Completing a Glyph for Groundhog's Day and Interpreting Data

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 because our winter here in Kansas has been pretty cold and snowy.

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 really a 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. 

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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.

Yes or No? Stay or Go? Solving for the Unknown in a linear equation.


When my basic college algebra classes begin solving equations containing one unknown, I tell them, they are inquisitive detectives looking for the unknown. My students' greatest difficulty is deciding what stays and what goes in an equation. In other words, which term should be cleared by using the inverse operation and which term should stay where it is?

I  start by referring to the written equation as a teeter-totter or a see-saw which must always stay balanced. In other words, the equal sign is the pivotal point and both sides of that = sign must be the same.  We also discuss the importance of the"Whatsoever thou doest to one side of the equation, we must doest to the other". (Out of necessity, I admit that I was with Moses when he received the Ten Commandments, but it "fell upon me" to convey The First Commandment of Solving Equations to future mathematicians.)

One Unknown

We begin with very simple equations such as: x + 9 = 12. Here's the rub; a few of my students know the answer and do not want to show any of their work. Maybe some of you have this type of student as well. Since, after 40+ years, I am still unable to grade what is in their minds, I insist that all steps are written down. I explain that it's like riding a tricycle to ride a bicycle to ride a unicycle.

First, I instruct the students to look at the equation and determine which terms are out of place. (Side note: Because my students are easily confused, at the present, we keep all of the unknowns on the left side and all of the numbers on the right side of the equal sign.) Let's go back to our sample of x + 9 = 12. Because the x is already on the left side of the equation, the students write a "Y" over it for the word, "Yes". The 9 is on the wrong side of the equal sign, so the students write a "N" over it for "No".  Finally, they write a "Y" over the 12 since it is the correct place. They now have exactly what they want, a Y and N on the right side and a Y on the left side. They now must clear anything that has a "N" over it.  The students recognize they if they use the inverse operation of addition, they can clear the 9. They therefore subtract 9 from each side of the equation resulting in an answer of 3.

Many algebra teachers will have the students write the step x + 0 = 9.  You may wish to include this step in the process, but since my college students readily see that +9 and -9 make zero, they put an X over the two opposites to show that they cancel each other out or when added together, they equal zero.

What if the equation is: 3 = y - 4? This always freaks my students out; yet, if they do the yes/no process, they will discover that they have two "no's" and one "yes", not a yes, no = yes.  This means they can rewrite the equation as y - 4 = 3 to get a yes, no = yes. The problem can now easily be solved like the one above.



Unknown on both sides
of the equation

The next step is what to do when an unknown appears on both sides of the equal sign.   Usually, my students are sure they are incapable of solving such a difficult problem, but let's use the yes/no method and see what it looks like. 

Notice in the sample on the left that we have a yes, no = no, yes. We start by clearing the "N" on the left hand side of the equation by using the inverse of -9. We then go to the right side and clear the y by using the inverse operation of addition. (Yes, I am aware both can be cleared at the same time, but again simple and methodical is what is best for my mathphobics.) We then divide each side by 4 resulting in the answer of 3. When the problem is completed, my students are amazed and proud that they could solve such a long equation. (You might notice in the illustration, a dotted line is drawn vertically where the equal sign is. This helps my visual students to separate the two sides of the equation.)

If any of you try this approach with your students or have a different method, I would love to hear from you. Just leave a comment and a short statement of how this process worked for you or what process you use that is even better. That way, we can learn from each other.

I have made math tutorials for the college where I teach, and one of them goes through this process in detail. If you are interested and would like to hear me sing as well, go to:  Yes/No. 

Celebrating the 100th Day of School with the book "The Wolf's Chicken Stew"

It is almost 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!

So-o-o Much More to Learn About Snowflakes!

Snow is much more than white, wet and cold. There are many unusual facts about snow that make it unique and one of the more complex types of precipitation.

• Although snow appears white because of the countless tiny surfaces of each snowflake crystal reflecting most the wavelengths of light, snowflakes are actually colorless. Snow may take on other colors thanks to particulates (microscopic solids or liquid droplets) in the air or even from different strains of algae.
• Many places around the world hold certain world records pertaining to snow. The most snow to fall in a 24-hour period occurred in 1921 in Silver Lake, Colorado. It received 76 inches of snow. That's over six feet!
• Snowflakes come in many different shapes, and their sizes are determined by how many ice crystals connect together.
• The largest snowflakes ever recorded fell in the state of Montana. The snowflakes were 15 inches in diameter.
• The average snowflake falls at a speed of 3.1 miles per hour.
• Snow that has been compacted after multiple melting and refreezing cycles is know as snow pack.
• A snow storm describes a heavy snowfall that results in several inches of snowfall. A blizzard is classified as a snow storm combined with wind, which obscures visibility.
• Snow can be heavy or light depending on its water content.
• An avalanche occurs when snow that has accumulated on a mountain is disturbed by a thermal or physical impact, which causes the snow to rush downhill in a large mass. Preceding an avalanche is a phenomenon known as an avalanche wind caused by the approaching avalanche itself, which adds to it destructive potential.

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If you find these snow facts interesting, try working a crossword where all of the words begin with the word "snow." This resource includes two winter crossword puzzles; each with 25 words that all begin with “snow.” One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same vocabulary is used for each crossword, each grid is laid out differently. Answers keys for both puzzles are included. Click under the title page to download your copy.