Everything Has to Do With Math

I was talking to my friend Catherine. She was saying that she didn't like to put on a wet swimsuit. So I told her the trick I use if I am in a place where the only suit I have is wet: run it under hot water from the sink and wring it out before putting it on. She enthusiastically welcomed my tip and said that it was something worth putting on my blog for everyone to see. When I replied that it didn't have anything to do with math, she replied, "Everything has to do with math!" She proceeded to note that it had to do with the measure of body temperature compared to the temperature of the wet suit. When the temperature of the suit is raised to a temperature equal to or higher than body temperature, there is less discomfort. Not a bad observation for a social worker!

So is it true that everything has to do with math? I have thought about asking students to tell how they used math over their summer vacation. While most will think that they didn't at all, I hope I can eventually get them to realize that math is associated in one way or another with most everything we do. So let's see if it works for what I do.

I just finished washing the dishes. (No, I don't have a dishwasher.) I put the glasses and silverware in the soapy water first and save the dirtier and larger dishes for later. The reason I save the dirtier dishes for later is that I want my dishes to end up clean and the ratio of dirt particles to water needs to be low. When I finally put the really dirty dishes into the water, it increases that ratio of dirt to water. Ratio? Math?

So how else have I used math over this summer vacation? Well, while I was sitting and healing from (yet another) surgery on my foot, I got involved in one of those farm simulation games on Facebook. I plow, plant, and harvest and watch my coins accumulate. I have to buy the seeds from the store, and I try to figure out which will be the best crop for me to grow. It's all based on math!

Thankfully, I haven't spent the whole vacation in a recliner with my foot up. On our trip to Newport, RI, I used a map, roadside mileage markers, and the car's speedometer to try to figure out how much longer it would take. The everyday estimates we make are all based on our knowledge of math.

So is it really true that everything has to do with math? I think it is, whether I can explain the connection or not. But it is a good mental exercise to try to figure out those connections. Maybe I'll contemplate it further when I'm floating in the pool this afternoon!

See Who Laughs!

This is a joke my father used to tell. I tell it to my classes and then watch their reaction. I can tell right away who gets it and who doesn't.

One day a man went into a pizza parlor and ordered a pizza.
The waiter asked him,"Would you like your pizza cut into six slices or eight slices?"
After thinking for a moment, the man replied,"Well, you'd better cut it into six slices; I could never never eat eight!"

This is a good time to point out that fractions that have the same numerator and denominator always equal 1 or 6/6 =8/8

The Book That Might Disappear

My husband came home from an educators’ conference with several new books and one of them caught my eye in addition to hearing him mention it several times. The name of the book is Mathematics: Worksheets Don’t Grow Dendrites. It is written by Marcia L. Tate who is an educational consultant. She has written several books that have the Worksheets Don’t Grow Dendrites mantra in their title and this one is about math. She maintains that learning occurs the best when it centers around activities that involve and engage the student. This is a concept that I have believed for years, but finding or dreaming up enough activities to teach all the math concepts in my curriculum is quite a challenge—something I have spent many years doing.

As I began to flip through the book, it became obvious that it is a valuable resource. Chapter 2 is titled “Drawing and Artwork”. I see a project for “Gallon Man” which is used to help children remember the number of quarts in a gallon, pints in a quart, and cups in a pint. My middle school students have a hard time remembering this and here is an art project that can help! I love it: art projects that teach math!

The other chapters look good too, with a lot of practical ideas that can be used or expanded. You know, my husband loses things pretty easily and this book just might disappear for a while!

My Special Number: 25

For many years I assigned an end-of-unit project to my sixth graders titled My Special Number. This was when students would pick a number on which to perform a number study. Today I offer my own version of this assignment.

My special number is 25. It is a number that is described as odd, composite, and square. It is odd because it is not divisible by two. It is composite because its factor pairs are not only 1 x 25, but also 5 x 5. Having 5 x 5 as a factor pair is also what makes it a square number. In fact it is the smallest square number that is the sum of two other square numbers. ( 9 + 16 = 25) This relationship is found in many right triangles (known as 3-4-5 triangles) used for illustrating the Pythagorean Theorem.

