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Receive A Free End of the Year Ebook of Activities

Complete the 2023 school year by downloading these Free End of the Year Lessons by members of The Best of Teacher Entrepreneurs Marketing Cooperative (TBOTEMC). There is something free for everyone in this 16 page eBook so take a look! Here are just a few examples of what you can download for free:

Also check out these past free Back to School eBooks.   Below are the links to the past eight End of the Year eBooks by TBOTEMC.  If you are interested, just click on the year to download the FREE resource.

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A Go Figure Debut for an Author and Teacher Who is New

Meet Gail Hennessey, a teacher and an author. She taught for 33 years and then retired in 2006. During her teaching career, she was named the National Council for Social Studies Outstanding Elementary Social Studies Teacher of the Year as well as the New York State Council for the Social Studies Elementary Social Studies Teacher of the Year. (1989)

With her masters in social studies education, she taught 6th grade world cultures for most of her career. In her classroom, she tried to incorporate the cultures the students studied. Students listened to music, learned some of the language, read literature, did art, sampled foods, etc. of the culture or time period they were studying.

Her room was filled with inspirational banners, photographs of the many countries she and her husband had visited as well as photos of her dogs, her 6th grade dance photo, and her 6th grade report card for the students to view. In addition to, she had flags of the world hanging from the classroom ceiling. Her room was quite “busy.” Gail felt that if a student wasn’t interested in what she had to say, there was bound to be something in the room to catch their interest (at least she hoped so).

Gail loved the interaction with kids and seeing their faces when they learned about topics for the first time. For Gail, the hardest part of teaching was when she just couldn’t seem to reach a student in seeing the importance of learning being the key to their future success and happiness. Still, she didn’t give up! Many times, years later, some of those same students said they were glad she kept on them to do their best. Every once in a while, a student will come to her house for a visit or contacts her via social media. It makes her day!

Gail loves to garden (see her among her flowers on the right) and to read (she recently joined a book club), In addition, she continues her writing. She has been writing for children’s publications for over 40 years, and has written regularly for Scholastic Publications and for Time for Kids Magazine. Her work has appeared in most children publications plus she has written 35 books for children. Her last two published books were by Red Chair Press (Mrs. Paddington and the Silver Mousetraps, 2019, and Fashion Rules!, 2020). She continues to write regularly for Highlights for Children (last year she got an interview with Dr. Jill Biden - quite a thrill), Jack and Jill Magazine, and several Cricket Magazines.

Gail’s TPT store
 contains 339 resources with 36 of them offered for free. She declares that her resources help students to bloom. Many are social studies items which vary in grade level. Her featured free item is a Pi Day Interactive Notebook Activity

Use this Interactive Notebook Activity to share with students some fun facts about Pi. Not only is it great for Pi Day, but for any day you are looking for an interactive notebook activity to use with your students. It is appropriate for grades 4-8.

Her highlighted paid item is about Katherine Johnson. She was a physicist, space scientist and mathematician, who played a very important role with NASA’s early space missions. The movie Hidden Figures highlights the role of NASA's "computers" such as Katherine Johnson and their contributions. Part of my Ms. Bie Ografee Talk Show Series of Reader's Theater Scripts. There are comprehension questions, a Did You Know section, a teacher page with extensions/links and an answer key.  This is a great STEM biography for grades 5-8!

Gail has a website where you can find lots of free materials in geography, news, short reads, bell ringers and more.  She also has a blog which she calls Gail’s Glimmerings. She keeps it up-to-date and has a variety of many interesting postings. I really enjoyed reading about the one on William Shakespeare. Check it out as it will be worth your while.

Are Multiple Choice Questions Testing All Levels of Bloom's Taxonomy?

According to Ron Berk (a keynote speaker and Professor Emeritus of Johns Hopkins University)the multiple choice question "holds world records in the categories of most popular, most unpopular, most misused, most loved and most hated" of all test questions.  Because of the many students teachers see each day and the little time teachers have to make tests and then grade them, multiple choice questions have become one of the favorite type of testing questions in education.  We see them on state assessments, national assessments, ACT tests, college tests, driving license tests, etc.  However, those who consistently use them aren't all that crazy about them and with good cause.

First of all, answering multiple choice questions doesn't teach students how to formulate answers; it teaches them how to select answers.  Many times choosing the right answer is more a literary skill rather than of content knowledge.  Multiple choice questions promote guessing, and if a guess is right, students get credit for something they didn't know.  Moreover, the instructor is deceived into thinking the student understands the concepts being tested.

