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Measuring Snow - A Craft for the Un-Crafty

I am not a very crafty person; so, I am always looking for items that are easy to make that I can give to my grandchildren. One year, I gave them a snowman making kit that included buttons, a carrot, six rocks and two sticks. This year, I am giving them a Snow Measuring Tool.  Not is it only fun to use, but it also helps them to practice using a ruler. Here is how you can make one!
 
Here is the list of supplies you will need:  

1) A paint stick - free at most paint stores
2) A permanent marking pen
3) Something to glue at the top of the stick (You can make it, or be like me and purchase one from a craft store.)

First, using a ruler, mark off every inch along the paint stick. I was able to make nine marks. (Notice I used the plain side of the paint stick and not the side with all of the advertising.) Now write the inches beside each corresponding mark.

When that is completed, glue the item you have chosen at the top of the stick.  I really wanted to use a snowflake, but my local craft store didn't have any; so, I settled on using one of Santa's reindeer.  Which one, I'm not sure since it didn't come with a name.(Hint: My husband used Gorilla Glue so the reindeer wouldn't fall off.)

When it snows, venture outside and stick the Snow Measuring Tool into the snow and read the number of inches that have fallen. If it isn't exactly on an inch mark, then have your child estimate using fractional parts.

While you are measuring the snow, think about this saying: "Ten inches of snow equals one inch of rain." I am sure you have heard that claim as it is a commonly shared belief that seems to be repeated every time it snows a few feet. But, is the saying true? The immediate answer is: Sometimes.

When the temperature is around 30 degrees, one inch of liquid precipitation (rain) would fall as 10 inches of snow, presuming the storm is all snow. But, the amount of moisture in each snowflake differs depending on the temperature which in turn changes the snow to rain ratio.

For example, if a big January snowstorm occurred with colder temperatures (such as 25 degrees), the snow ratio would be closer to 15 inches of snow to one inch of rain. In fact, weathermen take this into account when forecasting how much snow a location will receive. There have been storms with snow closer to 20 degrees, moving the snow ratio closer to 20 to one. And, when it's warmer, say 35-40 degrees, the ratio moves to 5" of snow to 1" of rain.

So, after your children measure the snow in your yard with their Snow Measuring Tool, try converting the inches of snow into inches of rain based on the 10":1" ratio. By doing so, you may become your neighborhood's weather forecaster or even better, a first rate mathematician!
Your children might enjoy this snowman glyph. It's is an excellent winter activity for reading and following directions, and requires problem solving, communication, and data organization.

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Get a FREE Winter E-book of Winter Activities for All Grades


Winter is upon us, and as teachers, we are always looking for fun, engaging activities for our students. Check out these free holiday lessons by The Best of Teacher Entrepreneurs Marketing Cooperative! This 22 page E-book, “Free Winter Lessons by The Best of Teacher Entrepreneurs – 2021,” includes a variety of activities for kindergarten through 12th grade from experienced Teachers Pay Teachers sellers. Since it is free, all you have to do is download it!

Here are some of the lessons included:

¯I Have Who Has Games
FREE Resource

¯STEM Challenge; Creating the Longest Chain

¯Two Different Winter Crossword Puzzles Featuring 25 
    Words that Begin with “Snow”

¯Winter Holidays Classification Exercise

¯Printable Holiday Coloring Book for 9-12th Grades

Sending You Warm Winter Wishes,
The Members of the Best of Teacher Entrepreneurs Marketing Cooperative.

Snowflake Facts and Snowy Words - Get a FREE Crossword

I love winter. Yes, it's true. I love sweaters, a fire in the fireplace, throwing snowballs, eating snow ice cream and even the cold! As you can see from the photo, my grandchildren and I think snow is glorious.

Speaking of snow, have you ever wondered about snowflakes, how they are formed, how many different kinds there are? Here are a few fun facts about snowflakes that you might not have known.

  1.  The size of a snowflake depends on how many ice crystals connect together.
  2. Snowflakes form in a variety of different shapes.
  3. One of the determining factors in the shape of individual snowflakes is the air temperature around it.
  4. Snowflakes always have six sides.
  5. A single ice crystal is known as a snowflake.
  6. In total, 80 different shapes of snowflakes have been identified so far.
  7. Did you know that the saying that no two snowflakes are alike is actually a myth? It was true until in1988 when a scientist in Wisconsin managed to find two identical snowflakes.
I could go on and on, but since seven is the number of completion, I'll stop. 

