2.2: Ordered Pairs
This activity is intended to supplement Algebra I, Chapter 1, Lesson 6.
ID: 11638
Time Required: 15 minutes
Activity Overview
In this activity, students will investigate ordered pairs. They will graphically explore the coordinates of a point on a Cartesian plane, identifying characteristics of a point corresponding to the coordinate. Students will plot ordered pairs of a function, list these in a table of values, and graph them in a scatter plot.
Topic: Functions & Relations
- Cartesian coordinate system
- Characteristic of ordered pairs in a quadrant
- Graph ordered pairs on a scatter plot
Teacher Preparation and Notes
- Before beginning the activity, students should clear all lists and turn off functions. To clear the lists, press STAT [EDIT] and scroll down until the arrow is in front of ClrAllLists or ClrList. Press enter twice. To clear any functions, press \begin{align*}Y=\end{align*} and then press CLEAR when the cursor is next to each \begin{align*}Y=\end{align*} equation.
- This activity can serve as an introduction to ordered pairs, quadrants, graphing points and see the connection between a function and a graph.
Associated Materials
- Student Worksheet: Ordered Pairs http://www.ck12.org/flexr/chapter/9611, scroll down to second activity.
Problem 1 – Ordered Pairs
First, students explore the coordinates of a point in the various quadrants. They will enter a given coordinate into lists \begin{align*}L1\end{align*} and \begin{align*}L2\end{align*}, where \begin{align*}L1\end{align*} is the \begin{align*}x-\end{align*}value and \begin{align*}L2\end{align*} is the \begin{align*}y-\end{align*}value. There should only be one number in each list at all times. Then students will graph the coordinate as a scatter plot using Plot1.
Students should press ZOOM and select ZStandard to see the standard viewing window. After selecting ZStandard for the first coordinate, they can then press GRAPH for the other coordinates.
Explain to students that a point on the \begin{align*}x-\end{align*} or \begin{align*}y-\end{align*}axis, when the first or second number in an ordered pair is equal to zero, is not in a quadrant since it is on the boundary between quadrants.
After students answer the questions about what quadrant an ordered pair is in, they will explore where ordered pairs are in general. They need to turn off Plot1 and then press GRAPH. When students move the cursor, the coordinates will not be integers, but they should still be able to conjecture where the \begin{align*}x-\end{align*} and \begin{align*}y-\end{align*}values are positive and negative.
Ask students to tell you where specific points will fall, without using the calculator.
- Where will \begin{align*}(5, 1)\end{align*} fall? Quadrant 1 If it is in Quadrant 1, where will \begin{align*}(-5, 1)\end{align*} fall? Quadrant 2 \begin{align*}(5, -1)\end{align*}? Quadrant 4 \begin{align*}(-5, -1)\end{align*}? Quadrant 3
- Continue with similar questioning until all students feel comfortable with the four quadrants.
Then students are to apply what they learned by plotting points to solve a puzzle. The solution of the puzzle is “MATH ROCKS.”
Problem 2 – Order Pairs
Students are given a function for the cost of ordering pears. They need to enter 5 ordered pairs into lists \begin{align*}L1\end{align*} and \begin{align*}L2\end{align*}. Then they will set up Plot1 to display the scatter plot of the pairs.
To set an appropriate window, students can press WINDOW and change the settings individually or press ZOOM and select ZoomStat.
Pressing TRACE and using the arrow keys will allow students to see the \begin{align*}x-\end{align*} and \begin{align*}y-\end{align*}value of a point.
Lastly, students will graph the line \begin{align*}y = x\end{align*} and then adjust the slope so that it goes through the ordered pairs of the scatter plot. This means that they will need to add a number before \begin{align*}x\end{align*} and then change that number as needed.
Students should see that the slope of the line is the same as the coefficient of the function given for the cost of ordering pears.
The Manual-Fit regression can also be used to allow students to adjust the line of fit on the graph screen. Press STAT, arrow to the CALC menu and select Manual-Fit. Press ENTER when Manual-Fit appears on the home screen. Students can then adjust the slope and \begin{align*}y-\end{align*}intercept until the equation fits their data. Once students are satisfied with the line, they can press \begin{align*}Y=\end{align*} to see the equation.
Extension
Extension 1
Students are to find some other real-life data and then represent it as a set of ordered pairs, table, and scatter plot. Teachers can show students how to use the Graph-Table split (found in the MODE screen) to see the graph and table at the same time.
Extension 2
Students are to come up with their own puzzle like the one page 1 of the worksheet, which spelled “math rocks”. They can share their puzzle with a friend or the class. Or students can draw a picture on a coordinate grid and identify key coordinate pairs. They then create two lists of \begin{align*}x-\end{align*} and \begin{align*}y-\end{align*}values to exchange with a partner. The partner will then redraw the image. Also, students could be given an image or two for practice. Trees and leaves make good examples.