Practice Makes Perfect

As I get farther into my practice of student teaching, I am continually surprised by how much more difficult teaching is than it looks. Every Wednesday and Thursday I watch my teacher teach math to 7th and 9th graders, and I think, "I could do that, easy. I just have to do what he does, easy." During the last couple weeks, I've started taking over parts of lessons and have found out that it is not easy to emulate his lessons. I forget to say things I had planned on saying, I forget to show specific ways of solving problems, I forget to wait for the kids to be quiet before I start talking, I forget the students names (well, there are 150 names to learn), and sometimes I forget how to solve the word problems by the method I'm supposed to teach (oops). Although it is starting to get easier as I get more comfortable teaching, I'm realizing that it's going to be a less easy process than I was expecting...I guess that's why I get to have 6 more months of practice!

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. 

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.