Math Background

Graphing Integers: When Students Ask

  • Why is the x-coordinate in ordered pairs always first?
    Many things in mathematics and in everyday life are done by agreement so that we will all understand one another. If we didn't have an agreement for the order of the x- and y-coordinates in ordered pairs, some people would read them with the x first and others would read them with the y first. This would cause confusion about how to graph the point. We agree to do other things in math as well. For example, we agree that the x-coordinates to the right of the y-axis are positive and the x-coordinates to the left of the y-axis are negative. In everyday life, we agree to drive on the right side of the road in the United States. However, in Australia they agree to drive on the left side of the road. Knowing these agreements can be very helpful!
  • Why should I bother learning this?
    The discovery of a way to locate points on the coordinate plane was a major mathematical achievement. Coordinate geometry linked algebra and geometry and opened the doors to many other areas of mathematics and science, such as the study of calculus. Your students will need to be able to graph relationships as they proceed through school. Coordinate graphs are commonly used in newspaper and television reports, in medical research journals, and business presentations to show relationships between two variables, such as production levels compared to costs in a business, exposure to tobacco smoke compared to cancer rates, amount of money earned compared to education level, student-to-teacher ratio compared to the quality of education, and the height of a person compared to age. Have your students look in newspapers and magazines for graphs that show relationships.
  • Are all graphs of equations going to be straight lines?
    Have students examine the equation x² = y. Have them make a table of values for x and y and then graph them. They will see that the graph is not a straight line. Tell them that many of the equations they will study when they are older are not linear equations. Stress that the equations they will study this year are linear and will help them understand equations they will study in the years ahead.

Houghton Mifflin Math Grade 5