Read Aloud on Negative Numbers

When I was given the assignment to read a book aloud to my middle school math class, I was lost as to what I should read. After getting the suggestion from my cooperating teach to find a book about negative numbers to read to the 7th graders, I searched around the internet and found this book, Less Than Zero, by Stuart J. Murphy.

Less Than Zero is a book in a series of books by Murphy relating mathematical concepts in story form. This particular book has the following succinct summary on the back cover:

Perry the Penguin needs 9 clams to buy an ice scooter—but he’s not very good at saving. As Perry earns, spends, finds, loses, and borrows clams, a simple line graph demonstrates the concept of negative numbers.

To add to the summary, Perry has ‘less than zero’ clams for a part of the story because he borrows clams to buy things besides his ice scooter. In the end, Perry gets enough clams to buy his ice scooter by getting a loan of 4 clams from a neighbor that he will pay off by working shoveling snow, so he ends the story with a debt of negative 4 clams/hours of work.
 
This book has two possible messages to talk about with students. One message is about negative numbers and what negative numbers mean when applied to amounts of money. The other message is telling students that if they borrow more money than they have, then they will be negative in how much money they have. Furthermore, the second message also puts being negative money as something unfavorable and should be avoided.

Although I read it with middle school students, it could be used with almost any age to introduce negative number concepts, graphing practice, or just as a story about saving money. My students thoroughly enjoyed it, and I hope you find a use for it with your students. 

Wading through it all

This blog was set up as a course assignment, and I have blogged as assigned periodically over the last 6 months. My posts have felt like they came very naturally as a response to something I read or experienced, yet this week seems like I have nothing useful to contribute to the great blogosphere.

I feel like there is so much information out there and being constantly added to (I actually got stuck in all of it for a few hours trying to come up with something to blog about) that I don't feel like I should always contribute to all that noise. Although I do find endless awesome sites and ideas on the internet, it can take a while to get there. Wading through all that information can be time consuming, tiring, and stressful. My technology class has been introducing great tools for finding information and sorting/filing great information, but even using all of those tools can get overwhelming at times.

My teacher says of twitter that there is just too much information out there for you to keep track of; you just need to dip your bucket into the river every once in a while to see what you can get.

Within the last couple months, I have applied this concept to my entire internet usage. I have discovered a great way to make me a happier person and reduce my stress level over finding information by stepping away from my computer much more often. A rule I have for myself is if I find myself browsing things for more than a half hour that don't help me complete an assignment for school or specifically help me do something that I'm learning to do, I need to get off the computer and do a physical activity or hobby. It has actually helped my mood and outlook on my life, and I have started doing things that make me happy rather than just looking at websites that I will probably forget about the next day.

And speaking of which, I have spent far too long on the computer today, so I shall say goodnight to the internet for tonight...well, maybe at least for a couple hours...

Comfortable classrooms

When I had my class on the middle school learner last spring, we talked a great deal about how classroom environments could be made more comfortable for the students and match their physical needs better. Most of what we talked about we're great ideas, but I feel that ideas like tables students could stand at and squishy balls to play with are rarely implemented. It probably doesn't come to fruition due mainly money and partly simple follow through. However, I observed a class today that through the generously of a PTA grant had exercise balls available for students to sit on instead of chairs. Although it wasn't necessarily apparent whether they aided in attention over the 40 minutes I was observing, I was so thrilled to see the students getting their wiggles out during class in a generally non disruptive way. Great use of grant money in my opinion.

Math Manipulatives in Algebra

I just started observing a junior high class and was pleasantly surprised when the teacher pulled out Manipulatives to help the students visualize balancing algebraic expressions. I had never seen or experienced their use in learning algebra, and it gave me wonderful new ideas of how to use them in my future teaching.

The Manipulatives are used to represent the x terms and the integers and differentiate positive and negative terms. In this way students need to follow logical rules of keeping the equation balanced by literally taking away or adding the same thing to both sides. The long bars represent 1x and each small square represents 1. Furthermore, both bars and squares are positive when green/yellow, and negative when red. I think it's a quite brilliant way of physically representing a potentially abstract concept for learners. I definitely plans on utilizing this type of manipulative strategy in my future classrooms.

Below is an example of an equation being represented by the manipulatives. 3x-5 is represented by 3 green bars and 5 red squares while x-3 is represented by 1 green bar and 3 yellow squares. To solve for x, students would first remove a green bar from both sides and rewrite the equation to be 2x-5=3 with the visual matching. They would next add five yellow tiles to each side which would cancel out the red squares on the one side while adding with 3 to be 8 on the other side. The equation would then be written as 2x=8. The final move of the Manipulatives would be to divide the positive eight squares evenly with the two remaining green bars(x's). This would mean there would be 4 squares per bar, meaning x=4. I wish I had pictures for each step, but I don't at the moment. I'll try to update when I get a chance to take pictures of other examples.