While researching snowflakes, I started wondering how many words I could find that began with the word "snow" as I  wanted to make a winter crossword puzzle. I found 25 although there were plenty more. I just didn't want to make the clues to my puzzle overwhelming. 

FREE
The title of this new FREE resource is Snowy Words. It includes two winter crossword puzzles; each with 25 words that all begin with “snow.” One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same vocabulary is used for each crossword, each grid is laid out differently. Answers keys for both puzzles are included. AND don't forget, you can downloaded for free!


A Go Figure Debut for an Algebra Teacher Who Is New!


Our featured teacher is a math instructor from Humble, Texas. Kristel has been teaching for eleven years in grades 7-12. (Only one year teaching middle school, the rest has been in high school.) Most of her time has been spent teaching Algebra 2.

Kristel began her career in Arizona (7 years) and has since moved to Texas with her husband and two young daughters. Since moving to Texas, they have added a little boy to their family. She enjoys the fall weather because she can spend more time outside with her kids. She also loves dancing (former dancer/cheerleader), drawing, photography, and making digital resources. She confesses that she is a little obsessed with office supplies and candles.

Kristel really enjoys getting to know her students and helping them to feel safe at school. Like most of us, she loves watching students reach their full potential and helping them build their critical thinking skills. Due to COVID, her classroom has evolved into something more individualized, and technology driven.

Every class period, she gives students a warm-up that includes both an academic question and a “Is there anything you want to tell me?” question. Students really enjoy this and love to tell jokes, important things in their lives (dances, upcoming performances, or games), silly facts, or kind words. In addition, she provides students with instructional videos she creates to get the notes they need for a particular topic, and students spend the majority of the class practicing skills and working with their peers. This also allows Kristel to help students in a more individualized way.

FREE
Kristel began her TPT journey during the COVID shut down of 2020.  Her store, Kristel’s Math Lab, currently contains 27 products with three freebies and 24 paid items. Most of her resources are geared toward Algebra 2, but many times, they can be used in Algebra 1 or other high school math classes.

Her highlighted free item is a digital worksheet called Multiplying Polynomials. If you are looking for an engaging way to help students practice multiplying a monomial by a monomial, then this will be the perfect way to do so. This no prep activity was created using Google Sheets™ and includes 12 self-checking problems. (two versions included).

$10.00
Her paid resource is a bundle called Systems of Equations and Inequalities. It includes four digital quizzes made with Google Forms™ and includes systems of equations using the graphing method, systems of equations using the substitution method, systems of equations using the elimination method and solving systems of inequalities. Each quiz contains 20 multiple-choice questions and is self-checking.

Because she is a full-time math teacher and a mother of three, her product creation is not as fast as she would like it to be. She is currently working on a digital interactive notebook (contains lots of student activities) on systems of equations, and she plans to add more digital worksheets (using Google Sheets™) over polynomial operations very soon.

If you teach math like I do, then I recommend visiting Kristel’s store for unique, engaging, and exceptional math resources. I already have!

Skip Counting and Learning How to Multiply Using Pattern Sticks

Most elementary teachers use a Hundreds Board in their classroom.  It can be used for introducing number patterns, sequencing, place value and more. Students can look for counting-by (multiplication) patterns. Colored disks, pinto beans or just coloring the squares with crayons or colored pencils will work for this. Mark the numbers you land on when you count by two. What pattern do they make? Mark the counting-by-3 pattern, or mark the 7's, etc. You may need to print several charts so your students can color in the patterns and compare them. I usually start with the 2's, 5's and 10's since most children have these memorized.

On the other hand, the Hundreds Board can also be confusing when skip counting because there are so many others numbers listed which easily create a distraction.  I have found that Pattern Sticks work much better because the number pattern the student is skip counting by can be isolated. Pattern Sticks are a visual way of showing students the many patterns that occur on a multiplication table.  Illustrated below is the pattern stick for three. As the student skip counts by three, s/he simply goes from one number to the next (left to right).


