Reflection: Representations of Relations

The one thing I am really nervous about when starting this new school year is the bell schedule, 35 minutes for one period. What can I get done in 35 minutes? Can I get a Desmos activity done in 35 minutes? Could we do a class project in 35 minutes? I feel like I will be cutting out important discussions or big "ah-ha" moments with less time.

So I went back to thinking about when I start the second day of class with mathematics, I want there to be context in what the students see and do in math. In my last post about Representations of Relations I received this comment:



They changed the focus of that first lesson to make the rest of the year one cohesive goal.



As part of the curriculum group for Advanced Algebra, we set the pacing guide and decided that representations of relations along with the distributive property should be taught first. One thing I want to get across to students that first week is everyone having their voices heard and problem solving.

So each wall of the classroom will have the same layout from the previous post,

• one wall will have ordered pair along with a piece of butcher paper with notice/wonder at the top. 
• second wall will have a mapping with a different piece of butcher paper with notice/wonder.
• third wall will have a table with butcher paper labeled the same way.
• fourth wall will have the New York Times graph and butcher paper.

I want to have students stand (and gather by the board) and take 1 minute to look and 2 minutes to discuss with a partner what they see. I will ask what students notice first, then wonder. At the end I want them to discuss what was similar or different with the four different relations.

I still have to cover distributive property at the end, but as an exit ticket I want them to reflect on the experience and answer the following question:

Why did the New York Times select a graph to represent this relation?  

I want a connection more to relations, what question should I ask that encompasses what they learned and that representing functions is useful?

Representations of Relations

This is going to be my fifth year teaching Algebra 2, this year I am changing schools so it will be called Advanced Algebra. I was doing some curriculum writing with my new team of teachers and the first section we are going to cover as a class is Representing Relations my first reaction was...



At this point with just coming back to school students may not remember what relations are, what functions are, or domain and range.

I thought back to Dan Meyer's talk of headaches and aspirin and why do students need to know there are different ways to represent relations: ordered pairs, tables, graphs, and mapping.

I took the second graph from New York Times: What's Going on in this Graph?  and re-organized the information differently.

Give the students the following information:
This data is organized from by: country (guns per 100 people , mass shooters per 100 million people).
United States (85, 28)
Canada (26, 9)
Afghanistan (2, 20)
Iraq (37, 4)
France (35, 15)
Yemen (55, 40)

Ask the students what they notice? what do they wonder? As the teacher write down everything they say. One question I have is what is the data saying? Is there a different way to represent the data?

Give the students the following information:



What do they notice and wonder now? What has changed? You can show them mapping as well, but eventually you will need to introduce other things, but the last one is the graph from The New York Times.




How do the three representations differ, do they all tell the same story? Do some tell the story better? I'm not sure if this is the way to start the year out, but nothing is perfect. I want students to feel that there is some context to mathematics other than its day 1 therefore we do lesson 1.