Many multiple choice questions do not challenge students to think.  Instead they encourage the students to memorize.  In my opinion, test bank questions are the worst.  A simple analysis of this type of question in a variety of disciplines suggests that about 85% of the multiple choice questions test lower level knowledge, levels I (remembering) or II (understanding) of Bloom's Taxonomy.

I can do it!
When I first started at the community college where I teach math, the math assessments which the department used were mostly multiple choice.  I asked about testing our students using levels V or VI of Bloom's and the reaction I received was disheartening.  One instructor implied that our math students would be unable to answer such questions.  I guess his expectations were a great deal lower than mine. I am positive he hadn't read an article by two professors at Kansas State University.

According to Victoria Clegg and William Cashin of K.U., "Many college teachers believe the myth that the multiple choice question is only a superficial exercise - a multiple guess - requiring little thought and less understanding from the student.  It is true that many multiple choice items are superficial, but that is the result of poor test craftsmanship and not an inherent limitation of the item type.  A well designed multiple choice item can test high levels of student learning, including all six levels of Bloom's Taxonomy of cognitive objectives."  (Idea Paper No. 16, Sept. 1986)

So what are some things that make challenging multiple choice questions? Let's take a multiple choice test to help us answer that question.

Choose the best answer.  Which multiple choice question is the hardest to answer?
  1. The one where it’s absolutely obvious that all choices are wrong answers.
  2. The one where the question and/or answers are so badly written that two or more answers could be correct depending on how the student interprets the question.
  3. The one where the list of possible answers are true or false; it depends on how the the student reads the question.
  4. The one question where it is really two questions in one, but the options only answer one part of the question.
  5. All of the above – except that there is no "all of the above" option given.
I trust you see the humor in this question.  Unfortunately, I have seen one or all of the above on math tests given in our department.

Now let's look at two different multiple choice questions from a mealworm test available on Teachers Pay Teachers.  The first one is pretty straight forward and requires little thinking on the part of the student. On Bloom's, it would represent a level I question - remembering.

Which tool will help you best see the mealworm up close?
  1. Ruler
  2. Mirror
  3. Hands Lens
  4. Eyedropper
The next question from the same test requires the student to understand what a good scientific investigative question is. This would be a level IV question which is analyzing.

Which question can be answered by investigating?
  1. Will the mealworm eat the fruit?
  2. How far can a mealworm travel?
  3. Will more mealworms go to the paper with an apple slice on it or to the one with no fruit on it.
  4. Why do mealworms move?
How about this one from a butterfly test?  (also available on TPT)  What level of Bloom's does it represent?

How does the life cycle of a butterfly differ from the life cycle of a frog?
  1. Only the butterfly has an egg.
  2. Only the butterfly has an adult stage.
  3. Only the frog has a tadpole.
  4. Only the frog has a pupa.
Again it is level IV because the student is asked to compare; yet, this test is for the grades 3-5 while the meal worm test is for grades 5-8.  I give you examples from both so you can see that challenging multiple choice questions can be written for most grade levels.


If you would like help writing good, challenging questions of all kinds, you might check out Bloom's Taxonomy Made Simple.  It is a five page handout that breaks the six levels of Bloom's down into workable, friendly parts, using the familiar story of The Three Little Pigs. Examples of good ideas of how to write assessment questions using all six levels of Bloom's are given.  For your practice, a follow-up activity of 16 questions is included.

The Mysterious Case the Exponent Zero - Why any Number to the Zero Power Equals One

Sometimes my college students like to ask me what seems to be a difficult question. (In reality, they want to play Stump the Teacher.)  I decided to find out what sort of answers other mathematicians give; so, I went to the Internet and typed in the infamous question, "Why is any number to the zero power one?"  It was no surprise to find numerous mathematically correct answers, most written in what I call "Mathteese" - the language of intelligent, often gifted math people, who have no idea how to explain their thinking to others.  I thought, "Wow!  Why is math always presented in such complicated ways?"  I don't have a response to that, but I do know how I introduce this topic to my students. 

Since all math, and Imean all math, is based on patterns and not opinions or random findings, let's start with the pattern you see on the right.  Notice in this sequence, the base number is always 3.  The exponent is the small number to the right and written above the base number, and it shows how many times the base number, in this case 3, is to be multiplied by itself. 

(Side note: Sometimes I refer to the exponent as the one giving the marching orders similar to a military commander. It tells the base number how many times it must multiply itself by itself. For those students who still seem to be in a math fog and are in danger of making the grave error of multiplying the base number by the exponent, have them write down the base number as many times as the exponent says, and insert the multiplication sign (×) between the numbers. Since this is pretty straight forward, it usually works!) 

