Ordered Pairs on the Coordinate Plane
I can remember learning about longitude and latitude and looking at maps long before I learned about the coordinate plane. And I know I played battleship before learning about ordered pairs in math class! Battleship is a great way to introduce the concept, but those coordinates do not have negative numbers.
To get kids thinking about positive and negative integers in ordered pairs, allow them to physically navigate around the coordinate plane…and turn it into a fun game! A great way to do this is to create a life-sized coordinate plane and have students walk along the axes to find the location described by an ordered pair. By physically moving horizontally and vertically along the grid, they start to understand more about integers, as well as positive and negative directions. Students will start to name ordered pairs so quickly once they’ve had this hands-on experience. After trying this lesson out, teaching about the coordinate plane and ordered pairs became one of my favorite lessons!
There are a few ways to make a life-size coordinate plane. The hallways at my school had square foot tiles, and this was perfect for taping off a coordinate grid. I even had the students help me locate the origin, (0,0) and label the axes. Another way to make a large grid is to use an old sheet or shower curtain. You can draw out the x and y axis and label each number line before your start. Something like this can be laid on the floor or hung up on a wall. Of course, if you hang it up, the students can’t physically walk on it, but they can still navigate through it, place sticky notes at specific ordered pairs, or just walk up and point or place a game piece.
In this game, students will work in pairs. One student knows the ordered pair and has to provide directions for the other student to make it to the correct spot on the board.
Set up for the Lesson: Ordered Pairs on the Coordinate Plane Floor Plans
- Make a large coordinate plane, with an x and y axis. You can draw it out on a sheet or a large board, but if you really want to have your students jump into it, map it out on a floor! Tape it off, label the origin, and tick off the numbers along each axis. The intervals should be about 1 foot apart, to allow room for students to stand. Give a range of at least -10 to 10 for both, but you can make it larger if you have the space. You do not need to label the axes with numbers. If you don’t, students will have to use their sense of direction and understand where the negative values are located.
- Give one copy of the Coordinate Plane and Ordered Pairs Worksheet for each student.
- Put shapes and mystery cards at several ordered pairs in every quadrant of the coordinate plane. (Do not write the ordered pair on the shapes and mystery cards.) Prizes can include little treats, dollar store items, balls, candy, new pencils, stickers, etc.
- Make cards or sticky notes with ordered pairs written on them. Create ordered pairs for every point if needed. Once the cards are made, this game can be played over and over, because you can place prizes and mystery cards in different places each time! If you want, you can even have the students write the cards, just make sure you don’t have repeats. (For example, one student can write all of the ordered pairs when x= 1, another can write pairs for x=0 etc…)
Some of these will match the prizes; others will lead to empty spots or even mystery spaces. Mystery cards can include “You’re stuck, lose a turn”, “Go back to the origin”, “Give a prize to the other team”, “Switch places with your partner”, “Get any shape and gobble it up”. These can be a card with a ? on it with instructions written on the back.
- Be sure to have a special note or card for the origin (0,0). This will be the first card you will locate together as a class.
- Divide the class into pairs.
Launch the Lesson: Ordered Pairs on the Coordinate Plane Floor Plans
Students should already be familiar with integers on a number line. A great way to describe the coordinate plane is to show how it is made up of two number lines. The x-axis is the horizontal number line (you can show it on your large grid), and the y-axis is a vertical number line (show how it crossed through the x-axis). Have the students find and label the x and y axes on the first page of their Coordinate Plane and Ordered Pairs Worksheet. Explain that they cross at point 0 on the x-axis and 0 on the y-axis. Have them draw a dot where they intersect and label it with the word “origin” and (0,0). You can ask them, why is this point labeled (0,0)? Then take that a step further and ask them how to label the rest of the tick marks on each axis. Be sure to walk around and help students label the axes from -10 to 10.
Here are the worksheets for the activity:
Coordinate Plane and Ordered Pairs Worksheet – SE (Doc)
Coordinate Plane and Ordered Pairs Worksheet – SE (PDF)
Coordinate Plane and Ordered Pairs Worksheet – TE (Doc)
Now talk about the importance of the origin and have the students think about the word. The origin is not just where the two lines intersect, but it is the ordered pair (0,0) and is also the starting point. Origin means to originate – so tell the students to remember to always start at the origin and map out the ordered pairs from there.
Lead the Students
Lead the students to understand that the coordinate plane is made up of infinitely many points. The intersection of the two axes divides the plane into four regions called quadrants. The signs of the coordinates vary in each quadrant.
The most difficult part about ordered pairs is that students can forget or confuse which number is the x value and which is the y. One way to help your students remember is to tell them that x comes first in the alphabet, so it comes first in the ordered pair. Another way to think about it is to remind students that the first number is x, and tells you how far to move horizontally and the second number is y, and indicates how far to move vertically. (x,y) (horizontal, vertical). Make sure students write (x,y) on their worksheet.
