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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.

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.


Mary Kay

Likes to work alone; shy and withdrawn;  wears a great deal of make-up.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



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.

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!

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!


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.

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?

Free Back to School eBook for PreK through High School

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.

FREE End of the Year Ebook

The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC) has offered FREE End of the Year lessons since 2015. It is now 2021, and we hope that teachers and parents still find these FREE lessons for grades K-12 useful and helpful so that their students and children can continue to learn during the summer. 

On each page of the Ebook, you will find links to FREE lessons  as well as priced lessons for many subject areas created by members of TBOTEMC. 

Here are only some of the FREE items found in this year’s End of Year eBook.
Past eBooks 

There are 16 freebies altogether in this 25 page eBook. In addition, you can explore links to thousands of free lessons from our past holiday eBooks, Teach Talk eBooks, and social media sites. So wrap up the 2021school year right with Free End of the Year Lessons by The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC). All you have to do is download the free book and click on the link of the resource you like.

Math Games! An Effective Way to Teach Math

I currently teach remedial math students on the college level. These are the students who fail to pass the math placement test to enroll in College Algebra - that dreaded class that everyone must pass to graduate. The math curriculum at our community college starts with Basic Math, moves to Fractions, Decimals and Percents, and then to Basic Algebra Concepts. Most of my students are smart and want to learn, but they are deeply afraid of math. I refer to them as mathphobics.

We all have this type of student in our classrooms, whether it is middle school, high school, or college. When working with this type of student, it is important to bear in mind how all students learn. I always refer back to the Conceptual Development Model which states that a student must first learn at the concrete stage (use manipulatives) prior to moving to the pictorial stage, and well in advance of the abstract level (the book). This means that lessons must include the use of different manipulatives.

I use games a great deal because it is an easy way to introduce and use manipulatives without making the students feel like “little kids.” I can also control the level of mathematical difficulty by varying the rules; thus, customizing the game to meet the instructional objectives my students are learning. However, as with any classroom activity, teachers should monitor and assess the effectiveness of the games. 

When using games, other issues to think about are:
  1. Excessive competition. The game is to be enjoyable, not a “fight to the death”.
  2. Mastery of the mathematical concepts necessary for successful play. Mastery should be at an above average level unless teacher assistance is readily available when needed. A game should not be played if a concept has just been introduced.
  3. Difficulty of the rules. If necessary, the rules should be modified or altered in order that the students will do well.
  4. Physical requirements (students with special needs). These should be taken into account so that every player has an opportunity to win.
In addition to strengthening content knowledge, math games encourage students to develop such skills as staying on task, cooperating with others, and organization. Games also allow students to review mathematical concepts without the risk of being called “stupid”. Furthermore, students benefit from observing others solve and explain math problems using different strategies.

Games can also….
  1. Pique student interest and participation in math practice and review. 
  2. Provide immediate feedback for the teacher. (i.e. Who is still having difficulty with a concept? Who needs verbal assurance? Why is a student continually getting the wrong answer?)
  3. Encourage and engage even the most reluctant student.
  4. Enhance opportunities to respond correctly.
  5. Reinforce or support a positive attitude or viewpoint of mathematics.
  6. Let students test new problem solving strategies without the fear of failing.
  7. Stimulate logical reasoning.
  8. Require critical thinking skills.
  9. Allow the student to use trial and error strategies. 
Mathematical games give the learner numerous opportunities to reinforce current knowledge and to try out strategies or techniques without the worry of getting the “wrong” answer. Games provide students of any age with a non-threatening environment for seeing incorrect solutions, not as mistakes, but as steps towards finding the correct mathematical solution. 

If you want a challenging but fun and engaging math game, try Contact. It is a fun and attention-grabbing way for students to review basic math facts and to use critical thinking without doing another “drill and kill” activity.

Science Investigations Packet for Grades 3-4

Learning to love math and science is important for so many reasons as our world becomes more dependent on technology. Science can spark imagination, initiate problem solving, require logical thinking, and so much more.  As any scientist knows, the best way to learn science is to do science. This is the only way to get to the real business of asking questions, conducting investigations, collecting data, and looking for answers. Active, hands-on, student-centered inquiry is at the core of good science education.