Martian Fingers
For fun, I purchase those scary, wearable fingers at Halloween time. (buy them in bulk from The Oriental Trading Company - click under the fingers for the link.) Each of my students wears one for skip counting activities. I call them the Awesome Fingers of Math! For some reason, when wearing the fingers, students tend to actually point and follow along when skip counting.

Most students enjoy skip counting when music is played. I have found several CD's on Amazon that lend themselves nicely to this activity.  I especially like Hap Palmer's Multiplication Mountain.  My grandchildren think his songs are catchy, maybe too catchy as sometimes I can't get the songs out of my mind!

Think about this.  As teachers, if we would take the time to skip count daily, our students would know more than just the 2's, 5's and 10's.  They would know all of their multiplication facts by the end of third grade. And wouldn't the fourth grade teacher love you?!?

IMPORTANT:  If you like this finger idea, be sure that each student uses the same finger every time to avoid the spreading of germs. Keeping it in a zip lock bag with the child’s name on the bag works best. (Believe it or not, when I taught fourth grade, the students would paint and
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decorate the fingernails!)

To help your students learn their multiplication facts, you might like the resource entitled Pattern Sticks. It is a visual way of showing students the many patterns on a multiplication table.

Glyphs Are Really A Form of Graphing - Completing a Turkey Glyph

Sometimes I think that teachers believe a glyph is just a fun activity, but in reality glyphs are a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and requires a legend/key to understand the glyph. The creation of glyphs requires problem solving, communication as well as data organization.

Remember Paint by Number where you had to paint in each of the numbers or letters using a key to paint with the right color? How about coloring books that were filled with color-by-number pages? Believe it or not, both of these activities were a type of glyph.
$3.00

For Thanksgiving, I have created a Turkey Glyph. Not only is it a type of graph, but it is also an excellent activity for reading and following directions.

Students are to finish the turkey glyph using the seven categories listed below.
  1. Draw a hat on the turkey (girl or a boy?)
  2. Creating a color pattern for pets or no pets. 
  3. Coloring the wings based on whether or not they wear glasses. 
  4. Writing a Thanksgiving greeting based on how many live in their house. 
  5. Do you like reading or watching TV the best? 
  6. How they get to school. (ride or walk)
  7. Pumpkins (number of letters in first name)
At the end of the activity is a completed Turkey Glyph which the students are to "read" and answer the questions. Reading the completed glyph and interpreting the information represented is a skill that requires deeper thinking by the student. Students must be able to analyze the information presented in visual form. A glyph such as this one is very appropriate to use in the data management strand of mathematics.  If you are interested, just click under the resource cover page..

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.
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.

A Go Figure Debut for a South Wales Teacher Who's New!

Meet Walton 
Walton started teaching 20 years ago, in the Peace Corps in Vanuatu (Vanuatu is a double chain of 13 principal and many smaller islands in the south-western Pacific Ocean.) a few months after September 11th! He was teaching English to Francophone (French-speaking),
students trying to get their GED-equivalent so they could go to school in France. It was a great little program to fill the gap between the local educational system and the requirements of French universities. So he fell in love with teaching with these hard working students in a ni-Van (abbreviation for Ni-Vanuatu) high school!

Since then, he has taught and tutored in public and private schools throughout the world including Kazakhstan and Russia. One year, he did an orientation for Afghan students who were planning to come and study in the U.S. in high school which was very rewarding.

Walton stopped teaching full-time in 2012, when he was teaching at the University of New Haven and since then have been doing private tutoring online as well as materials writing. So his classroom is his desk! The good news is that adjusting to COVID wasn't a big problem as he was already teaching online-although However, he feels for anyone who had to adjust on the spot and especially his son's poor teachers who had to teach hybrid! Walton has had materials published by OUP, Compass Publishing, and Macmillian, as well as his own materials which makes him a Freelance Writer and Editor.

His favorite part of teaching is when a student is working to grasp something, and they just can't get it. Then you figure out how to present it just the right way or something just clicks in their heads and they get it! It just makes it worth all the hard times and struggle. And you can see their excitement and enthusiasm. It's especially fun when they start overusing something because they are so proud of themselves for getting it!

For hobbies, Walton likes to read mystery novels and play Minecraft by himself but also with his nine year old son. In the summer, he and his son go fishing almost every day. It's been fun for him to watch his son learn problem solving and experimentation as they try to figure out what the fish are biting at, where they are, and so on.