Now it’s time to play the game. Tell the students that they must direct their partner to at least 3 different ordered pairs on the board. The goal is to capture as many shapes and prizes as they can!
The Activity: Ordered Pairs on the Coordinate Plane Activity
- Send 2 students to stand on the origin.
- Their partners must pick a card from the table. The cards have ordered pairs and can be in a stack or spread out, face up. (Depending on how difficult you want to make it).
- One of the partners read the card silently (without revealing the ordered pair) and help direct their partners to that ordered pair on the board. The student giving directions cannot just say the ordered pair. They must provide directions like “Take 2 steps to the right along the x-axis”.
- The directions will be read only once, so tell the students to be pay attentively.
- The student being directed can turn and face any direction, but they can only move vertically or horizontally (not diagonally). Give the students helpful feedback and praise when they use math terminology or directional words. When the student arrives at the spot, he/she will say the ordered pair aloud. The student giving directions holds the card up and the class decides whether they are correct.
- If a student ends up on a prize or shape, they “gobble it up” and pick a new card.
- If they land on a blank space, they check the ordered pair and pick a new card.
- If they land on an obstacle, they read the card and follow the instructions.
- After 3 cards each, see who gobbled up the most prizes.
- Send in 2-3 more students and play again.
- For the first few rounds, it is good for the other students to watch and learn. You can discuss what was successful and what patterns students started to see.
- If needed, the groups that are not navigating can use the blank coordinate plane on the worksheet. Here they should follow the directions given by one team on their own graph. When they reach the destination, plot the point, label it with the initials of the student who got there and write the ordered pair next to it.
Reflecting on the Activity Ordered Pairs on the Coordinate Plane
Ask the students to discuss and explain the hardest part. You can ask questions such as:
- What was harder, giving or receiving the directions?
- Which way did you walk when there was a negative x value?
- What direction did you walk when the y was positive?
- Where would you end up if both x and y were negative?
- Can you describe what the coordinate plane looks like? Does it remind you of anything?
- What patterns did you notice?
Once students know how to locate ordered pairs, a great extension is to do coordinate plane pictures. This is like a mathematical dot to dot. There are several free resources, like this one, and many students like finding the pairs and revealing a picture.
Another extension is to create a mathematical battleship game. I have had students make their own coordinate planes on graph paper, label the origin and axes from -10 to 10. These can then be put into plastic sleeves. This way they can use dry erase markers to place their ships. A ship is made of 2,3,4 or 5 ordered pairs in a row, connected with a line like this:
Hide your sheet or place a book between you and a partner and play battleship, but instead of saying “B-4” you say an ordered pair like “(-2,4) “. If your opponent has a ship dot on (-2,4) they say “hit”
FREE Ordered Pairs on the Coordinate Plane Worksheets and Resources
These are all PDF Files. They will open and print easily. The Student Edition Files are labeled SE and the Teacher Editions Files are labeled TE. Click the links below to download the different resources.
- 3-6 Assignment SE – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Assignment TE – Rational Numbers and the Coordinate Plane (Members Only)
- 3-6 Bell Work SE – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Bell Work TE – Rational Numbers and the Coordinate Plane (Members Only)
- 3-6 Exit Quiz SE – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Exit Quiz TE – Rational Numbers and the Coordinate Plane (Members Only)
- 3-6 Guide Notes SE – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Guide Notes TE – Rational Numbers and the Coordinate Plane (Members Only)
- 3-6 Interactive Notebook – Rational Numbers and the Coordinate Plane (Members Only)
- 3-6 Lesson Plan – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Online Activities – Rational Numbers and the Coordinate Plane (PDF)
- 3-6 Slide Show – Rational Numbers and the Coordinate Plane (PDF)
Ordered Pairs on the Coordinate Plane Worksheets 6th Grade and Resources
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- 3-6 Slide Show – Rational Numbers and the Coordinate Plane (PPT – Members Only)
- 3-6 Online Activities – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Lesson Plan – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Interactive Notebook – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Guided Notes TE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Guided Notes SE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Exit Quiz TE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Exit Quiz SE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Bell Work TE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Bell Work SE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Assignment TE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
- 3-6 Assignment SE – Rational Numbers and the Coordinate Plane (Doc – Members Only)
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This Lesson is From Unit 3 – Rational Numbers
- 3-1 Positive and Negative Numbers
- 3-2 Positive and Negative Numbers on the Number Line
- 3-3 Comparing and Ordering Rational Numbers
- 3-4 Writing and Interpreting Inequality Statements
- 3-5 Absolute Value of Rational Numbers
- 3-6 Absolute Value and Ordering Numbers
- 3-7 Rational Numbers and the Coordinate Plane
- 3-8 Ordered Pairs on the Coordinate Plane
- 3-9 Distance on the Coordinate Plane