Explaining the Difference Between Odd and Even Numbers

Sometimes we think everyone knows the difference between an odd and even number. When I was teaching my remedial math college class, we were learning the divisibility rules, the first of which is that every even number is divided by two. I wrote the number "546" on the board and asked the class if this was an odd or even number. I had one student who disagreed with the group answer of even. I asked him why he thought the number was odd, and he replied, "Because it has a "5" in it. " It was obvious this student got all the way through high school without a clear understanding of odd and even numbers. So the moral to this story is to be sure to discuss the difference between an even and an odd number with your students.

A good definition for an even number is that it can be put into groups of two without any left over, like giving each person a partner. But when you have an odd number of things and put them into groups of two, one will always be left out.

Try this approach. Make your hands into fists and place them side by side as seen in the illustration. Say a number. Now count, and as you count, put up one finger for each number said, alternating between hands, with fingers touching.

For instance, if you said “3”, you would count one, (left pointer fingerup) two, (right pointer finger up and touching the other pointer finger) three, (left middle finger up). Three is an odd number because one finger does not have a partner to touch.

Here is the sequence to use if the number given were "2". Two is an even number because each finger has a partner.

Repeat this several times, giving the students odd as well as even numbers. By always having a concrete visual (their fingers) will help the kinesthetic and visual learner to "see" the odds and evens.

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Activities such as this can be found in a math booklet entitled Number Tiles for The Primary Grades.  It contains 17 different math problem solving activities that extend from simple counting, to even and odd numbers, to greater than or less than to solving addition and subtraction problems.

Mathematics Tips for Parents for Those Long Summer Months

Success in school starts and continues at home, but many parents feel inadequate when it comes to helping their children with math. While parents can usually find time to read a story to their children, thereby instilling a love for books, they are often at a loss as to how to instill a love and appreciation for mathematics.  Like reading, mathematics is a subject that is indeed necessary for functioning adequately in society.  Here are some tips to help you as you work with your child this school year.

Recognize that you make an important difference in your child's education.   Most children develop a sense of numbers way before the "regular" school years.  If you have a young child, take advantage of those early years through activities at home that teach and at the same time are enjoyable.  You might take your child on a counting walk in your neighborhood to count how many trees, shrubs, plants, houses, birds, dogs, etc. you see.  Look for twigs or pine cones or leaves, etc. and have your child count as many as s/he can. Then lay them side by side to compare the length and ask your child, "Which is the longest, which is the shortest? Are there any that are the same length?"

Provide experiences at home that help your child be successful, and seek ways to let children, even very young children, know that they are needed and important.  Cooking is a fun way to do this. Help your child follow the directions on a Kool Aid packet or frozen juice can to make refreshments for the family.  Help your child cut a fruit or vegetable into halves, fourths, thirds, etc. Let them help prepare a meal while asking, "What do you do first? Second? Third?"  or better yet, allow them to measure the ingredients for a recipe.

Children do not need a lot of motivation when it comes to recognizing and learning the value of coins.  You know they are interested when they start bugging you for money.  However, it is not sufficient for children to be able to just recognize coins, they must also know the value of these coins.  The best way to accomplish this is to use real money.  You might show your child two or more coins and have him/her tell you the total value of the coins.  Or hold up a coin.  After your child identifies it, discuss what the coin would buy at the store.  When going to the grocery store, give your child his/her own money to buy something.  Have them select an item that costs less than the money you have given them.  You can also do a similar activity by asking them to determine what are the fewest number of coins it would take to pay for the item. Give your child a practical math experience by estimating how long it takes to prepare a meal from start to finish.

Parents' attitudes toward mathematics have an impact on children's attitudes; so, be patient with your child.  A wrong answer on a math test or a homework assignment is not a time for scolding.  It tells you to look further, to ask questions, and to find out what the wrong answer is saying about your child's understanding.  Ask your child to explain how they solved the problem.  Most importantly, relax!  Know that neither you nor the teacher needs to be perfect for your child to learn math.  Remember, one bad math assignment/test will not destroy your child's ability to learn math.

But what if you need some assistance?  Luckily, in today's world, we can find mathematical help at the click of a button.  Below are some great places to go and find outside help if your child is struggling or if you need more information for yourself.