FREE
His featured  free product, The Candy Thief, is a critical thinking mystery activity where students use clues to solve a mystery. This one has a Halloween theme, as students figure out who stole someone's Halloween candy and is designed for younger learners. There are three witness, but one of them is lying. Can your students ready their statements and figure out who the liar is? It is a great warm-up, critical thinking game, conversation starter, and filler of a time killer for early finishers.

$3.00
Walton has chosen to highlight as his paid product, Scary Story Writing Lesson Plan. This complete Halloween writing lesson plan uses the genre-based approach to writing to teach students how to write a scary store In the Halloween Scary Story Lesson Plan, students read several scary stories, including “Movie of Death,” They also talk about horror movies they are familiar with. They are then guided through an analysis of key features of a scary story. These include typical settings for a scary story, building tension, the concept of a twist and endings. Finally, students write their own scary story with those genre-specific elements. It's a fun lesson on how to write a scary story by giving students examples of scary stories and tools to analyze the elements of a scary story.

I find Walton's resources very unique and engaging. With Halloween just around the corner, check out what he has to offer. There is probably something in his store that you can use this month!

"BOO" to Fractions? Recognizing Equivalent 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. What do ghosts eat for breakfast?  Scream of Wheat and Ghost Toasties!








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 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:

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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.


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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.




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.
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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!

October - Is It "Fall" or "Autumn"? Doing Science Investigations with Leaves

October is just around the corner.  October means football (Ohio State, of course), cooler weather and gorgeous leaves. (It is also when my husband and I were married.) In October, we see the leaves turning colors, and the deciduous trees shedding their leaves.

Another name for fall is autumn, a rather odd name to me.  Through research, I discovered that the word autumn is from the Old French autumpne, automne, which came from the Latin autumnus. Autumn has been in general use since the 1960's and means the season that follows summer and comes before winter.
Fall is the most common usage among those in the United States; however, the word autumn is often interchanged with fall in many countries including the U.S.A. It marks the transition from summer into winter, in September if you live in the Northern Hemisphere or in March if you live in the Southern Hemisphere.  It also denotes when the days are noticeably shorter and the temperatures finally start to cool off. In North America, autumn is considered to officially start with the September equinox. This year it was on September 22nd.
With all of that said, the leaves in our neighbor's yard have already begun to fall into ours which aggravates my husband because he is the one who gets to rake them. Maybe focusing on some activities using leaves will divert his attention away from the thought of raking leaves to science investigations.  
Remember ironing leaves between wax paper?  We did that in school when I was a little girl (eons and eons ago).  Here is how to do it.
  1. Find different sizes and colors of leaves.
  2. Tear off two sheets about the same size of waxed paper.
  3. Set the iron on "dry".  No water or steam here!
  4. The heat level of the iron should be medium.
  5. Place leaves on one piece of the waxed paper.
  6. Lay the other piece on top.
  7. Iron away!
You can also use this activity to identify leaves.  According to my husband who knows trees, leaves and birds from his college studies, we "waxed" a maple leaf, sweet gum leaf, elm leaf, cottonwood leaf (the state tree of Kansas - they are everywhere), and two he doesn't recognize because they come from some unknown ornamental shrubs.

$5.25
Maybe you would like to use leaves as a science investigation in your classroom.  I have one in my Teacher Pay Teachers store that is a six lesson science performance demonstration for the primary grades. The inquiry guides the primary student through the scientific method and includes 1) exploration time, 2) writing a good investigative question, 3) making a prediction, 4) designing a plan, 5) gathering the data, and 6) writing a conclusion based on the data. Be-leaf me, your students will have fun!

(A preview of the investigation is available. Just click on the resource cover on your right.) 

A Go Figure Debut for an Australian Who is New!

Cece is from New South Wales and has been teaching between grades 1-5 for almost six years. For two years, she was a substitute/relief teacher. Her favorite thing about teaching is being able to have a positive impact on students and seeing their excitement when learning new things about the world around them. 

Her classroom is a safe space and well-organized. She believes there is a place for everything, and everything has a place. (Personally, so do I.) She believes in nurturing curiosity and providing students with the opportunity to actively seek answers to questions. This is achieved by providing a mixture of activities to support different learning styles.

