start by having the students make two fists that touch each other. I then have them put one finger up on one hand and one finger up on the other hand. Then the fingers are to make pairs and touch each other. If there are no fingers left over (without a partner), then the number is even.  (see sequence below)


Let's try the same procedure using the number three. Again, begin with the two fists. (see sequence below) Alternating the hands, have the students put up one finger on one hand and one finger up on the other hand; then another finger up on the second hand.  Now have the students make pairs of fingers. Oops!  One of the fingers doesn't have a partner, (one is left over); so, the number three is odd. (I like to say, "Odd man out.")   


So, does this work for zero?  If we start with two fists, and put up no fingers then there are no fingers left over.  The fists are the same, making zero even. (see illustration below)


So the next time you are working on odd and even numbers, make it a "hands-on" activity.


The Calculator Argument

Once upon a time, two mathematicians, Cal Q. Late and Tommy Go Figure, were having a discussion...an argument, really.

"Calculators are terrific math tools," said one of the mathematicians.

"I agree, but they shouldn't be used in the classroom" said the other.

"But?" asked Tommy Go Figure, and this is when the argument started. "That is just crazy!  I agree that having a calculator to use is a convenience, but it does not replace knowing how to do something on your own with your own brain."

"Why should kids have to learn how to do something that they don't have to do, something that a calculator can always be used for?" Cal Q. Late argued.

Tommy retorted,  "Why should kids not have the advantage of knowing how to do math?  To me, a calculator is like having to carry an extra brain around in their pockets.  What if they had to do some figuring and did not have their calculators with them?  Or what if the batteries were dead? (Here's a good reason for solar calculators.) What about that?"

Cal reminded Tommy, "No one is ever in that much of a rush. Doing math computation is rarely an emergency situation. Having to wait to get a new battery would seem to take less time than all the time it would take to learn and practice how to do math. That takes years to do, years that kids could spend doing much more interesting things in math."

"Look," Tommy went on, exasperated, "kids need to depend on themselves to do jobs. Using a calculator is not bad, but it should not be the only way kids can do computation. It just doesn't make sense."

Cal would not budge in the argument. "The calculator is an important math tool. When you do a job, it makes sense to use the best tool there is to to that job. If you have a pencil sharpener, you don't use a knife to sharpen a pencil. If you are in a hurry, you don't walk; you go by car. You don't walk just because it is the way people used to travel long ago."

"Aha!" answered Tommy. "Walking is still useful. Just because we have cars, we don't discourage kids from learning how to walk. That is a ridiculous argument."

This argument went on and one and on...and to this day, it has not been resolved. So kids are still learning how to compute and do math with their brains, while some are also learning how to use calculators.  What about you?  Which mathematician, Cal Q. Late or Tommy Go Figure, do you agree with?

------------------------------------------------------

Of course, this argument was made up, but it is very much like the argument schools and teachers are having about what to do with kids and calculators. What do you think?  Leave your comment for others to read.

"BOO" to Fractions?


Here is a Halloween riddle: Which building does Dracula like to visit in New York City? Give up? It's the Vampire State Building!! (Ha! Ha!) Here is another riddle. Why didn’t the skeleton dance at the party? He had no body to dance with!   

Okay, so what do these riddles have to do with teaching math? I have been attempting to come up with ways for my students to recognize fractional parts in lowest terms. As you know from this blog, I have used Pattern Sticks, the Divisibility Rules, and finding Digital Root. These are all strategies my students like and use, but to be a good mathematician requires practice - something most of my students dread doing. I can find many "drill and kill" activities, but they tend to do just that, drill those who don't need it and kill those who already know how to do it. So to drill and "thrill", I created six fractional word puzzles for specific times of the year.

The one for October is Halloween Fraction Riddles. It contains eight riddles that the students must discover by correctly identifying fractional parts of words. For instance, my first clue might be: the first 2/3's of WILLOW. The word WILLOW contains six letters. It takes two letters to make 1/3; therefore, the first 2/3's would be the word WILL. This causes the students to group the letters (in this case 4/6), and then to reduce the fraction to lowest terms. The letters are a visual aid for those students who are still having difficulty, and I observe many actually drawing lines between the letters to create groups of two.


At first, I thought my students would breeze through the activities, but to my surprise, they proved to be challenging as well as somewhat tricky - just perfect for a Trick or Treat holiday. Maybe this is an activity you would like to try with your intermediate or middle school students. Just click on this link: Halloween Fraction Riddles.

A Go Figure Debut for a South African Who Is New!

