Pet Choices

Pet Choices

Description:  This activity fits in a unit with the purpose, “Students will interpret visual information in order to make informed consumer decisions.”  It is designed to get them thinking deeply about how we represent data visually, introducing the ideas of a coordinate plane (quadrant 1 only) in a very informal way – without numbers.

Teacher Note:  If your students are new to working in groups, consider introducing the sentence frames for Math Practice 3, “Construct viable arguments and critique the reasoning of others.” before you begin the activity.

Download: Sentence_Frames_for_MP.3.pdf

Preparation:  Print and cut out pet and vocabulary images, one set per pair of students.  You will also need graph paper.

Download: pet_choices_for_coordinate_plane_plus_vocabulary_XSHiChk.pdf


Directions: 

1)  Pair students.  Give them each a set of 15 cut out pet images.  “You and your partner are going to organize some data to help you decide what your new pet should be.”

2)  “First, select 10 pets and arrange the images in a column, ranking them with most fun at the top and the least fun at the bottom.”

2)  “Now, use the same pet images.  This time, place them in a row, in order of the-least-effort-to-own at the left and the-most-effort-to-own at the right.” 

3)  Tell them, “But now that we have rearranged to show the least to most effort, we can’t see which pet you decided was the most fun!  You want to choose a pet that is the most fun and the least effort.  How can we show both kinds of rankings in one organized, visual way?”  Let groups arrange images and talk to each other until they realize that they had made a vertical number line (most fun to least fun) then a horizontal number line (least effort to most effort) and that the combination of a vertical and horizontal number line would be a Coordinate Plane

[In some classes, you may need to lead the connection by reviewing.  “First we arranged pets in a column from most fun to least fun.”  Draw a vertical line on the board and label the ends.  “Next, we arranged pets in a row from least effort to most effort.”  Separately, draw a horizontal line on the board and label the ends.  “Now we are looking for a way to represent both of these things at once."]

4)  Give students grid paper (oversized paper if you have it).  Ask them to create and label the axes (you are looking for something like “fun” and “effort”) and to arrange their 10 choices of pets on the graph.  As you circulate, comment on what you see as their impression of ‘lots of fun and very little effort,’ ‘not much effort, but not very fun either’ (nearest origin), etc. in order to make sure that the message they are sending with their placement is the message they intend. 

5)  The fact that two variables can exist for one pet and be demonstrated at one time is a difficult concept.  Follow up by asking the group:

·         “Where on your graph do you find the pets who are not much fun and a lot effort?”

·         “Where do you find pets who are more fun than effort?”  (The line y = x is very helpful here.  This is not the time to use the equation for it, but instead use language like ‘when fun is equal to effort’.)

·         “How can you look at someone else’s graph and identify which pet they might choose?”

·         Include similar questions, as needed.

Give them time to move any pieces that don’t give the message they intended.  Give additional practice (optional) by asking students place the other pets where they belong. 

6)  Vocabulary:  Next, pass out the vocabulary word cut-outs (x-axis, y-axis, origin, coordinate plane).  See what students already know by their resulting discussion as they label their graphs.  Review vocabulary with the whole group, referencing individual conversations you overheard.  Be conscious of the fact that the words ‘plain’ and ‘plane’ sound the same.  You may decide to incorporate the word ‘horizontal’ and reference ‘horizon’ as it comes up in descriptions.

7)  Debrief:  Share with students the graph which inspired the activity they just did, The Official "Fun vs. Effort" Graph of Pets  Ask, “What do you notice?” and collect observations.  Ask, “What do you wonder?” and collect additional observations.  Here are some follow-up questions:

·         “What is the author’s favorite pet? -- How do you know?” 

·         “Which pet is misplaced?  Explain how the pet’s location is different from where you would have put it.” 

·         “How is this kind of graph different than other graphs we’ve looked at?”            

8)  Additional practice can be found by using the Notice and Wonder strategy (in the debrief) to make sense of the graph from this NY Times article.  [When copied, it can be viewed without the author’s commentary.]

9)  Extension:  “What situations in your life can you put on a coordinate plane?  Describe or sketch one.” 

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