Study Shack is a great place to find or make flashcards, play hangman, do matching activities or crosswords.  It has activities for grades 1-6 as well as addition, multiplication, algebra and geometry.  Cliff's Notes for Math is site that has notes, examples and quizzes for your older children.  The subject areas include Basic Math through Calculus.  There are many on-line math dictionaries.  My favorite is A Math Dictionary for Kids because it includes animation and interactive activities.  Even You Tube is a great resource for students struggling with a concept and needing an alternative way of seeing it. 

Finally, talk about people who use math in their jobs, including builders, architects, engineers, computer professionals, and scientists. Point out that even if your child does not plan to pursue a career in which s/he will use math, learning it is still important because math teaches you how to solve problems and how to think logically. AND we use math everyday!

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Here is another resource that may prove useful. It is a ten page, comprehensive, extensive and wide-ranging list of over 200 hyperlinked Educational website addresses for all subjects.

• Organized by a wide range of subject areas
• Broken down into subcategories (i.e. science, then earth science, ecology, etc.)
• Click on the URL and you are automatically taken to the site.

Different Ways to Write Tally Marks

Tally marks are the quickest way of keeping track of a group of five. One vertical line is made for each of the first four numbers; the fifth number is denoted by a diagonal line drawn across the previous four (i.e., from the top of the first line to the bottom of the fourth line). The diagonal fifth line cancels out the other four vertical lines making the entire set represent five.

Tally marks are also known as hash marks and can be defined in the unary numeral system. (A unary operation in a mathematical system is one element used to yield a single result, in this case a vertical line.) These marks are most useful in counting or tallying ongoing results, such as the score in a game or sport, as no intermediate results need to be erased or discarded. They also make it simple to add up the results by simply counting by 5’s. Here is an illustration of what I mean.

• The value 1 is represented by | tally marks.
• The value 2 is represented by | | tally marks.
• The value 3 is represented by | | | tally marks.
• The value 4 is denoted by |||| tally marks.
• The value five is not denoted by | | | | | tally marks. For the number 5, draw four vertical lines (||||) with a diagonal (\) line through them.

I have seen many interesting ways to teach tally marks to younger children. Many teachers will use Popsicle sticks so that the students have a concrete hands-on way of making tally marks. Some have even tried pretzel sticks although there is a good chance some will disappear during the lesson. 

But have you ever seen these kind of tally marks?

My husband, who teaches science, received this data collection paper from a student. The students were tossing coins marked TT, Tt, and tt to determine different genetic traits and tallying the results. The ones seen above are Japanese tally marks. (The student lived in Japan.) I was fascinated about how they were made so I asked him to have this student show me the sequence of how to draw the marks.

I'm not sure what they mean or why they are made this way, but if you look at the 2nd mark you will notice that it looks like a "T" for two. The fourth mark sort of looks like an "F" for four, but so does the third one. As you can see, each complete 正 character uses 5 strokes; so, a series of 正 would each represent 5, just like the English ones. However, to be honest, I am at a total lost to what this really means; so, I resorted to the internet. Here is what I learned. 

Instead of lines, a certain Kanji character is used. In Japan, this mark reminds people of a sign for “masu” which was originally a square wooden box used to measure rice in Japan during the feudal period. Here is what the tally marks would look like if we compared the two systems.

The successive strokes of 正 () are used in China, Japan and Korea to designate tallies in votes, scores, points, sushi orders, and the like, much as is used in Europe, Africa, Australia and North America. Tallies beyond five are written like this 正 with a line drawn underneath each group of five, followed by the remainder. For example, a tally of twelve is written as 正正丅. 

So the next time your visit Japan or go to a Japenese restaurant to order Sushi, look for the tally marks as the waiter takes your order.

HELP! Many of My College Students Don't Know Why We Call Our Number System Base 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!

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Get to know your students better by using this EDITABLE Student Math Information Form. It is an easy and effective way to gather information such as…

• How do your students feel about math?
• What are their interests outside of school?
• What do they hope to learn in your class?
• What other math classes have they taken?

Making Butterflies from Recycled Materials - Earth Day Ideas

When one of my granddaughters was in kindergarten, she came home one day with egg carton caterpillars.  I know most of us have made one of these in our lifetime, but to her, this was the best craft ever!