Liezel's TPT Store
Since my husband teaches science on the middle school level, I thought this week, I would feature a science teacher. After all, science and math are closely related because both content areas rely on a similar problem-solving approach and tools such as observation, comparison, measurement, and communication. Even some big ideas are the same: change (function), systems, and classification. Let's meet Liezel who graduated from the University of Stellenbosch (in South Africa) with a B.Sc. in Biochemistry.

Liezel has taught in the UK as well as South Africa. At the moment, she is teaching at a Cambridge International School in the beautiful Garden Route in South Africa. She loves creating new and interesting resources. Her students always joke that she should have been a primary school teacher since she is always adding clip art, borders, etc. to everything! (I do, too – even on the college level.) Currently, she teaches biology, chemistry and physics from grades 7-12 (AS levels - the equivalent of grades 12 and 13 here in the U.S.)

She loves creative, interactive lessons, and as a scientist, she tries to do as much lab work with her students as possible. She also loves to read! She is a mother to a gorgeous two year old “princess” and an eight year old Jack Russel Terrier.


Liezel's store is called The Lab which is a very suitable name for a science teacher. She currently has 65 resources in her store, five of which are free. These reasonably priced resources are appropriate for high school as well as middle school. Her store features interactive notebooks, task cards, crossword puzzles, and much, much more.

FREE Resource
One of Liezel's interactive science notebook activities is a free resource on plant cell structure and function. The students are given an outline of a plant cell, and then they are to cut out the provided labels and then place the functions in the correct place.

My husband has downloaded this free resource and uses it as a review activity. He says it is a different way for his 8th graders to practice and go over vocabulary.

Just $2.00
Liezel also has an interesting product for $2.00 entitled Physics Formulae Flash Cards.  It is a set of 14 flash cards to help in the review of various Physics Formulae. Included in this resource are 14 flash cards (4 on a page) plus two blank cards for any extra formulas you wish to add. Liezel punches a hole in each card and then has her students keep them on a key ring to use for reviewing.

Now that you know more about The Lab, why not head on over to her store and welcome her?  While you are there, you might check out what she has as well as become one of her followers.  OR follow her on Facebook: https://www.facebook.com/thelabnews and Instagram: @thelab_by_liezelpienaar  I don't know about you, but I am looking forward to reviewing more of Liezel's unique products!


Conducting Effective Parent/Teacher Conferences

If you are like most teachers, you are preparing for your first round of parent/teacher conferences. Now that I teach on the college level, this is one activity I currently don't have to do, but when I did, I really did enjoy them. Why? Because I was prepared with more than just the student's grades. Here are some of the ways I got ready.

First, in preparing for parent/teacher conferences, what can you do on a daily basis? Is the conference based on simply talking about grades or are there additional items that need discussing? How can an observation be specific without offending the parent or guardian? How is it possible to remember everything?

I kept a clipboard in my classroom on which were taped five 6” x 8” file cards so they overlapped - something like you see in the two pictures above. Each week, I tired to evaluate five students, writing at least two observations for each child on the cards. At the end of the week, the file cards were removed and placed into the children's folders. The next week, four different students were chosen to be evaluated. In this way, I did not feel overwhelmed, and had time to really concentrate on a small group of children. By the end of 4-5 weeks, each child in the class had been observed at least twice. By the end of the year, every child had been observed at least eight different times.

Below are sample observations which might appear on the cards.

Student
Date
             Observation
IEP
ESL

Mary Kay
  8/20


  8/28
 Likes to work alone; shy and withdrawn;  wears a great deal of make-up.

 She has a good self concept and is  friendly. Her preferred learning style is  visual based on the modality survey.

X


    Donald
  9/19


  9/21
 Leader, at times domineering, likes to  play games where money is involved.

 His preferred learning style is auditory  (from the modality survey). He can be a  “bully,” especially in competitive games.  He tends to use aggressive language with  those who are not considered athletic.



Checklist for P/T Conferences
By the time the first parent/teacher conferences rolled around, I had at least two observations for each child. This allowed me to share specific things (besides grades) with the parents/guardians. As the year progressed, more observations were added; so, that a parent/guardian as well as myself could readily see progress in not only grades, but in a student's behavior and social skills. The cards were also an easy reference for filling out the paperwork for a 504 plan or an IEP (Individual Education Plan). As a result of utilizing the cards, I learned pertinent and important facts related to the whole child which in turn created an effective and relevant parent/teacher conference.

