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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!

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?

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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.

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.

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.


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.





FOIL - It Doesn't Always Work!

In more advanced math classes, many instructors happen to hate "FOIL" (including me) because it only provides confusion for the students. Unfortunately, FOIL (fist, outer, inner and last) tends to be taught as THE way to multiply all polynomials, which is certainly not true. As soon as either one of the polynomials has more than a "first" and "last" term in its parentheses, the students are puzzled as well as off course if they attempt to use FOIL. If students want to use FOIL, they need to be forewarned: You can ONLY use it for the specific case of multiplying two binomials. You can NOT use it at ANY other time!

When multiplying larger polynomials, most students switch
to vertical multiplication, because it is much easier to use, but there is another way. It is called the clam method. (An instructor at the college where I teach says that each set of arcs reminds her of a clam. She’s even named the clam Clarence; so, at our college, this is the Clarence the Clam mehod.)

Let’s say we have the following problem:

(x + 2) (2x + 3x – 4)

Simply multiply each term in the second parenthesis by the first term in the first parenthesis. Then multiply each term in the second parenthesis by the second term in the first parenthesis.

I have my students draw arcs as they multiply. Notice below that the arcs are drawn so they connect to one another to designate that this is a continuous process. Begin with the first term and times each term in the second parenthesis by that first term until each term has been multiplied.
When they are ready to work with the second term, I have the students use a different color.  This time they multiply each term in the second parenthesis by the second term in the first while drawing an arc below each term just as they did before.  The different colors help to distinguish which terms have been multiplied, and they serve as a check point to make sure no term has been missed in the process.

As they multiply, I have my students write the answers horizontally, lining up the like terms and placing them one under the other as seen below. This makes it so much easier for them to add the like terms:

This "clam" method works every time a student multiplies polynomials, no matter how many terms are involved.

Let me restate what I said at the start of this post: "FOIL" only works for the special case of a two-term polynomial multiplied by another two-term polynomial. It does NOT apply to in ANY other case; therefore, students should not depend on FOIL for general multiplication. In addition, they should never assume it will "work" for every multiplication of polynomials or even for most multiplications. If math students only know FOIL, they have not learned all they need to know, and this will cause them great difficulties and heartaches as they move up in math.

Personally, I have observed too many students who are greatly hindered in mathematics by an over reliance on the FOIL method. Often their instructors have been guilty of never teaching or introducing any other method other than FOIL for multiplying polynomials. Take the time to show your students how to multiply polynomials properly, avoid FOIL, if possible, and consider Clarence the Clam as one of the methods to teach. 


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


The Caffeine Queen is my newest Go Figure Debut. We have a great deal in common, especially when it comes to THE Ohio State University…..Go Bucks! She has taught both regular education and special education. Like most effective teachers, she is always on the lookout for exciting new teaching strategies. She describes herself as a hands-on teacher who enjoys creating items that are kid friendly. 

She believes RESPECT should be a two way street in any classroom. She says her shining teacher moment occurs daily when she receives hugs from her students! She thinks a fun and welcoming classroom atmosphere, along with engaging and interesting lessons, is truly the recipe for success. The internet world has really brought her teaching to life, and she desires to share some of those ideas and insights with other teachers.

She currently has 54 products in her store, most priced under $4.00. Her store features many math resources for the elementary as well as for middle school. If you visit her blog, you can read interesting and motivating articles about how she teaches math. I particularly like her May 2nd article about multiplication and how she uses shapes to help those who are struggling with two digit problems that require regrouping. Even I can relate to her April 5th post about fractions because my college students still struggle with them!

Her featured free item is a one-page divisibility rules poster that can be used during math class when students are working on factoring, simplifying fractions, etc. A smaller version of the poster is included for students to use in their Interactive Student Notebooks (ISN) or binders so that it is always within reach. Finally, a short worksheet for individual students or partners is included so that they can work on the newly learned rules while committing them to memory.

Her highlighted paid resource is a graphic organizer designed to make teaching the standard multiplication algorithm of two digit multiplication a bit easier to understand. Several different versions of the organizer are included.

The first three ready-made worksheet pages are multiplication without regrouping, with answer keys included. (The standard algorithm is difficult enough for beginners to conquer without having to immediately worry about regrouping.) Once students are comfortable with multiplying without regrouping, they are ready to begin regrouping. Hopefully, regrouping will go more smoothly because of the time spent solving problems without regrouping, and since the students are now familiar with the process of two digit multiplication.

Right now take a few moments to investigate the Caffeine Queen’s store and blog. Once there, why not become a follower, or download something that is free, or better yet, pick up an educational resource for your classroom?


Let's Go Fly A Kite!


This was a comment I received from a fourth grade teacher, "Would you believe on the state 4th grade math test this year, they would not accept "diamond" as an acceptable answer for a rhombus, but they did accept "kite"!!!!!  Can you believe this? Since when is kite a shape name? Crazy."

First of all, there are NO diamonds in mathematics (see Nov. 20, 2014 post entitled Faux Diamonds), but believe it or not, a kite is a geometric shape! The figure on the right is a kite. In fact, since it has four sides, it is classified as a quadrilateral. It has two pairs of adjacent sides that are congruent (the same length). The dashes on the sides of the diagram show which side is equal to which side. The sides with one dash are equal to each other, and the sides with two dashes are equal to each other.

A kite has just one pair of equal angles. These congruent angles are a light orange on the illustration at the left. A kite also has one line of symmetry which is represented by the dotted line. (A line of symmetry is an imaginary line that divides a shape in half so that both sides are exactly the same. In other words, when you fold it in half, the sides match.) It is like a reflection in a mirror.

The diagonals of the kite are perpendicular because they meet and form four right angles. In other words, one of the diagonals bisects or cuts the other diagonal exactly in half. This is shown on the diagram on the right. The diagonals are green, and one of the right angles is represented by the small square where the diagonals intersect.

There you have it! Don't you think a geometric kite is very similar to the kites we use to fly as children? Well, maybe you didn't fly kites as a kid, but I do remember reading about Ben Franklin flying one! Anyway, as usual, the wind is blowing strong here in Kansas, so I think I will go fly that kite!