She told me that her teacher was raising butterflies in her classroom, and soon the butterflies would hatch.  Anticipation and excitement reigned until the day she came out of school telling everyone that one of the butterflies had hatched.  However, much to her chagrin, the teacher was going to let it go.  My granddaughter just couldn't understand why or how her teacher could do that!

But, here is the good part!  She got to make a cocoon out of a toilet paper cylinder.  She covered it by gluing on white cotton balls.  Then she made a butterfly out of tissue paper and a small plastic bag tie.  She put the butterfly inside the cocoon and then pretended to have the butterfly hatch!  This was done over and over and over until the cocoon was no more.  Luckily, I was able to get pictures before both were literally destroyed!

Now, what does all of this have to do with math?  I contemplated all the ways to use recycled products to make items for the classroom.  Thus Trash to Treasure was created. It is full of art ideas, fun and engaging mini-lessons as well as cute and easy-to-construct crafts all made from recycled or common, everyday items.

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Find out more than 14 ways to use milk lids for math. Did you know that you can practice math facts using clear plastic containers? Learn how to take two plastic plates and turn them into angle makers. How about using two plastic beverage lids to make card holders for kindergartners or for those whose hands are disabled? Discover ten ways to use carpet squares as well as nine ways to use old calendars. How about playing hop scotch on old carpet squares? Were you aware that butter tubs can become an indoor recess game to practice addition or multiplication facts? These are just a few of the fun and exciting activities that use recycled items found in this resource entitled Trash to Treasure.

Because these numerous activities vary in difficulty and complexity, they are appropriate for any PreK - 4th grade classroom, and the visual and/or kinesthetic learners will love them.

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Earth Day is April 22nd. How Will You Celebrate?

Earth Day began in 1970, when Gaylord Nelson, a U.S. Senator from Wisconsin, wanted nation-wide teaching on the environment. He brought the idea to state governors, mayors of big cities, editors of college newspapers, and to Scholastic Magazine, which was circulated in U.S. elementary and secondary schools.

Eventually, the idea of Earth Day spread to many people across the country and is now observed each year on April 22nd. The purpose of the day is to encourage awareness of and appreciation for the earth's environment. It is usually celebrated with outdoor shows, where individuals or groups perform acts of service to the earth. Typical ways of observing Earth Day include planting trees, picking up roadside trash, and conducting various programs for recycling and conservation.

Symbols used by people to describe Earth Day include: an image or drawing of planet earth, a tree, a flower or leaves depicting growth or the recycling symbol. Colors used for Earth Day include natural colors such as green, brown or blue.

The universal recycling symbol as seen above is internationally recognized and used to designate recyclable materials. It is composed of three mutually chasing arrows that form a Mobius strip which, in math, is an unending single-sided looped surface. (And you wondered how I would get math in this article!?!) This symbol is found on products like plastics, paper, metals and other materials that can be recycled. It is also seen, in a variety of styles, on recycling containers, at recycling centers, or anywhere there is an emphasis on the smart use of materials and products.

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Inspired by Earth Day, Trash to Treasure is a FREE resource. In it, you will discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom. Because these numerous activities vary in difficulty and complexity, they are appropriate for any PreK-3 classroom, and the visual and/or kinesthetic learners will love them.

To download the free version, just click under the cover page on your left.

Techniques for Remembering the Slope for Vertical and Horizontal Lines

I work in the Math Lab at the community college where I also teach. Last week, I had two College Algebra students who were having difficulty with slope.  They knew the equation y = mx + b, but were unsure when it came to horizontal or vertical lines. By the way, they were using their graphing calculators which I made them put away. (The book said no calculators.) I feel that if they construct the lines themselves, it puts a visual image into their brain much better than if the calculator does it for them. Sure enough, one of the sections in their math books gave the picture of the line from which they had to write the equation. They were amazed that I could just look at a graph and know the slope, give the equation, etc. When I taught high school math, my students couldn't use a graphing calculator until the middle of this particular chapter as I wanted them to physically draw the lines.

First, for those who have no idea what I am talking about, slope is rise over run.  Rise is how far a line goes up, and run is how far a line goes along.  At the right, the line goes up 3 and has a run 5; therefore, the slope is 3/5.  Rise/Run (Rise divided by Run) gives us the slope of the line.