Because 25 is a factor of 100, it is used in a variety of ways. A twenty-five cent coin is a quarter and it takes four to equal a dollar. 25% is equivalent to ¼.

The number 25 has significance in various religions and philosophies. According to Abellio, twenty-five is the symbol for the Universal Word of God. St. Augustin used it to represent the law. In the Bible, King Solomon builds a temple to God that is 25 cubits high, and a Levite could begin practicing his ministry at the age of twenty-five.

But today, the number twenty-five has a special significance. Today marks the day that indicates that FOR TWENTY-FIVE WONDERFUL YEARS I HAVE BEEN MARRIED TO THE BEST HUSBAND I COULD POSSIBLY HAVE!

The Daily Fraction

One ongoing activity that I like to do with my seventh grade classes is the daily fraction. This lends itself well to seventh grade because by then, students have been taught most fraction skills. There are a few that just didn’t get it, while some others have attained mastery, and the daily fraction works with both kinds of students. This activity takes about one minute a day and serves to review and for some re-teach a number of fractions concepts. It is a great point of discussion for students to notice and participate in.

I start at the beginning of the year by making a fraction template on a piece of white cardstock or construction paper. The template has the divide line with 180 as the denominator. I laminate it twice to withstand the daily write-on/wipe-off process. On the first day of school I use a dry erase marker to write a 1 as the numerator and say to the class, “When you go home today, one one-hundred -eightieth of the school year will be completed.”

On the second day, the one has been erased and a 2 is in its place. I ask the students to reduce the fraction and they realize that 1/90 of the school year is completed that day. We compare the two fractions noting that 1/90 is greater that 1/180.

Many days I ask the students to write the reduced form of the fraction on the back of their warm-up sheet, then discuss implications. I might ask them how close to 1/8or 1/4 of the year we are (midterm progress reports or report cards). I might ask for the percent of the year that has gone by or the fraction that is left.
Seventh-graders like to keep track of the year’s progression. Some years, students have felt that the year zoomed by and other years, it seemed very slow to them. But every day they are getting a little reminder of fraction skills through this number study.

So today is the 166th day of our school year. That's 83/90 of the school year completed with 7/90 to go. Or we could say that 92% of the year is finished with 8% left to complete. That translates to fourteen more days of school left!

Sweet Success

About a month ago, I wrote about a student who needed to learn some of the multiplication facts. We picked ten facts she needed to learn and wrote them on flash cards. We practiced and drilled and she got better. She made 90% or nine out of the ten. Now that is a high score that would bring an A grade in any school.

But consistently the one fact that she could not remember was 7 x 6 = 42. Whenever that fact would come up, the look on her face clearly communicated to me not only that she didn’t know it, but that she knew this was the one that she didn’t know and was convinced she would never be able to remember.

So one day, I let her use some art supplies to make a poster that now hangs in my room. And sure enough, even with her back to the poster, she can remember that 6 x 7 is 42. The visual and tactile experience of creating this poster focused on what she needed to learn has brought her to 100% success.

It's All About Pizza

Even though I have started my fractions groups by using giant cookies and a recipe for mushroom sandwiches, the example I use the most when talking about fractions is pizza. I spent some time this morning cutting out large red paper circles. Some of them I cut into halves and some I cut into fourths. I will use them as visuals when I talk about pizza slices and improper fractions and mixed numbers.

Improper fractions simply tell how many pieces there are and what kind of pieces they are. They are usually not the best way to express a number, but sometimes they are necessary. So if I have nine fourths, I have nine pieces that have been cut into fourths (which means four for every whole pizza). Using my visuals, students can see that every group of four makes a whole pizza. They find that two whole pizzas can be made with one piece left over. After some practice with this concept, I help them to verbalize the analog for how to change an improper fraction to a mixed number.

Then we move on to starting with a mixed number and changing it to an improper fraction. The pizza slices come in handy once again as students can beak down the wholes to see how many parts there are. Together, we come up with the steps for doing this process without the pizza slices.

The worst part of all of this is that the kids complain that these exercises make them hungry. It has an effect on me too—“Hello, Pizza Hut? I’d like to order a large pizza to be delivered to the school!”