Notice our sequence starts with 31 which means 3 used one time; so, this equals three; 3means 3 × 3 = 9, 33 = 3 × 3 × 3 = 27, and so forth. As we move down the column, notice the base number of 3 remains constant, but the exponent increases by one. Therefore, we are multiplying the base number of three by three one additional time.

Now let's reverse this pattern and move up the column. How do we get from 243 to 81? That's right! We divide by three because division is the inverse operation (the opposite) of multiplication. How do we get from 243 to 81? That's right! We divide by three because division is the inverse operation (the opposite) of multiplication. Notice as we divide each time, the exponent by the base number of 3 is reduced by one. Let's continue to divide by three as we move up the column. 27÷ 3 = 9; 9 ÷ 3 = 3. Now we are at 3= 3 which means we must divide 3 by 3 which gives us the quotient of 1. Notice, to fit our pattern, the 3 in the left hand column would have to be 30; so, 3must equal one!

This works for any number you wish to put in the left hand column. Try substituting the base number of three with two. Work your way up the sequence dividing by two each time. You will discover that two divided by two equals one (20 = 1). Therefore, we can conclude that any natural number with an exponent of 0 is equal to one. (Zero is not included; it's another mystery to solve.)

What happens if we continue to divide up the column past 30 ?   (Refer back to the sequence on the left hand side.)  Based on the pattern, the exponent of zero will be one less than 0 which gives us the base number of 3 with a negative exponent of one or 3-1 .    To maintain the pattern on the right hand side, we must divide 1 by 3 which looks like what you see on the left. Continuing up the column and keeping with our pattern, 3 must now have a negative exponent of 2 or 3-2 and we must divide 1/3 by 3 which looks like what is written on the left.

Each time, the exponent by the base number of 3 is reduced by one. Let's continue to divide by three as we move up the column. 27÷ 3 = 9; 9 ÷ 3 = 3. Now we are at 31 = 3 which means we must divide 3 by 3 which gives us the quotient of 1. Notice, to fit our pattern, the 3 in the left hand column would have to be 30; so, 3must equal one! This works for any number you wish to put in the left hand column. Try substituting the base number of three with two. Work your way up the sequence dividing by two each time. You will discover that two divided by two equals one (20 = 1). Therefore, we can conclude that any natural number with an exponent of 0 is equal to one. (Zero is not included; it's another mystery to solve.)

As a result, the next two numbers in our pattern are..............??

Isn't it amazing how a pattern not only answers the question: "Why is any number to the zero power one?" But it also demonstrates why a negative exponent gives you a fraction as the answer. (By the way math detectives, do you see a pattern with the denominators?)
         Mystery Solved!   Case Closed!

This lesson is available on a video entitled:  Why Does "X" to the Power of 0 Equal 1?



Want simple, visual answers to other difficult math questions? Try this resource entitled Six Challenging Math Questions with Illustrated Answers. Many of the answers feature a supplementary video for a more detailed explanation.

It Depends on the Angle - How to Distinguish between Complimentary and Supplementary Angles

My Basic Algebra Concepts class always does a brief chapter on favorite to teach! We usually spend time working on angles and their definitions. My students always have difficulty distinguishing complimentary from supplementary angles. Since most of my students are visual learners, I had to come up with something that would help them to distinguish between the two.

The definition states that complementary angles are any two angles whose sum is 90°. (The angles do not have to be next to each other to be complementary.) As seen in the diagram on the left, a 30° angle + a 60° angle = 90° so they are complementary angles. Notice that the two angles form a right angle or 1/4 of a circle.

If I write the word complementary and change the first letter "C" into the number nine and I think of the letter "O" as the number zero, I have a memory trick my mathematical brain can remember.

Supplementary Angles are two angles whose sum is 180°. Again, the two angles do not have to be together to be supplementary, just so long as the total is 180 degrees. In the illustration on your right, a 110° angle + a 70° angle = 180°; so, they are supplementary angles. Together, they form a straight angle or 1/2 of a circle.

If I write the word supplementary and alter the "S" so it looks like an 8, I can mentally imagine 180°.

Since there are so many puns for geometric terms. I have to share a bit of geometry humor. (My students endure many geometry jokes!)

You might be interested in a variety of hands-on ideas on how to introduce angles to your students. Check out Having Fun With Angles.  It explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.