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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.

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.
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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.

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.

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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.) 

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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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.

How Many Classroom Management Rules Does A Teacher Really Need?


Now that most of us are getting geared up for a new school year, it's time to think about what classroom rules need to be established. Maybe the ones you had last year just didn’t work, and you are looking for a change. I could recommend many "Do this or this will happen" or "Please don't do this as it will break my heart" statements, but lists can become very long and mind-numbing. Maybe that is why God only gave Ten Commandments. Fewer rules means less has to be memorized. So, maybe we need to ask ourselves: “How many classroom rules are really needed?” 

I would suggest making a few general rules that are clear and understandable since being too specific often leads to complicated, wordy rules that might cover every possible situation. Most of the time, I post six simple classroom rules (only two words each) in my room which encompass my main areas of concern. I find them to be more than sufficient to govern general behaviors, and because alliteration is used, the rules are easy for all of my students to remember.

1.  Be Prompt – In other words, be on time to school/class/group.

2.  Be Prepared – Bring the items you need to class or to a group. Study for upcoming tests. Have your homework completed and ready to turn in. 

3.  Be Polite – This rule focuses on how we treat each other. Show respect for your teacher(s) and your fellow students in the classroom, in the school, and on the playground.

4.  Be Persistent - The final rule spotlights the need to stay on task and complete an assignment even though it might be difficult. 

5. Be Productive - Always put forth your best effort! Grades are achieved; not received; so, do your best at all times.

6. Be Positive – Bad days happen! If you are having one of those days, I do understand. Please just inform me before class that you are having a bad day, and I will try to leave you alone during class discussion. This is not to be abused.

I firmly believe that class rules must cover general behaviors, be clear as well as understandable. Being too specific often leads to complicated, wordy rules that might cover every possible situation, but are impossible to remember.  (A good example are the IRS tax rules which I still have difficulty comprehending). 
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Here are a few things to consider when communicating your classroom rules.
  • Establish clear expectations for behavior from day one.
  • Use techniques such as interactive modeling to teach positive behavior.
  • Reinforce positive behavior with supportive teacher language.
  • Quickly stop misbehavior.
  • Restore positive behavior so that children retain their dignity and continue learning.
If you are interested in using these six rules in your classroom, check them out on Teachers Pay Teachers. Each two word rule is written as a one page chart, and is ready to download and laminate to hang in your classroom.

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Free Back to School eBook for PreK through High School

Free!
It's almost time for the start of a new school year, and here is something you can enjoy all year long - these 21 FREE lessons created by members of The Best of Teacher Entrepreneurs Marketing Cooperative. (TBOTEMC is a group of teachers who work together to market their products.) On each page you will find a link to one free resource and a link to a priced resource. Have fun downloading these free lessons for grades PreK through 12th grade for the entire school year.

Here are a few samples of what is included:

  • Apple Number Puzzles for PreK and Kindergarten
  • Compound Word Activities and Compound Word Puzzles for PreK through 2nd Grade
  • Multiplication Matching Game for 2nd or 3rd Grade
  • Coupon Based Classroom Management System for Grades 5-8
  • Icebreakers Task Cards Getting to Know You Questions for Back-to-School Samper
  • Choosing a Career for 9-12th Grades and Homeschool – Free Guide
In addition, click on six other Back to School eBooks as well as six Winter Holiday Lessons eBooks, six Valentine Day Lessons eBooks and seven End of the Year Lessons eBooks. Plus, you can peruse the four eBooks that each contain 100+ Free Lessons and Teaching Ideas. We wish you the very best as you start off the new school year!

Using Bloom's Taxonomy in Geometry Class

As one of their assignments, my college students are required to create a practice test using pre-selected math vocabulary. This activity prompts them to review, look up definitions and apply the information to create ten good multiple choice questions while at the same time studying and assessing the material. Since I want the questions to be more than Level 1 (Remembering) or Level II (Understanding) of Bloom's Taxonomy, I give them the following handout to help them visualize the different levels.  My students find it to be simple, self explanatory, easy to understand and to the point.

Level I - Remembering


 What is this shape called?



Level II - Understanding


Circle the shape that is a triangle.



Level III - Applying

       Enclose this circle in a square.




Level IV - Analyzing

What specific shapes were used to draw the picture on your right?

Level V - Evaluating

How is the picture on your right like a real truck?  How is it  different?

Level VI - Creating

Create a new picture using five different geometric shapes. (You may use the same shape more than once, but you must use five different geometric shapes.)


As teachers, we are only limited by our imagination as to the activities we ask our students to complete to help them prepare for a test. However, we still need to teach and provide information so the students can complete these types of tasks successfully. With the aid of the above chart, my students create well written practice tests using a variety of levels of Bloom's. When the task is completed, my students have also reviewed and studied for their next math exam. I consider that as time well spent!



If you would like a copy of the above chart in a similar but more detailed format, it is available on Teachers Pay Teachers as a FREE resource.