To keep the conference on the right track, I also created a checklist to use during parent/teacher conferences.  It featured nine characteristics listed in a brief, succinct checklist form. During conferences, this guide allowed me to have specific items to talk about besides grades. Some of the characteristics included were study skills and organization, response to assignments, class attitude, inquiry skills, etc. Since other teachers at my school were always asking to use it, I rewrote it and placed it in my TPT store. It is available for only $1.95, and I guarantee it will keep your conferences flowing and your parents focused! When you have time, check it out!

Using the Periodic Table to Create Bulletin Boards

As many of you know, my husband teachers middle school science.  Together, this is our 80th year of teaching; so, you can tell that we both still love what we do. In fact, we can't imagine doing anything else.

Free Resource
My husband isn't one to do bulletin boards, never has been and never will be. My daughter (also a teacher) and I usually construct them for him. For many months now, I have been looking for individual tiles of the periodic table.  I saw a bulletin board on Pinterest (one of my favorite places to gather ideas) that I wanted to recreate for my husband's science lab.  I finally turned to Teachers Pay Teachers (where I should have gone in the first place) and asked in the Forum if anyone had such an item. I found that The Triple Point had just what I was looking for. It was a set containing 118 images (png) of Periodic Table tiles, one for each of the 118 elements. Since the resource was free, I downloaded it immediately.

After copy the individual tiles onto card stock and laminating them for durability, I laid out the bulletin board (see below). To be honest, my husband did staple everything onto the board as well as arrange the other items. Didn't he do a great job?


In case you can't read the meme in the middle, it says, "That will be $5.00 for the Electrons; the Neutrons are Free of Charge." After all, every classroom needs a bit of humor!

Give Reading A Helping Hand!

I believe the Conceptual Development Model should be constantly used when creating lessons for students, no matter what their age or grade level. (I even use it on the college level.) This particular model helps to bring structure and order to concepts found in almost any discipline. Here is an example of how I used the model in reading.

When I taught third grade, I noticed that my students often had difficulty identifying the different components of a story. I knew I needed a concrete/pictorial example that would help them to remember. Since we always had our hands with us, I decided to make something that would be worn on the hands. By associating the abstract story concepts with this concrete object, I hoped my third graders would make connections to help them visually organize a story's elements. I also suspected it would increase their ability to retell, summarize, and comprehend the story.

I purchased a pair of garden gloves and used fabric paint to write the five elements of a story on the fingers...**characters, setting, problem, events, and solution. In the middle of the glove I drew a heart and around it wrote, "The heart of the story." (theme) Towards the wrist was written "Author's Message." (What was the author saying?)

After we read a story, I would place the glove on my hand, and we would go through the parts of the story starting with the thumb or characters. (a person, animal, or imaginary creature in the story). We then proceeded to setting (where the story took place.) We did not progress through all the story elements every day, but would often focus on the specific part that was causing the most difficulty. The fun came when one of the children wore the glove (Yes, it was a little big, but they didn’t seem to mind) and became the "teacher” as the group discussed the story. As the student/teacher talked about each of the fingers, we would all use our bare hands without the glove.

I also made and copied smaller hands as story reminders. This hand would appear on worksheets, homework, bookmarks, desks, etc. Sometimes the hand contained all the elements; sometimes it was completely blank, and at other times only a few things would be missing. The hand became known as our famous and notorious Helping Hand.

Why would I allocate so much time to this part of the curriculum? Because…

1) If a student learned the elements of a story, then they understood and knew what was happening throughout the story.

2) If a child is aware of who the character(s) were, then they cab identify the character’s traits during the story.

3) If the child knows the setting of the story, then they recognize where an event was taking place.

4) If they know the problems that are taking place, then they can be a part of the story and feel like they are helping to solve it.

Such visual tools allow a teacher the flexibility to focus on one single story element or present a more complex or intricate view of all parts of a story. By knowing the components of a story, students are more engaged and connected to their reading. It’s as if they assimilate the story and become a part it. So, are you ready to Give Reading a Helping Hand in your classroom?

**The five parts of a story may be identified as introduction, rising action, climax, falling action, and resolution or other similar categories.

A Go Figure Debut for an Ohioan Who's New!

Today I feature another teacher from the great state of Ohio. Nancy has been teaching third grade for 22 years at the same rural school district. She is married and has one son. She enjoys traveling and photography. Since math is her favorite subject to teach, she was moved right to the top of my debut list. Her product ideas come from helping struggling students and creating hands-on activities so they can practice these skills.