Having children do science investigations can be fun, but having the students accurately record things can be extremely difficult. Since my husband teaches science, he helped me to create my investigation packet on Teachers Pay Teachers - a 12 page generic science investigation packet for grades 3-4. The inquiry packet guides the student through the six steps of the scientific method: 
Only $4.30
  1. Investigating Properties 
  2. Interactions
  3. Making a Plan 
  4. Determining the Investigative Question 
  5. Prediction and Data Collection 
  6. Writing a Conclusion Based on the Data. 
This packet consists of an introduction, simple and clear step-by-step directions on how to use the packet, a three page student investigation packet, a blank graphing grid, a property word list, an optional student checklist and a four point grading rubric for the teacher. 

Wherever a child is, and wherever they go, there will always be a place and a time to learn science. Every room is a classroom; every question is a discovery; every moment is a teachable moment. Let this resource guide your students through a science investigation so their curiosity is piqued, and they are inspired to find an answer.

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See You Later Alligator, Teaching Greater Than and Less Than

I originally posted this article back on May of 2011, but as I view products on Pinterest or on Teachers Pay Teachers, I feel a need to revisit it. I have seen alligators, fish, movable Popsicle sticks, etc. as ways to teach greater than or less than to children. Even though these may be good visual tools, to be honest, there are no alligators or even fish in mathematics.  Because many students still fail to understand which way the symbol is placed, (once in awhile I have a college student who is confused) here is a different method which you might wish to try. First of all, every child knows how to connect dots; so, let’s use that approach. 

Suppose we have two numbers 8 and 3. Ask the students, “Which number is greater?" Yes, 8 is greater. Let’s put two dots beside that number. 8 : Now ask, “Which number is smaller or represents the least amount?" You are right again. Three is smaller. Let’s put one dot beside (in front of) that number. Now have the students connect the dots.....

Free Resource
It will work every time! When two numbers are equal, put two dots beside each number and connect the dots to make an equal sign. What makes this method a little different is that the students can visually see which number is greater because it has the most dots beside it; so when reading the number sentence, most of the time it is read correctly.

In a free handout entitled Number Tiles - Math Activities for the Primary Grades a greater than and less than activity is included which can be used over and over again. It's yours for free. Just click on the title to download your free copy.

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The Wolf's Chicken Stew - Celebrating the 100th Day of School

This week is the 100th day of school for my youngest grandson.  He is so-o-o excited because his teacher has many special things planned. I even made him and his sisters a pair of 100 eyeglasses to wear! (See photo below.)

His teacher gave him a plastic bag in which he is to place 100 items. Because he has to count them out, I decided it was time that he learned to count by tens.  We linked ten multi-link cubes together and made ten different groups of ten, each a different color.  When it is time for him to count out his items, he will show his classmates that it is much quicker to count by tens to get to 100.

I also sent a book with him for his Pre-K teacher to read, The Wolf's Chicken Stew by Keiko Kasza. It deals with numeration and number sense and is appropriate for grades PreK-3. You might be unfamiliar with the book, but it's about a wolf named Wolf (a wanna-be bad guy) who wants a fat hen for his delicious chicken stew.  Before seizing Mrs. Chicken, he decides to fatten her up first.  He is a great cook; so, he spends the next few nights in the kitchen making 100 scrumptious pancakes as well as 100 donuts, and a 100 pound cake and anonymously leaving them on her porch for Mrs. Chicken to eat. However, at the end of the book, Wolf unwittingly makes 100 new friends.

I hope you can locate this book to read to your students.  If you do, here are some fun ideas and engaging activities you might try.
  • Rewrite the ending of the story.
  • Talk about how this wolf is different from a real wolf. 
  • Retell the story using different food items that the wolf might have used to fatten up Mrs. Chicken. 
  • Using connecting links, connect 100 of them. Then find items in the classroom that weigh 100 links using a balance scale. 
  • Use the picture where the wolf is making pancakes and write the recipe. 
  • Using the picture of the 100 pound cake, write as many words as possible that describe the cake. 
  • Hide 100 "chicks" (made out of paper) around the classroom and see if the children can find them all.
  • List reasons why this is fictional story and not a real story.
Whatever you do, have fun with your students.  Remind them that they are "1 out of 100"! And a BIG thank you to each of you for giving 100% to teaching!

Tally Marks - Different Ways to make them

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 character uses 5 strokes; so, a series of 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 () 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  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.