In her spare time, Cece likes to paint. She also enjoys expressing her creativity by designing resources for Teachers Pay Teachers! In addition, she takes yoga classes every weekend to keep in shape and also as a way to unwind and relax (something every teacher needs).

Currently, her store, Teach Super, contains 56 products, 49 paid and seven free. Her resources are designed to promote student participation, provide educationally rich learning experiences, and encourage students to learn. All her resources are tried and tested in her classroom to make sure they are useful and helpful to other teachers.

FREE!

One of her free resources is called Synonym Path Activities. This is a perfect literature center activity that involves students connecting similes to make a path down the page. Students may color the path or draw a line. This activity can be used as a whole-class activity or as a literature center. You can also have students make and write sentences words from the included grid.

$15.00

Cece's featured paid item is The Ultimate Relief Casual Substitute Teaching Resource Book (250+ activities!) This 53 page book contains a huge collection of activities and resources ideal for all the casual/ relief/ supply/ substitute teachers out there. It is so important to have fun, no-prep ideas/activities up your sleeve when a substitute is taking over the day. The book contains a 250+ collection of go-to activities for all KLA's (Key Learning Areas of a curriculum or the subjects) and year levels. They require very little to no resources or preparation. This “all you need” resource will ensure you feel more confident coming in each day, ready for anything.

Take some time to check out her store and resources. You will find it well worth your time.

Let's Go Fly A Kite - Using the Correct Geometry Term for Diamond!



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, 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 on 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.
Clip Art by My
Cute Graphics

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!

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$2.50
This set of two polygon crossword puzzles features 16 geometric shapes with an emphasis on quadrilaterals and triangles. The words showcased in both puzzles are: congruent, equilateral, isosceles, parallelogram, pentagon, polygon, quadrilateral, rectangle, rhombus, right, scalene, square, trapezoid and triangle.  The purpose of these puzzles is to have students practice, review, recognize and use correct geometric vocabulary. Answer keys are included.

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There's A Place For Us! Teaching Place Value

When my college students (remedial math students) finish the first chapter in Fractions, Decimals, and Percents, we focus on place value. Over the years, I have come to the realization how vital it is to provide a careful development of the basic grouping and positional ideas involved in place value. An understanding of these ideas is important to the future success of gaining insight into the relative size of large numbers and in computing.  A firm grasp of this concept is needed before a student can be introduced to more than one digit addition, subtraction, multiplication, and division problems. It is important to stay with the concept until the students have mastered it. Often when students have difficulty with computation, the source of the problem can be traced back to a poor understanding of place value.

It was not surprising when I discovered that many of my students had never used base ten blocks to visually see the pattern of cube, tower, flat, cube, tower, flat.  When I built the thousands tower using ten one hundred cubes, they were amazed at how tall it was.  Comparing the tens tower to the thousands tower demonstrated how numbers grew exponentially.  Another pattern emerged when we moved to the left; each previous number was being multiplied by 10 to get to the next number.  We also discussed how the names of the places were also based on the pattern of:  name, tens, hundreds, name (thousands), ten thousands, hundred thousands, etc. 

I asked the question, "Why is our number system called base ten?"  I got the usual response, "Because we have ten fingers?"  Few were aware that our system uses only ten digits (0-9) to make every number in the base ten system.

We proceeded to look at decimals and discovered that as we moved to the right of the decimal point, each number was being divided by 10 to get to the next number. We looked at the ones cube and tried to imagine it being divided into ten pieces, then 100, then 1,000. The class decided we would need a powerful microscope to view the tiny pieces.  Again, we saw a pattern in the names of each place:  tenths, hundredths, thousandths, ten thousandths, hundred thousandths, millionths, etc.


I then got out the Decimal Show Me Boards.  (See illustration on the left.)  These are very simple to make. Take a whole piece of cardstock (8.5" x 11") and cut off .5 inches. Now cut the cardstock into fourths (2.75 inches).  Fold each fourth from top to bottom. Measure and mark the cardstock every two inches to create four equal pieces. Label the sections from left to right - tenths, hundredths, thousandths, ten thousandths. You can type up the names of the places which then can be cut out and glued onto the place value board.

