Completing a Glyph for Groundhog's Day

On February 2nd in 1887, Groundhog Day, featuring a rodent meteorologist, was celebrated for the first time at Gobbler’s Knob in Punxsutawney, Pennsylvania. According to tradition, if a groundhog emerges from its hole on this day and sees its shadow, there will be six more weeks of winter weather! (YIKES!)  No shadow means an early spring. I'm hoping for the latter.

No matter whether he sees his shadow or not, it is always fun for students to do special activities on Groundhog's Day.  In my Teachers Pay Teachers Store, I feature a Groundhog Day Glyph. Glyphs are a really form of graphing, and students need the practice. In addition, glyphs are an excellent activity for reading and following directions, and they involve problem solving, communication, and data organization. 

Only $3.00

This glyph has the students coloring or gluing different items on a groundhog based on information about themselves. Students are to finish the groundhog glyph using the eight categories listed below.

1) Head covering
2) In the Sky
3) Eyes
4) Around the Groundhog’s Neck
5) Flowers
6) Umbrella
7) Color the Groundhog
9) Name

Examples of the first three categories can be viewed on the preview version of the resource. So that each student has the same groundhog to start with, a printable outline is provided on page 4 of this six page activity. This handout also contains a page where the students are asked to identify the characteristics of someone who did their own groundhog glyph. An answer key is included. Kindergarten teachers can easily adapt this activity since the instructions include pictures.

A Go Figure Debut for an Argentinian Who is New!

Hernan's TPT Store

I “met” Hernan several years ago when he was just starting out as a seller on Teachers Pay Teachers. I was his ""helper", answering questions about Teachers Pay Teachers and how to make his resources better. Over the years, I have seen his store change and his resources multiply. I am very pleased to finally be able to feature him on my blog.

Hernan comes from an Argento-Italian family. His father is from Misiones, another Argentinian state, and his mother is from Calabria, Italy. He and his family currently live in the state of Cordoba.

Hernan has been teaching English as a second language in Buenos Aires, Argentina for about 17 years. Teaching makes him feel so happy that sometimes he has to stop planning on weekends to take care of his family.  He describes his classroom as full of motivational posters and engaging games. He uses different styles of teaching, adopting a methodology focusing on specifically COMMUNICATION SKILLS. His students love real conversations such as going shopping or being at the airport. He even has the costumes and everything ready for the performances.

Most of his products are bilingual and focus on Social Studies/biographical units. Lectura Facil or easy reading is a set of children stories with questions for comprehension in Spanish language only. In addition, there are  some sets of ELA and math products in English with lots of printables for students.  Out of the 540 resources in his store called Ready to Teach English and Spanish, 74 are free. 

FREE Item

One of his free items is a small set of printables that were done to have fun in winter. It is titled Fun in Winter Freebie Set of Printables for Kinders and First Graders.  Each printable sheet contains one or two activities for advanced kindergartners and first graders. These worksheets cover basic content for math and ELA subjects: counting up to ten, colors, alphabet letters, vowels, CVC words, months of the year, winter vocabulary and tracing training. These tasks are easy and fun to enjoy at winter time.

Black History - Influential People - Save Money Growing Bundle (Bilingual Set) is a growing bundle of worksheets and reading comprehension related to Black History. Some of the influential people included in this set are:

$29.00

• Benjamin Banneker
• Bessie Coleman Frederick Douglass  
• George Washington Carver 
• Henry “BOX” Brown 
• Martin Luther King Jr. 
• Mary McLeod Bethune
• Rosa Parks 
• Ruby Bridges
• Sarah Breedlove Walker
• Sojourne Truth
• Thurgood Marshall

Each set contains the following activities in English and the Spanish language:

1. A reading text (short biography) of the leader.
2. Reading comprehension questions sheet.
3. Write facts sheet.
4. A bubble map to write words related to the leader.
5. A KWL chart.
6. Facts square chart.
7. An interactive activity.
8. A Venn diagram to compare and contrast with another Black History Leader.
9. A poster of the leader in color.

Some ways to utilize these Social Studies sheets are at centers, for classwork, or they can be assigned as homework.

Hernan also writes a blog entitled Ready to Teach where you can see examples of the resources he creates. Yes, it is written in Spanish and English so you don't have to be bilingual to read it! 

I strongly suggest you check out this very talented teacher and even download one or two of his free items. Not only are his products top notch but more importantly, they are made with a passion for teaching.

Homework - Is It an Essential Part of School?

Dictionary.com defines homework as "schoolwork assigned to be done outside the classroom (distinguished from classwork)", but is homework beneficial? Teaching on the college level, I see many benefits to those students who have been required to complete real homework in high school. Here are just a few.

1) Homework can improve student achievement. Studies show that homework improves student achievement in terms of better grades, test results, and the likelihood of attending college.

2) Homework helps to reinforce learning and to develop good study habits and life skills. Homework assists students in developing key skills that they will use throughout their lives, such as accountability, self-sufficiency, discipline, time management, self-direction, critical thinking, and independent problem-solving. Homework assignments given to students actually help students prepare for getting a higher education degree. In fact, the more time a student spends honing his skills, the higher his chances are to enter the University of his dreams or later acquire the work he always wanted to do.

3) Homework can make students more responsible. Knowing that each homework assignment has a specific deadline that cannot be postponed makes students more responsible. It requires grit (perseverance), teaches them time management and causes them to prioritize their time for academic lessons.

As you read this list, I know there are many of you, especially those who have small children or teach younger children, who disagree. I am not here to argue about whether homework is appropriate in the lower grades, but I do want to advocate real homework on the high school level. When I say real homework here is what I mean.

In high school, students might finish their homework in the hall right before class and still earn a good grade; that just isn't possible in college. Homework may be due on a certain day, but it is acceptable if it is turned late. This typically doesn’t float on the college level. In high school, a student gets to the end of a semester and needs a few more points to pull up a grade because of missing or incomplete assignments; so, the student asks the teacher for extra credit work. Extra credit does not exist on the college level! You do the work you are given when you are given it!

I teach college freshmen, many who are woefully unprepared for the academic rigors and demands that are expected. For every one hour students take in college, they should expect two hours of outside work. In other words, if a student is taking 12 hours, they should expect to spend 24 hours on homework (12 x 2).  Of course this formula doesn't always work perfectly, but it is a good starting point. Usually, college freshmen are in disbelief that they are expected to spend so much time on work outside of class. In reality, they should expect to spend as much time on homework in college as they would at a job because college is a full time job!


When I hand out my syllabus, many of my freshmen are astonished when they discover the amount of homework I expect and require them to do (readings, papers, on-line research, projects, etc.) AND to compound the problem, many instructors (including me) expect it to be done and handed in on time! Unfortunately, several students have to test the waters to find out that late papers are not accepted.

For those college students who've had little real homework in high school compounded by teachers who have allowed it to be turned in late, those students are aboard a sinking ship that is leaking fast! Sadly, those are the 2-3 students who fail my required class and have to retake it the next semester.

Only $1.25

So, as you can see, the decision to agree with or disagree with assignments is really up to the student, but also they need to remember that the learning institution they attend has rules in place regarding assignments. And if homework is assigned, then it will need to be completed and handed in on time, or the impact on the final semester grade will certainly be negative.
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Want a quicker and easier way to grade math homework? Try one of these two math rubrics. I still use them on the college level, and they save me a great deal of time!

The Mysterious Case of Zero, the Exponent - 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 I mean 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; 32 means 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 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, 30 must 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 right.

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, 30 must 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?

Only $3.75

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