When a line is horizontal, it has no rise, only a run. So the numerator would be zero (for no rise) and the denominator would be a number such as 5 for the run.  0 ÷ 5 = 0  This is true for any horizontal line.

A vertical line is different.  It has rise, but no run; therefore there would always be a number in the numerator, but always a zero in the denominator.  Since we cannot divide by zero, the slope is considered undefined. (I do use rise over run stating that a horizontal line might have 0/5 which is equal to 0 and that a vertical line might have 3/0 is undefined because we can't divide by zero. Our college algebra book uses O/K for okay and K/O for knock out which I like, but I still think the students need to know why.)

I wanted these two students to have a picture that would help them remember the difference.  I thought of a table for the horizontal line and asked them what would happen if the legs of the table were uneven.  They agreed that the table would have slope.  Therefore, the table would have a slope of zero if the legs were even.

I then went blank.  In other words, by creative juices stopped working, and I could not think of a picture that would help them visualize undefined. Since Teachers Pay Teachers has a forum,, I asked my fellow math teachers if they had any ideas.  Here is what some of them came up with.

The Enlightened Elephant suggested using a ski slope. She talks about skiing down a "cliff", which would not be possible (although some students try to argue that they could ski down a vertical cliff) and so the slope is "undefined" because it doesn't make sense to ski down a cliff.  Skiing on a horizontal line is possible so it's slope is zero,  She also talks about uphill (positive slope) and downhill (negative slope). 

Math by Lesley Elisabeth tells her students to use "HOY VUX" (rhymes with 'toy bucks')

             Horizontal - Zero (0) slope - y = ?   

             Vertical - Undefined slope - x = ?

All horizontal lines are y =7 or y = -3 etc., and all vertical lines are x =1 or x = 6, etc. Students forget this so the acronym HOY VUX helps them to remember. Once they've mastered the slope concept in Algebra I, for the rest of the school year, for Algebra II (especially equations of asymptotes - a line that continually approaches a given curve but does not meet it at any finite distance) and even in calculus classes for tangent lines, HOY VUX is just faster and more practical. 

Animated Algebra created a video lesson on the Slope Intercept.  She has a boy skateboard down a negative slope, literally right on the graph line. Karen then shows the same boy taking an escalator up on a line that has a positive slope. Later in the lesson, she rotates the line clockwise, each movement with a click, to show the corresponding slope number to link the line to the slope.  She includes lots of other visual cues to help students focus on and pay attention to the concepts.

When Dividing, Zero Is No Hero - Why We Can't Divide by Zero

Have you ever wondered why we can't divide by zero?  I remember asking that long ago in a math class, and the teacher's response was, "Because we just can't!"  I just love it when things are so clearly explained to me. So instead of a rote answer, let's investigate the question step-by-step.

The first question we need to answer is what does a does division mean?  Let's use the example problem on the right.

1. The 6 inside the box means we have six items such as balls. (dividend) 
2. The number 2 outside the box (divisor) tells us we want to put or separate the six balls into two groups. 
3. The question is, “How many balls will be in each group?” 
4. The answer is, “Three balls will be in each of the two groups.” (quotient)

                                      

Using the sequence above, let's look at another problem, only this time let's divide by zero.

1. The 6 inside the box means we have six items like balls. (dividend) 
2. The number 0 outside the box (divisor) tells us we want to put or separate the balls into groups into no groups. 
3. The question is, “How many balls can we put into no groups?” 
4. The answer is, “If there are no groups, we cannot put the balls into a group.” 
5. Therefore, we cannot divide by zero because we will always have zero groups (or nothing) in which to put things. You can’t put something into nothing.

Let’s look at dividing by zero a different way. We know that division is the inverse (opposite) of multiplication; so………..

1. In the problem 12 ÷ 3 = 4.  This means we can divide 12 into three equal groups with four in each group.
2. Accordingly, 4 × 3 = 12.  Four groups with three in each group equals 12 things.

So returning to our problem of six divided by zero..... 

1. If 6 ÷ 0 = 0....... 
2. Then 0 × 0 should equal 6, but it doesn’t; it equals 0. So in this situation, we cannot divide by zero and get the answer of six.

We also know multiplication is repeated addition; so in the first problem of 12 ÷ 3, if we add three groups of 4 together, we should get a sum of 12. 4 + 4 + 4 = 12

As a result, in the second example of 6 ÷ 0, if six zeros are added together, we should get the answer of 6. 0 + 0 + 0 + 0 + 0 + 0 = 0 However we don’t. We get 0 as the answer; so, again our answer is wrong.