Here are some examples of how I use the boards.  I might write the decimal number in words.  Then the students make the decimal using their show me boards by putting the correct numbers into the right place.  Pairs of students may create two different decimals, and then compare them deciding which one is greater.  Several students may make unlike decimals, and then order the decimals from least to greatest.  What I really like is when I say, "Show me", I can readily see who is having difficulty which allows me to spend some one-on-one time with that student.


Show Me Boards can also be made for the ones, tens, hundreds and thousands place.  Include as many places as you are teaching. I've made them up to the hundred thousands place by using legal sized paper. As you can see in the photo above, my two granddaughters love using them, and it is a good way for them to work on place value.

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A good way to practice any math skill is by playing a game. Your students might enjoy the No Prep place value game entitled: Big Number.  Seven game boards are included in this eleven page resource packet. The game boards vary in difficulty beginning with only two places, the ones and the tens.  Game Board #5 goes to the hundred thousands place and requires the learner to decide where to place six different numbers.  All the games have been developed to practice place value using problem solving strategies, reasoning, and intelligent practice.

Securing Calculators in Your Classroom so they don't walk off!

I teach at a community college which I love. I also spend three hours a week in the Math Lab which is a place where our students can come for math tutoring, to study or just to work in a group. It is staffed by math instructors. We try to have the supplies available that our students might need like a stapler, hole punch, white boards, pencils, scrap paper etc. We also have a set of scientific calculators which our students may borrow while in the Math Lab. 

Most of our items tend to remain in the Math Lab. Of course, a few pencils disappear now and then, but generally, most supplies seem to stay put EXCEPT for the calculators. Now I must say, students who take these home do so unintentionally. They just pick it up, slip it in their backpack and head out the door. Fortunately, most students are honest and eventually return the calculators to us. The dilemma is we only have so many calculators; so, we want to make sure that if a student needs one, it is on hand. We needed to find a way to make sure the calculators didn’t walk off.

One of our team members came up with an innovative but simple solution.
She purchased small clip boards and attached the calculator to it by using Gorilla tape. The calculators are still accessible, but much too big or bulky to accidentally stick into a backpack. In addition, since they are on a clip board, they are easy to stand and display in the white board trays. At the end of the day, it is simple to count them to make sure none are missing. This idea has worked so well, that some of our math instructors are now using this method in their classrooms.

So if you teach math, and have a set of classroom calculators, why not give this idea a try?

Getting Students to Work Together in Cooperative Groups

One of my colleagues completed a Leadership Project with her ten students that I want to share with you. She had two similar 100 piece puzzles. (The puzzles are fairly inexpensive at Walmart or Dollar General.) Kay took these two similar puzzles which had alike colors/pictures on them and mixed them up. She then separated them into two baggies, and put each baggie in one of the original two boxes.

The class numbered off, 1-2-1-2...and so on, and then separated into two groups. At first, the students thought this was going to be a race to see which group could complete their puzzle first; however, each group started at the same time, writing the starting time on the board. After that, Kay didn’t say a word, and answered no questions! She simply observed the students. The students tried asking her, "Hey we don’t have all the edges; these pieces don’t match; are these the right puzzles?" Something is wrong; what's up?"

Kay waited to see who would take the lead to combine the groups, and how they joined. She wondered, "Would they join peacefully? Would they gather and form one group; two new groups; work together, or divide again?"  As she continued to observe, she began to write names on the board of those who were positive and took leadership. She then wrote the time on the board when they commenced to form one group.

When they finished, she held a Socratic Seminar (an Avid strategy) about how they felt concerning the activity. One student, who did not want to join a group in the beginning, became so involved during the project that he actually was the leader in getting the groups together.  It was one of those fantastic teacher moments!

Kay's students learned quite a bit from the activity since in reality, this is how life, social, and work environments are. She pointed out that they may not have a project that is going well, but by joining together with another group, you can problem solve, gain assistance, and acquire more pieces to your puzzle to accomplish your project.
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Since working together doesn't seem to be a skill that comes naturally, I use this activity with my college freshman as they begin their final group projects. Plus, as you think about your class and are puzzled about how you can get your students to work well in cooperative groups, keep this activity in mind.  It might just put the pieces together for you.

If your class enjoys cooperative learning, try this rubric for grading co-op groups.