A New Math Word

My husband's seventh grade class has come up with a new math term! In science they have learned that the prefix "eu" means true. So eubacteria, as opposed to archeabacteria, means true bacteria.  And eukariotic means true nucleus. 

In math, they are learning about variables. Now the definition of variable is "a value that can change". In the the equation y=2x + 5, the variables are x and y. And their values can change.

But sometimes variables or letters are used just to hold a place and the value is pre-determined. An example of this is in the equation 2x +3 = 7. In this case x=2 and the variable is holding the place of the 2.

So the new math word? Here it is: EUVARIABLE!!! It means a true variable and not just a place holder.

Congratulations to my husband and his seventh graders! Good thinking!

Integer Hi-Lo

I came up with a new game and my last period eighth grade group named it! I needed to review multiplying integers with them.

I started by dividing the students into groups of two, three, or four and giving them a deck of cards. I wrote on the board that black cards were positive and red cards were negative. I told them it was that way with the phrases "in the black" and "in the red."

The dealer hands out all the cards to the players. The cards are placed face-down and the players don't look at them. Whoever has been designated to go first puts out one card. If it is black, they are looking for the highest product; if it is red, they are looking for the lowest product. Then the first player lays out another card and announces the product of his two cards. The next player puts out two cards and announces their product until all players have done this. They then decide who has the high or low depending on what they are looking for based on the first card out. The winner takes all the cards and puts them under their deck face-down.

Players are trying to end up with all the cards. If there are more than two people playing, I cut the game off when one person has no cards and the person with the most is declared the winner. If the class ends, the person with the most cards wins.

This is a good game not only for multiplying integers, but also comparing integers. Sometimes students struggle with the concept that -50 is less than -1, and this game helps them review magnitude.

A Kiss For You!

This morning I was going over multiplication with one of my math groups. After doing some basic drill, we were using individual white boards to practice multiplying multi-digit numbers using the standard algorithm. I would give them the problem and wait for them to do it individually. Then I would do the problem on my own white board using think-aloud, so they could compare their work. They were doing a fine job, and only making a few mistakes.

At one point I went to my desk and wrote a note on a piece of scrap paper: "I am going to do the problem wrong. I wonder if anyone will notice. A kiss if they do!" I then proceeded to do the problem incorrectly. It was just one mistake that I made; I said that 7 x 5 =40. At first no one said anything. Then when I paused, one of them said, "What?" I replied that I would be happy to do it again, and proceeded to do that section of the problem again making the same mistake. This time, they spoke up. I showed them my note and praised them for finding my mistake and handed over a Hershey kiss to each one.

They were thrilled! And so was I. A big part of doing math accurately is watching for and catching mistakes. My initial motivation for this was that I had a bag of kisses in my desk that I needed to use up. I had bought the candy for an activity with another group, and being diabetic myself, had no other use for them. But I was reminded that making a mistake and praising students for catching it is a good thing to do!

There's A Lot of Math in a Tree

On the day before school started, I was asked to teach a last period class for remedial students that would help them improve their math skills in addition to the regular grade 8 math class they already were taking. I welcomed the opportunity and it has been a good experience this fall. But there was no room assigned for the class that first week, so students were told to meet me at the office and together we walked outside to the woods behind the school. I handed them meter sticks and clipboards, told them to find a partner and sent them to measure trees in the woods. They were to find the d.b.h. or diameter breast height. This gave us some wonderful data for reviewing measures of central tendency such as mean, median, mode and range. Using all the data, we were able to make some generalizations about the trees in the forest.

Currently, my husband is in a science/math forestry unit with his seventh and eighth graders. The extension forester comes in and they have been doing some incredible explorations that have captured the students' interest and strengthened their math skills and science knowledge at the same time. They are measuring trees, calculating board feet and projecting the dollar amount that various wooded areas are worth.

At this time of year when the autumn colors are so vibrant, it's nice to find so much math in the trees!

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!