In 5th grade, students are introduced to quadrants on the coordinate plane. The coordinate plane has four quadrants, and it is important that students become comfortable with them because they will be working with the coordinate plane in many math classes throughout the years.

### Background Knowledge

Students in 5th grade have knowledge and experience in a couple of areas that have prepared them to learn about coordinate planes and quadrants. It can be helpful to activate, or remind, your students of this knowledge before beginning the lesson. The areas include:

• Number lines with positive and negative numbers
• The prefix quad referring to the number four

### New Terms

Fifth graders will be introduced to several new words or phrases as they learn about coordinate planes - in fact, coordinate plane is one of the new phrases. Reinforce these terms by helping your students create a math dictionary in the back of their notebooks.

Coordinate
A point on a graph, represented by an ordered pair, like this: (x, y).
Plane
A flat surface.
Coordinate plane
A graph that has two number lines that intersect at the zero point of each line. This divides the plane into four sections, or quadrants.
Axis
The two number lines on a coordinate plane, referred to as the horizontal and vertical axes. The horizontal axis is called the x-axis; the vertical axis is the y-axis.
One of the four sections of a coordinate plane.
Origin
The point (0, 0), where the x-axis and y-axis intersect on a coordinate plane.

Introduce the concept by helping your students draw a coordinate plane, giving terms and definitions along the way. They will need graph paper, a ruler and a pencil (and likely an eraser). You can use the whiteboard or the overhead projector to demonstrate and guide them in drawing their own coordinate planes.

Find the middle horizontal line on the graph paper, and draw a line along it. Find the middle vertical line, and draw a line on it. Add arrows to the ends of the line segments to indicate they are true lines that have no end. Have the students do the same on their papers.

Tell the students that you and they have just drawn the x-axis (or horizontal axis) and the y-axis (or vertical axis) of a coordinate plane. Have everyone place an x at the far left of the horizontal axis, and a y at the top of the vertical axis. Point out that the plane has been divided into four sections, called quadrants and that each quadrant is labeled with a Roman numeral - I, II, III and IV. Show that the quadrants are numbered beginning with the top right quadrant and moving counterclockwise. It may be helpful to hang a poster of a coordinate plan on the wall of your classroom, with the quadrants labeled.

Next you'll place numbers along the number lines. Write a zero on the origin, where the two axes cross. Point out that the positive numbers go to the right of the origin and negative numbers go to the left. Number your line as the students do theirs. Repeat the process for the y-axis, with the positive numbers at the top.

Ask students to give you a pair of numbers from 0-10 (keep the numbers positive at first). State that you are going to use these numbers as an ordered pair. On the board make a chart with two columns and five rows. Label the first column x and the second column y. Put the first number in the x column and the second number in the y column.

On your graph, place a dot on the point the ordered pair defines. Do this with three more pairs of numbers. Then, give the students the following ordered pairs: (1, 0), (5, 10), (9, 0), (0, 7) and (10,7). Have them connect the dots to draw a star.

### Make It Fun

#### Draw Pictures

Once the students have practiced graphing both positive and negative numbers in all of the quadrants, they can be given a coordinate worksheet that ends up with a picture - just as they did with the star above. You can find graphs online for boats, flowers, lions, owls and more. Once the students have done a few of these, they can probably make up some interesting ones of their own to share with the rest of the class.

#### Use Multimedia

Reinforce your lesson by showing videos that teach coordinate planes and quadrants to 5th graders in different ways. Although many videos are on YouTube.com and show a teacher giving a lesson, at Teacher's Domain (www.teachersdomain.org), there is a very short cartoon that shows how to find where you are if you're lost on an island. In addition, the Internet is full of math games, and some of them involve coordinate planes. Search for 'interactive quadrant games' or 'coordinate plane interactive games.'

Did you find this useful? If so, please let others know!

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