The Eleventh Hour? A Trick About Multiplying by 11

The mathematician magician is still here, sharing her tricks. This week it is the elevens. Before we demonstrate the trick, I have to get on my soap box for just a moment. In my humble opinion, all students should know their times tables through 12 even though the Common Core Standard for third grade says through 10 x 10. Remember, Common Core is the minimum or base line of what is to be learned. In Algebra, I insist that my students know the doubles through 25 x 25 and the square roots of those answers up to 625. It saves so much time when we are working with polynomials.

Now to our our amazing mathematical "trick". Let's look at the problem below which is 231 x 11.

 
First we write the problem vertically. Next, we bring down the number in the ones place which in this case is a one. Now we add the digits in the ones and tens place which is 3 + 1 and get the sum of four which is brought down into the answer.


Moving over to the hundreds place, we add that digit with the digit in the tens place 2 + 3 and get an answer of five which we bring down. Finally, we bring down the digit in the hundreds place which is a two. The answer to 231 x 11 is 2,541.

Now try 452 x 11 in your head. Did you get 4,972? Let's try one more. This time multiply 614 by 11. I'm waiting...... Is your answer 6,754?

Now it is time to make this process a little more difficult. What happens if we have to regroup or carry in one of these multiplication problems?

We will multiply 784 by 11. Notice that we start as we did before by just bringing down the number in the ones place. Next, we add 8 + 4 and get a sum of 12. We write down the 2 but carry or regroup the one. We now add 7 + 8 which is 15 and then add in the 1 we are carrying. That makes 16. We bring down the 6 but carry the 1 over. We have a 7 in the hundreds place, but must add in the one we are carrying to get a sum of 8. Thus our answer is 8,624.

Let's see if you can do these without paper or pencil. 965 x 11 768 x 11 859 x 11 After working the problems in your head, write down your answers and check them with a calculator. Try making up some four and five digit problems because this is a non-threatening way to have your students practice their multiplication facts. Have fun!

Anno's Mysterious Multiplying Jar - Learning About Factorials

Factorial is a word that mathematicians use to describe a special kind of numerical relationship. Factorials are very simple things. They are just products, indicated by the symbol of an exclamation mark. The factorial function (symbol: !) means to multiply a series of descending natural numbers. For instance, "five factorial" is written as "5!" (a shorthand method) and means 5 × 4 × 3 × 2 × 1 = 120. Factorials are used in determining the numbers of combinations and permutations and in finding probability.

Now all of that may seem above your mathematical head, but let me introduce you to the book Anno's Mysterious Multiplying Jar by Masaichir and Mitsumasa Anno.  It is a story about one jar and what is inside it. Anno begins with the jar, which contains one island, that has two countries, each of which has three mountains. The story continues like this until 10 is reached.  The colorful pictures are arranged within borders on the page as many times as the number of objects being discussed. For instance when four walled kingdoms are introduced, four kingdoms are on the page.

The explanation of 10! in the back of the book is also very helpful. Even if children do not understand the concept being taught, they will certainly appreciate the detailed colored drawings and imaginative story! The book is best for kids who have been introduced to at least basic multiplication facts, but younger kids will enjoy counting and looking at the pictures even if the rest of it is over their heads; so, this book helps with multiplying skills as well as the mathematical concept of factorials.

You might give the students a worksheet to keep track of how many islands, rooms, etc. there are. The final question is how many jars are there. Hopefully there will some students who catch on to the factorial concept, find the pattern and discover the answer! 

Here is an example of how you might use factorials in solving a word problem.  How many different arrangements can be made with the letters from the word MOVE?  Because there are four different letters and four different spaces, this is how you would solve the problem.

____   ____   ____   ____ 
Four Possible Spaces

All four letters could be placed in the first space. Once the first space is filled, only three letters remain to fit in the second space. Once the second space is filled with a letter, two letters remain to write in the third space. Finally, only one letter is left to take the fourth and final space. Hence, the answer is a factorial (4!) = 4 × 3 × 2 × 1 = 24 arrangements.

Try some problems in your classroom. Start with an imaginary character, Cal Q. Late, who is working at an Ice Cream Store called Flavors. A hungry customer orders a triple scoop ice cream cone with Berry, Vanilla, and Bubble Gum ice cream. How many different ways could Cal Q. Late stack the ice cream flavors on top of each other?

You could answer the question by listing all of the possible orders of the three ice cream flavors from top to bottom. (Students could have colored circles of construction paper to physically rearrange.)

Bubble Gum - Berry - Vanilla
Bubble Gum - Vanilla - Berry
Berry - Vanilla - Bubble Gum
Berry - Bubble Gum - Vanilla
Vanilla - Berry - Bubble Gum
Vanilla - Bubble Gum - Strawberry

Or, if we use factorials, we arrive at the answer much faster: 3! = 3 × 2 × 1 = 6

Learning about patterns and the use of factorials will stretch a students' mathematical mind. Why not try a few problems in your classroom? And by all means, check out Anno's Mysterious Multiplying Jar.