Postman Games: Addition of Signed NumbersThis week we worked on addition of signed numbers, and began with problems to work out centering around a postman named Sam. Sam is a strange postman because sometimes after he has delivered the mail, he comes back and takes it away again. Sam only delivers two types of mail: checks and bills. The bills are when you owe someone money and checks are when you get money. I showed him how to write positive and negative numbers, and then we went over the cards I had made up on index cards cut in half about whether you were richer or poorer if you got each card. Then I began giving him two cards and he had to write them down as problems and solve them. For example, if Postman Sam gave you a check for $4 and then another check for $3, are you richer or poorer, and by how much. I gave him a grid to put the first problem in, and after that he could refer to it as needed. We then went over the four possibilities for addition of signed numbers in Postman Stories:
- The mail carrier brings a check for ___, then he brings another check for ____.
- The mail carrier brings a bill for ____ , then he brings another bill for ____.
- The mail carrier brings a check for ___, then he brings a bill for____.
- The mail carrier brings a bill for ____, then he brings a check for ____.
We also went over how they are written.
Postman Games: Subtraction of Signed Numbers
Remember how we talked about the fact that Sam, the postman is not too good at delivering the mail, and sometimes he comes back and takes the mail away again. We used cards again to play a game, this time using subtraction of positive and negative numbers. He wrote them down again in his math journal, paying particular attention to the signs. The four possibilities were:
- The mail carrier brings a check for ___, and takes away a check for ___.
- The mail carrier brings a check for ___, and takes away a bill for___.
- The mail carrier brings a bill for ___, and takes away a check for ___.
- The mail carrier brings a bill for ___, and takes away a bill for ___.
Coordinate Graphing and Negative Numbers
Negative numbers are useful when constructing coordinate graphs. They allow students to project their linear graphs as far as they wish, and then speculate on the meaning of all points on the line.
We used the cards again, to make up addition problems to graph on a coordinate graph.
For, example, if he pulled a -4 card, he would then plug it into this formula:
-4 + X = 10
and then plot that on a coordinate graph to find its solution.
"Mathematics is more than performing basic arithmetic operations, but is a way of thinking. Negative numbers are a tool they can use to expand their thinking." -Bob Baratta-Lorton