She currently has 106 resources in her Teachers Pay Teachers store. Although she creates products for many subject areas, her emphasis is on math, most of which are suitable for grades 1-4.

Free Resource
Presently, Nancy has ten free products in her store. One of my favorites is entitled: Back to School: Stack and Solve Addition and Subtraction with Ballpark Estimates. It is a nine page resource booklet appropriate for grades 3-4. Students can practice adding and subtracting with regrouping while using ballpark estimates to check their work. Included are 24 cards, a recording sheet and an answer key.

Nancy's products are reasonably priced, but she also offers several bundles so that teachers can save even more money. One of those bundles is 64 pages and includes Line Plots: Build Them, and Line Plot Scavenger Hunt. Even though both items are sold separately, you save 20% by purchasing them in a bundle!

Just $6.00
The first part of this bundle is called Line Plots: Build Them. It contains four sets of line plot graphs. Each set has four task cards that are color coded for easy sorting. Also contained in the bundle is a blank line plot graph on which students can write the numbers with dry erase markers. Four task cards accompany this graph. Moreover, she has included a full page of task cards for projecting onto a board for a whole group activity.

The second portion of this bundle is called Line Plot Scavenger Hunt. Students move around the room solving 30 line plot cards. Students may work independently or with partners. Students should be familiar with finding the range and mode, and a calculator may be useful for some cards depending on the level of your students.

Additionally, Nancy has her own blog that is titled the same as her TPT store, Create, Learn, Explore. Her articles are well thought out as well as practical which means you can learn a great deal from her.


So take some time to check out Nancy's store and blog, and while you are there, be sure to download her free resource.


Setting Limits in the Classroom

One of the most practical books I have ever read is Setting Limits in the Classroom: A Complete Guide to Effective Classroom Management with a School-wide Discipline Plan (3rd Edition) by Robert J. Mackenzie. This year, many of our local schools are making it a require read and school wide book study. It will be used for daily group discussions as well as for application in the “real” classroom.

It is easy reading and contains many practical, no nonsense methods for classroom management that actually work. No theory here; just real life examples that can easily be applied in the classroom. Many of the chapters give effective ways to encourage the unmotivated child. (I'm sure that each year you have one or two sitting in your class.) It is a book worth purchasing, reading, and sharing. AND many of the suggestions carry over into managing your own children.

The paperback book can be purchased on Amazon.com for about $10.00. Mackenzie has written several books, one entitled: Setting Limits with Your Strong-Willed Child: Eliminating Conflict by Establishing Clear, Firm, and Respectful Boundaries. I haven't read this one, but I wish it had been available when I was raising my first son!

The Best Laid Plans. . .

Lesson plans have always been an Achilles heel for me.  I have taught for so-o-o long, that how to teach the lesson as well as knowing the content is not an issue.  I always have a Plan B, C, and D ready - just in case.  I now teach on the college level where no one checks my plans; however, I still write an outline for the day so I know that I have covered the important points. 

My first job, when I retired from our local school system, was teaching math at a private school.  Mind you, I had been teaching math for over twenty years; yet, the administrator wanted me to do detailed plans which had to be turned in every Friday. I grudgingly did them, but would add little comments in the comment section. That space became my way of quietly venting; so, I would write such things as:  "So many lesson plans; so little time. Writing detailed plans is not time well spent.  To plan or to grade, that is the question.  I am aging quickly; so, I need to make succinct plans."

My supervisor finally relented and allowed me to do an outline form of plans. However, he visited often to observe my teaching, which I didn't mind.  At least he knew what was happening in my classroom.  I have learned from teaching and observing student teachers that anyone can come up with dynamite plans, but the question is: "Do the plans match what the teacher is doing in the classroom?"  Remember Madelyn Hunter?  Oh, how my student teachers hated her lesson plan design, but they did learn how to make a good plan. To this day, I still do many of the items such as a focus activity and a lesson reflection at the end.

Science Lesson Plans for a Week in October
As many of you know, my husband is a middle school science teacher. He is the "sci" part of my name. Anyway, he is in his 40th year of teaching, and he still does lesson plans - not the detailed ones we did our first couple of years of teaching, but plans he has. He divides one of his white boards into sections using colored electrical tape as seen in the illustration on the left.  He then writes what each class is doing for the week in a designated square. In this way, the principal, parents, and students know the content that will be covered. Even the substitute (he is rarely sick) has a general idea of the day's activities. If plans change, he simply erases and makes the necessary corrections.

