Guide for Introducing Coordinate Planes
This series of activities and lesson notes is part of a unit in which the purpose is, “Students will interpret visual information in order to make informed consumer decisions.” The activities begin with informal exploration.

1.  Introduce the series, “Today we will think deeply about a way to represent data visually.”

 Pet Choices (approximately 50 minutes without extension).  Use the Open Author resource, Pet Choices.

2.  “Now let’s look at another visual representation of data.”

Drink Prices (approximately 15 minutes).  Use the Open Educational Resource (OER), Figure This! Challenge #70 along with any of the following ideas:

Use this as a whole class lesson.  Be slow to tell students who are making a conjecture if they are correct or not, giving everyone time to think through the ideas. 

Share the graph image and ask, “Is it more expensive to buy drinks at the grocery store or the convenience store?” Do not validate any answers, you are more interested in student reasoning; so after every answer given, ask, “How do you know?” 

To lead students into seeing a general pattern rather than just the information they can gather from individual data points, use this series of questions: 

o   “Name a drink that’s more affordable at the grocery store.” 

o   “Name a drink that’s more affordable at the convenience store.”

o   “What’s the most expensive drink?”  (Evian.)

o   “What’s the cheapest drink?”  (Nestea or Ginger Ale, depending on where you purchase it.)

o   “Is there a way to answer the question, Is it more expensive to buy drinks at the grocery store or the convenience store? for these and any other data (drinks) we add to this graph at a glance?” 

Take suggestions until someone describes, in some way, the idea of finding where $1 at the convenience store and $1 at the grocery store meet.  Finding multiple points where the dollar values meet will create a line from (0, 0) at a 45° angle.  Now is the time to use students’ language with specific dollar-value examples and help them move to more generalized statements such as “when the price at the convenience store is equal to the price at the grocery store.”  If they are ready, formalize the language of y = x from the generalized statements they use.  (See the answers link at the bottom of the OER for ways that this can happen using a table.)

3.  Now that students have had a chance to experience coordinate planes in quadrant 1, follow up by extending the lesson in the appropriate direction for the class.  There are three choices below.  Each activity takes approximately 45 minutes.

1)      Battleship (If needed, use to teach plotting points.  Directions for quadrant 1 below.)

2)      Pomegraphit (This internet-based activity uses 4 quadrants, informally through Desmos.)

3)      Awesome Coordinate Plane (This internet-based activity uses negative numbers and all 4 quadrants through Desmos.)

Battleship

Preparation:  Pass a sheet grid paper to each student.  Ask students to fold in in half.  On both halves, draw quadrant 1 of a coordinate plane on labeled from 0 to +10 on the x-axis and y-axis.  On the bottom half, ask students to plot the locations of five ships.  Ships must be placed vertically or horizontally and fit within the defined area. The five ships are:

⧠       Aircraft carrier, 5 points long

⧠       Battleship, 4 points long

⧠       Submarine, 3 points long

⧠       Destroyer, 3 points long

⧠       PT-Boat, 2 points long

Playing the Game:  (Model how this works by first playing one game with the whole class guessing where you placed your ships before using it with partnered students.) 

1.  Take turns guessing coordinates (attacking) that may be a location of a ship. 

2.  The person whose ships are under attack will let the attacker know if their coordinates were a hit or a miss.  The attacker then records whether or not their guess was a hit or a miss on their blank coordinate plane in order to keep track.

3.  Once all the coordinates of a ship have been hit, tell the attacker that the ship is sunk.

4.  Play until one person sinks all of the other person’s ships.