Friday, July 17, 2015

Single Riders

I noticed this sign while visiting a local amusement park this week, and as we waited for the ride I noticed that there were often several open seats for each cycle of the ride.  Now I'm a bit of a Disney fan, and even though they sometimes have long lines, there are rarely empty seats on the big ticket rides.  They do this with single rider lines, and assigning people to specific rows so that they know how many single riders they need to fill the space.  Less wait=happier park visitors!

Then the questions start. How much would it cost to add single rider lines? How many open seats are there really in an hour?  Day?  Are people actually annoyed that there are empty seats- and how much time would adding a single rider line really take off of the average wait.  Certainly Disney went through this process when they decided to add the single rider lines, but how much more volume does Disney have per day over my local amusement park?

When I think about  SMP#3- Constructing Viable Arguments and Critiquing the Reasoning of Others- I want my students to really look at the world around them and use math as a tool to prove whether something does or doesn't make sense. To do this, students really need to observe and question what they see. They need to know how to collect data and organize it in a way that can be communicated with others.

How do we as teachers help to build this capacity in our students?  How can we use SMP #3 in our classrooms to help students model their understanding of a concept and identify misconceptions that are common with that concept?  How do we build a classroom culture where students are comfortable critiquing and having their understanding critiqued.

More to come....suggestions and thoughts are welcome!

Thursday, July 9, 2015

Graphing Inequalties Exploration

This is an exploration lesson for students to discover the properties of linear inequalities in two variables. The link will download a copy of the files that I print out for students as well as a possible facilitation guide. The general idea behind the lesson is that students are taking a piece of a Cartesian plane and identifying whether points on the graph are or are not solutions to the inequality. If it is a solution, the point gets a "closed circle" sticker. If it's not, the point gets an "open circle" (a reinforcement sticker). Students work in small groups to fill up the plane with open and closed circles. I verify and ask questions as I walk around.

 When they are finished I pair up the groups and have them note things their graphs and inequalities have in common. There are 8 groups, but they are strategically paired. For example in the first rotation students are comparing inequalities that both have a boundary line with the same slope and y-intercept, but one is greater than or equal to, and one is less than or equal to. By the end of the discussion students should be able to identify solutions to inequalities in two variables, understand the concept of a boundary line, and connect what they know about slope and y intercept to the boundary line. 

The third part of the lesson is a set of cards for students to match up to inequalities. The purpose of this is to introduce the different boundary lines when the inequality is just less than instead of less than or equal to. For example, in the first pairing, all groups have inequalities with the same slope and y-intercept, but different inequality symbols.

Graphing Linear Inequalities Exploration Lesson