So what kind of plans are you required to do?  Maybe there are no requirements for you, but do you still write plans?  Are they in outline form or just brief notes to yourself?  I am interested in knowing what you do; so, please participate in the poll on the left. OR leave a comment to share your thoughts.

Lesson Plan Templates
By the way, do you need a lesson plan that is easy to use, and yet is acceptable to turn into your principal or supervisor?  Check out my three lesson plan templates. One is a generic lesson plan; whereas, the other two are specifically designed for mathematics (elementary or secondary) and reading.  Checklists are featured on all three plans; hence, there is little writing for you to do. These lists include Bloom’s Taxonomy, multiple intelligences, lesson types, objectives, and cooperative learning structures. Just click under the resource cover.

Common Classroom Irritations

Have you ever noticed that the same old problems keep resurfacing year after year in your classroom? Isn’t it funny how the little things sometime put us over the edge? I can always deal with that “special” child, but the continuous line at my desk about drives me crazy. Here are three different classroom irritations which I find to be the most annoying plus some possible solutions to think about before school starts.

A. Children Who Are Always at the Teacher’s Desk


1)  Give the student “question coupons or tickets.” Three is a good number. The child must give you one coupon each time s/he comes to your desk. When the child uses up all of her/his tickets, s/he can no longer come up to to your desk. The students soon learn to “think about” what questions they truly need to ask the teacher.

2)  Stack three cups on each child’s desk which the children change as needed. Green (or whatever color you chose) means the student is on task and has no questions. Yellow means the student needs to ask the teacher a brief question. Red means the student has no idea of what they are doing and needs help. This color requires that the teacher goes and assists the child.

B. Getting a Drink; Using the Restroom

1)  Set the number of times each student may go per the week.

2)  Have a restroom pass so only one student is out of the classroom at a time.

3)  Count when the children are getting a drink at the drinking fountain such as 1-2-3.  This way everyone is given the same amount to time.
.
4)  Keep a bottle of hand sanitizer by the door so children may use it before lunch to clean their hands. (Unfortunately, not all children wash their hands after using the restroom.)

C. The Pencil Sharpener

1)   Have a box of pre-sharpened pencils that all the children may use.

2)   Make a designated time when students may sharpen pencils. If you have an electric pencil sharpener, unplug it during the off limits time.

3)   Designate an individual to be the “pencil sharpener.” This can be a daily job in your classroom. This person performs the task of sharpening pencils before school, after school, or during any other designated time.

4)   Have two cups of pencils near the pencil sharpener, one for dull pencils and one for sharpened pencils. When a child’s pencil is dull, s/he places it in the dull cup and takes one from the sharp cup.

   
Greatest Irritations
Do you want additional ideas on how to solve common classroom irritations plus more ideas for the ones mentioned above? Check out the complete resource that fully discusses:

           1)  Children Who Are Always at Your Desk
           2)  The Pencil Sharpener
           3)  Getting a Drink; Using the Restroom
           4)  Tattling
           5)  Stress – Especially at Test Time
           6)  Teasing
           7)  Unmotivated Students


A Go Figure Debut for a Señora Who's New!

Holly is another TPT seller from the great state of Ohio (Go Bucks!) She has been a high school Spanish teacher for 15 years. She is a second generation teacher as her father was a math teacher (the best subject in the world!). She prides herself on creating activities that infuse culture with language, are of high interest, and are proficiency based. While grammar instruction is part of her job, Holly believes that experience with reading, listening, speaking and culture are the heart of the language.

Her shining teacher moment is when she receives a message like the one below written by a former student:

Appropriate for Grades 7-12
Holly's Teachers Pay Teachers store, Spanish Sundries, contains over 200 resources. Prices vary, with 32 items priced at just $1.00. One of her resources, a six page handout, is entitled Spanish Number Word Puzzles and was created to help students with number recognition and the spelling of the numbers 1-100 in Spanish. These puzzles also aid in the development of higher-order thinking skills as well as pattern recognition skills - all important factors as students progress through the study of Spanish. 

In addition, Holly's store contains several free resources such as her Vocabulary Hint Template, This is a tool that helps students draw connections between words they already know and words they are trying to learn. Holly states she has used this in her Spanish classes for many years, and that she always receives feedback from her students on how much it helps them to remember new vocabulary.

Holly also has a blog with a very interesting and unusual title: Throw Away Your Textbook.  Take time to head over there and read a couple of her articles, and even if you don't teach Spanish, Holly's store is worth checking out. With over 700 votes and an overall rating of four (the best you can receive on TPT), you know she offers quality educational resources.


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!