5.1+Extending+the+Coordinate+Grid

April 30, 2009 OC

Big Idea: Negative numbers help us to model many real world situations. Essential Question: How do I multiply and divide integers?

Notes: Negative Number X Negative Number = Positive Number Positive Number X Positive Number = Positive Number Negative Number X Positive Number = Negative Number 0 X Any number = 0 Negative Number / Negative Number = Positive Number Positive Number / Positive Number = Positive Number Negative Number / Positive Number = Negative Number 0 / Any number = 0

Problem 5.1

I can make a parallelogram by connecting the four points. Because the length of opposite connections of the shape is the same and the shape has two parallel sides.
 * A.  **** Describe how Melina located each of the four points on the coordinate grid. **
 * B.  **** What polygon could you make by connecting the four points? Justify your answer.  **


 * C.  **** On a coordinate grid, plot four points that are the vertices of a square, such that both coordinates of each point are positive integers. **


 * D.  **** On a coordinate grid, plot four points that are the vertices of a square, such that both coordinates of each point are negative integers. **


 * E.  **** On a coordinate grid, plot four points that are the vertices of a square, such that one point has two negative-integer coordinates, one point has two positive-integer coordinates, and each of the other points has one positive-integer coordinate and one negative-integer coordinate. **

One of the other pair of points that could be the other two vertices is (3, -3) and (-1, -3). The other pair of points that could be the other two vertices is (3, 5) and (-1, 5).
 * F.  **** Two vertices of a square are (3, 1) and (-1, 1). Find the coordinates for every pair of points that could be the other two vertices. **

** 1.   **** For each pairs of points, describe two minimal paths from the first point to the second point. ** 5 steps down and 9 steps across, 9 steps across and 5 steps down
 * Problem 5.1 Follow-Up **
 * a. (-4, -2) to (5, 3) **

9 steps across and 1 step up, 1 step up and 9 steps across
 * b. (-4, 3) to (5, 2) **

3 steps across and 2 steps down, 2 steps down and 3 steps across
 * c. (2, -4) to (-1, -2) **


 * 2.  **
 * a. Locate two points on the coordinate grid such that it will take 12 steps to travel from one of the points to the other on a minimal path. **
 * b. Will eveyone name the same two points for part a? Why do you think this is so?**

Everyone will not name the same two points for part a, because there are very many possibilities in the whole grid. There are almost enfinite numbers of possibilities that you can plot on a coordinate grid.