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It is apparent that how many groups of zero we have is not important because they will never add up to equal the right answer. We could have as many as one billion groups of zero, and the sum would still equal zero. So, it doesn't make sense to divide by zero since there will never be a good answer. As a result, in the Algebraic world, we say that when we divide by zero, the answer is undefined. I guess that is the same as saying, "You can't divide by zero," but now at least you know why.

If you would like a free resource about this very topic, just click under the resource title page on your right.

Domino Math - Using Dominoes to Problem Solve and Practice Math Concepts

Dots Fun for Everyone

It is believed dominoes evolved from dice. In fact, the numbers in a standard double-six set of dominoes represent all the rolls of two six-sided die. It is thought they originated in China around the 12th century. They have been used in a large variety of games for hundreds of years, and today, dominoes are played all over the world.

Games allow children to learn a great deal concerning mathematical concepts and number relationships. Often, they are required to use critical thinking skills as well as varied math strategies to solve them. Since dominoes make a great manipulative for hands-on learning, I created a book of domino activities for grades 3-5 that are great for students who finish early or for introducing a new mathematical concept or for use at a math center. Using dominoes for a math practice center is a way to engage students while giving them a chance to review math facts.

The activities and three games vary in difficulty; so, differentiated instruction is easy. The variety of pages allows you to choose the practice page that is just right for each student. This resource correlates well with the CCSS standards.

Dots Fun

The activities in Dots Fun for Everyone (grades 3-5) include four digit place value, using the commutative property, problem solving, reducing proper and improper fractions and practicing multiplication and division facts. The games involve finding sums, using <, >, and = signs and ordering fractions.

These domino math activities in Dots Fun (primary grades) include recognizing sets, place value of two and four digit numbers, creating domino worms, gathering data, using the commutative property, and practicing addition and subtraction facts. The games involve matching, finding sums, and using greater than, less than, and equal signs. For these 13 activities and four games, you may use commercial sets dominoes or copy the blackline which is provided in the resource. This resource links closely with the CCSS standards. 

Some of the domino activities in these two resources use games while others will extend, enhance or introduce a new math concept. Since children are curious and inquisitive, plus some may have never seen dominoes, allow time for play and exploration before beginning any instruction. This is constructive as well as a productive use of class time. If they are not given this, most children will fool around and investigate during the teaching time.

To view examples from these resources as well as a complete Table of Contents, download the preview or FREE versions available at my TPT store.

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Even Today with Spell Check and Technology, Spelling is Important!

Noah Webster, an American lexicographer (one who compiles a dictionary) was the first person to write a dictionary of American English. It may have taken him more than 25 years to do so, but this book permanently altered the spelling of American English by offering a standardized way to spell and pronounce words. He learned 26 languages, including Anglo-Saxon and Sanskrit, in order to research the origins of our country's tongue. You may not know this, but Webster used the Bible as the foundation for his definitions.

Before his dictionary, Americans in different parts of the country spelled, pronounced and used words differently. To create uniformity, Noah used American spellings like "color" instead of the English "colour" and "music" instead " of "musick". He also added American words that didn't appear in English dictionaries like "skunk" and "squash". When he finished in 1828, Noah's dictionary contained 70,000 words.

During Webster's lifetime, American schools were anything but productive. Sometimes 70 children of all ages were crammed into one-room schoolhouses with no desks, poor books, and untrained teachers. The textbooks came from England. Noah thought Americans should learn from American books so he wrote a spelling book for children. Known for generations simply as The Blue-back Speller, millions of American children learned how to uniformly spell and pronounce words. Webster also established a system of rules to govern grammar, and reading. Clearly, he understood the power of words, their definitions, and the need for precise word usage in communication. Without a common oral and written language, he felt the country would remain divided.

Fast forward to today with the use of texting. Writing skills have turned into sentence fragments while spelling consists of numbers, symbols or abbreviations. These habits carry over when students are at school; consequently many really don’t know how to spell or write well. No longer can students punctuate correctly since text messages often contain run on sentences with no punctuation, In addition, with the constant use of lowercase letters, students fail to use capital letters where they should. How do I know? I teach at a community college where about 60% of our students are in remedial English which involves sentence structure, basic grammar and spelling. When assigning a written assignment, I must include how many words a good sentence contains and how many sentences are in an acceptable paragraph. Even these requirements do not guarantee a complete sentence.

