Sunday, November 16, 2014

A function foldable I like

     I was introduced to foldables about ten years ago when I taught out of the Glencoe math series. Our Pre-Algebra and Algebra books had directions for a foldable at the beginning of each chapter that were created by Dinah Zike. Back then we used loose leaf paper and the lines were guides for the folds the kids made. There weren't pre-printed foldables or flipables or graphic organizers for students. The students made these foldables and took notes for each section in the chapter. They loved them and would not forget to bring them to class everyday. 
    There are a few of those original foldable templates that I use today. This is one of my favorites that I have adapted to use when I am introducing my 8th graders to functions. Instead of loose leaf paper, I use graph paper. I love making foldables from graph paper because it is so much easier to read. At our school, we ask each of the students to bring in a package of graph paper to their math teacher at the beginning of the year. We keep in the back of the room and if students need it for any other class they can just take what they need. Then we pass out the paper as needed and there is always more than enough for the entire year. That way there are no worries about students not having paper.
    The first step to make this foldable is to take a piece of graph paper and fold it in half. I call this folding the paper the hamburger way. If we fold it the other way it is the hot dog way.

    Then open it up and cut off four squares on the top left section of the graph. 

If you are using a composition notebook you should measure the width and cut the right side of the graph paper so it fits into your notebook.

   I use 5 sheets of paper, one for linear functions, absolute value functions, quadratic functions, cubic functions and rational functions. I could probably use less paper if I combined some of the functions together.

    Then you staple the pages together to make a booklet like so. It will open like a book and then also have flaps.

                         Just lift up the flap to add the function tables and graphs.

     When I teach functions, I prefer to use the large function tables that have four columns. This way the students see exactly where the numbers in the function table come from. This is beneficial for my students who struggle to follow the math involved to find the y value.

      I have an entire page empty on the left. I haven't figured out what I am going to place there. Maybe have students do a summary or state something in their own words???? Ideas are welcome.

                  Then I do the same for quadratic, rational and cubic functions.

     The students will be using a graphing calculator later but I like to initially start out with them making the tables and graphs to help their understanding. Since I write large I like this foldable because there is so much space because of the flap at the top. I have to admit it, I'm addicted to foldables. They just make me happy.
Til next time,

Wednesday, November 05, 2014

Our Halloween Contest

     This is the third year that the math department at my school has had a Halloween contest for our students. The students guessed how many candies were in a container that we had in a display case in our hall. The first year we did this, we had a large container filled with candy corn and last year the container was filled with small candy pumpkins. The containers looked very nice and the winners received all the candy. However that candy is just so sweet!  Ugh, it sends shivers down my spine thinking about how sweet it is. The winner received the container with the candy and had their picture taken. The picture was posted in the display case and it was placed in the yearbook as well. This year instead of candy I found pumpkin containers filled with cheese balls. We placed two containers in the display case and students gave their guesses to the math teachers. I actually found the actual number of cheeseballs in BOTH of the containers. Don't worry, I used plastic gloves. When the teachers were giving me their guesses to determine the two winners, we were all shocked at some of the guesses the kids made. 29 cheeseballs, 109 cheeseballs, 14  and 72 were numbers that kids actually thought were the total number of cheeseballs. WHAT!!!! How is it even possible? This just confirmed that our students need help improving their number sense.

These two young ladies both guessed there was a total of 2000 cheeseballs in both containers.
They were the closest to the 2012 actual total.

     So we have decided to do a couple of things to help our kids improve their estimating abilities. First of all, we decided that we are going to have bimonthly contest so the students have an opportunity to make an estimate more often than just once a year. For our winter theme, we are going to get a tall thin container, probably from IKEA, and put red and green peppermint candies in it. Valentines Day is going to be candy hearts. I would be fun to find something in the shape of a heart to be the container for that season. Spring will be something in spring colors and we still need to figure out May. ( Suggestions anyone?) I will also put a cup next to the containers and show how many items are in one cup to help them get a start on a good estimate.
     The next step, and I am sure some of you are yelling this at the computer screen right now, is to start using Andrew Stadel's, Estimation 180 site daily.  I showed this site to my department and everyone loved it. (Thank you Andrew for this awesome site.) So we are starting all together next week. I am going to run off the sheets that accompany the site for students estimates. It is going to be interesting to see how their estimates improve throughout the year.
     We are going to start with these two ideas along with everything we are already doing in class and see what happens. I'll keep you posted.
    Oh, one more thing. One of my students whispered this to me:
Student: "Mrs. Lichtenberger, Ms. Arman told me a secret."
Me: "What did she tell you?"
Student: "Length times width times height."
Me thinking: "Gee, who knew that was a secret?"

Til next time,

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