It seems we have moved away from standard spelling to inventive spelling (an abbreviated, expedient form); yet customary spelling has not gone out of style. It is required at school, in business, at work and in just everyday life.  In addition, the correct spelling of words affects academic success. Students are frequently assessed on their skills in written language because it is considered a strong indication of their intelligence.

Spelling is an indication of a number of things when a person applies for a job.  When correct spelling is used, words are readable and communication is clear. This convinces a prospective employer that the job applicant has been well educated. It also tells them that they take care of detail and take pride in what they
present.  Let’s face it, university applications and job resumes littered with spelling errors don’t make it very far becuz badd spilleng is hrd two undrstnd wen yuu reed it.

Furthermore, good spelling streamlines communication. By following the identical rules for spelling words, we can all understand the text we read. Likewise, good spelling avoids confusion. In a way spelling is similar to football. It is up to the person passing the ball to make sure the receiver actually catches it. The same goes for spelling. If you write with intent and proper spelling, the receiver of that text will understand it.

As teachers and parents, we should care about the fundamental part good spelling plays in our language and everyday lives. We owe it to our students to give them the necessary skills and essential spelling tools for learning and communication so they can be successful.

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If you liked this article and would like to purchase some useful spelling resources, check out these two games. Their purpose is to help and encourage students to practice spelling words in a non-threatening way while having fun learning to spell.

Ironing Coffee Filters to Make the Perfect Circle

When I teach angles or the properties of circles, I find that most children have difficulty cutting out a true circle (even with a blackline).  I have resorted to purchasing cheap coffee filters (not the cone shaped ones) and ironing them flat. You can iron several filters at one time, and once they are ironed, they form excellent ready-made circles. Here are some of the ways you can teach angles using these circles.

Writing Formulas on the Coffee Filter Circle

1. Introduce the fact that each and every circle contains 360 degrees.
2. Have the students fold their coffee filter in half. Discuss that this is a straight angle. Ask, “How many degrees does it contain if it is one-half of a circle?” (180 degrees)
3. Have the students fold the coffee filter one more time, into fourths. Talk about this angle being called a right angle and that it contains 90 degrees. Ask, "What fractional part of a circle is this?"
4. Have the students use this fourth of a circle to locate places in the classroom where it will fit (e.g. the corner of their desk, a corner of a book, a corner of the board).
5. Explain that these corners are right angles and without right angles, we would live in a crooked world. Nothing would be straight!
6. With older students, have them write the parts of the circle and the formulas needed for solving problems about circles on the coffee filter circle.

Linking Math and Literature for Older Students

Read Sir Cumference and the First Round Table (A Math Adventure) by Cindy Neuschwander. This is a story about a clever knight of King Arthur’s named Sir Cumference. By using ideas offered by the knight’s wife, Lady Di of Ameter, and his son, Radius, King Arthur finds the perfect shape for his table. Basic geometric vocabulary involving circles (circumference, radius, and diameter) is introduced.

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Want more hands-on ideas for teaching angles? Check out Angles: Hands-On Geometry Activities.

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Pinterest and the Benefits of Using Tailwind to Increase Traffic to your Teachers Pay Teachers Store

Maybe you have heard of Tailwind and maybe you haven't. To set the record straight, it is not a wind blowing in the direction of travel of a vehicle or aircraft or a wind blowing from behind. It is a Pinterest and Instagram Marketing, Scheduling and Analytics Tool.

I was first introduced to it on the Teachers Pay Teachers blog. Since I use Pinterest, I am always pinning new ideas, teaching strategies, Ohio State stuff (Go Buckeyes!), ideas for my college classes, etc., I decided to try using Tailwind instead of individually pinning each resource from my TPT store or blog. Before deciding if the paid plan was right for me, I was able to schedule up to 100 pins on Pinterest for free . What was nice is that there was no time limit on that free trial! It allowed me to schedule up to 100 pins on Pinterest while I could watch my analytics and the number of repins my items were receiving before deciding if the paid plan was worth the money.

I saw several benefits right away! More traffic was coming to my Pinterest Boards as well as to my Teachers Pay Teachers Store. I therefore decided to invest in Tailwind.  I am aware that pinning everything all at once isn’t ideal; consequently, it is important to space pins out a little so I'm not overwhelming my followers. Pinterest has even suggested that too much pinning in a short time period could be viewed as “spamming”, potentially hurting my rankings in search results and feeds. With Tailwind, I have the ability to create my own posting schedule, and I can use interval pinning to space out my pins so "spamming" doesn't happen. I can set a time period between when each image that is pinned anywhere from two days to 90 days apart. Tailwind even gives me the best times and days to post.

Here are some ways I am currently using Tailwind:

1. To schedule pins
2. To know when the best time to pin by using the Smart Calendar
3. To schedule multiple pins to different boards at the same time
4. To use interval pinning
5. To use Smartloops - They let you automatically repin the same type of content to specific boards without having to revisit them. 
6. To use the Tailwind Analytics - to know which are my best pins and where my repins are going
7. To find my best pins using Pin Inspector
8. Create new pins from scratch using Tailwind Create - I use this all the time to take an old, outdated pin and remake it into a new pin. You just add your images, and it will create hundreds of pin designs that you can choose from and instantly schedule into your Tailwind queue.
9. Use Ghostwriter AI to rewrite and personalize your pin descriptions

Even though I haven't tried these features, you can also:

1. Create a personalized marketing plan.
2. Create an email list so you can send and receive emails.
3. Customize your profile.

I know this sounds like a long advertisement for Tailwind, but I am so excited about the many benefits and results of this service, I just had to share it with you, my readers. If you are interested in joining Tailwind, I have a Tailwind tribe called Math Counts where any teacher who teaches kindergarten through high school can post math resources for free. Each person in the tribe adds their own pins in the queue. Once you see the pins in the queue, you can add them to your scheduled pins in Tailwind so your resources keep getting re-pinned to different boards. Tailwind has said that you do not have to be a paying member of Tailwind to be in a Tribe. Here is the link if you are interested in joining Math Counts. Just copy and paste it into any search engine.

https://www.tailwindapp.com/tribe/join?h=eYO2Fvg6qtxnGj

If you decide to join my tribe (which costs you nothing), you will also get a free month ($15 credit) if you ever decide to join the Plus plan. Most bloggers only need Tailwind Plus, which costs $119 per year when paid annually. If you choose to pay monthly then it costs $19.99 per month, or $240 per year. Note that Tailwind’s free trial lets you schedule up to 100 pins and 30 Instagram posts to test the platform before paying.

Getting started with Tailwind is easy. In the members area are five training videos that walk you through everything step-by-step and in much more detail than this blog post. There’s also an in-depth FAQ section, and if you get stuck with anything, their customer service is responsive and helpful. All I can say is that it makes running my Pinterest account much easier; I can be more strategic in my Pinterest marketing efforts plus it saves me a ton of time!  I hope you will check it out.

Valentine Rebus Fun - Using Rebus Puzzles to Solve "Heart" Problems

$5.25

Many of my students love figuring out rebus puzzles. (a visual puzzle in which words are represented by combinations of pictures and individual letters.)  In a nut shell, they are essentially little pictures which cryptically represent a word, phrase, or saying.  Since Valentine's Day is just around the corner, I decided to have some fun and create 26 rebus puzzles for the month of February.

Hearts and Valentines is resource that features familiar expressions that contain the word "heart". (e.g. "From the Bottom of My Heart" or "Cross My Heart") Each illustration in this 13 page resource uses a picture or symbol to represent a common word or phrase.  Students must use logic and reasoning skills to solve the 26 rebuses. So that you don't have to figure out each one, the answers are included.

Each day during the month of February, put up one "Heart" illustration as a student focus activity, OR, if you choose, place two or three up at one time or all of them up at the same time. Students are to figure out which Heart expression the picture represents. It can be fun, but also a very challenging Valentine's Day activity!  Look at the following images and try to work out what they mean.

The first one is "a heart full of love." Were you able to figure it out?

The second one is a bit more challenging. The answer is "a heavy heart." Did you solve it on your own?

Challenge your students to make some of their own "heart" rebus puzzles. A few in this handout were created by middle school students who prove they can be very creative!