This is written from an algebra teacher’s perspective but feel free to go through the process in your own area of instruction. Feel free to bookmark this post and dust it off as you plan your next school year. Or, use this example to help you for the second semester of the current year.
Today I decided to look at Algebra 1 curriculum pacing guides/calendars. I wanted to see how school districts lay out their school year. I also wanted to see the differences between pacing guides from one district to the next. I was not surprised to see that there aren’t very many differences between districts in their algebra 1 instruction. The biggest difference is that most districts plan their calendars around the state testing and that impacts the length of each of their units. It doesn’t seem to impact the order of the content very much however.
In the district I chose for this post, they had units of instruction followed by a review day and a test day. This added 2 days to the end of each unit. After listing the topics and the number of days, I looked at how they lined up with a 9 week “grading period.” I noticed the following:
+ School districts focus on linear relationships for the first 9 weeks.
+ School districts like to look at systems of linear equations (and inequalities) and will add things like sequences, exponents, and radicals in the second 9 weeks.
+ School districts like to start the second semester diving into quadratics starting with polynomials and ending with solving quadratic equations.
Armed with this knowledge I realized that from the start of the school year to the state test, there were two opportunities to do a nice, long (3 or 4 week) project. During the first 9 weeks you can do a project around linear relationships. And, during the third 9 weeks you can do a project around quadratic relationships.
The important thing to get out of the last paragraph is this: There is NOT enough time to have a great project other than those two time periods. That covers three quarters of the school year. It just can’t be done.
“But I wanted to do more projects in my classroom!” There is no reason you can’t keep pbl processes going throughout the school year. That is what great teachers do. You should be striving to include inquiry, reflection, and authenticity in every aspect of your teaching practice. But doing a full project, where we have all of the essential project design elements, can’t be done effectively in less than about 3 weeks. And it doesn’t make sense to spend 3 weeks on content that is normally covered in 1 week.
Armed with this information, let’s look at projects for linear relationships.
(A) What skills do the students need to be able to do?
- They need to understand how to represent information (data) on a 2-axis graph.
- They need to understand the slope or rate of change of the information being graphed.
- They need to understand how points of information (data) can be represented by a line passing through the points.
- They need to understand that if you can represent points with an equation then you can make predictions about unknown values using the equation.
- If you have information about two related situations, then the graph of these two situations might give more meaning in the area(s) where they intersect.
(B) What topics incorporate linear relationships?
- Areas where there are direct relationships between two values like cost per item and total cost.
- Equations in science where an input affects the output like buoyancy, force and potential energy.
- Topics in art where changing one value impacts the other value like amounts of a certain color and the spatial illusions of an image.
- And many other areas. All you need is an input and an output where both values are of the 1st degree.
(C) So what do you need to do next (for a linear project)?
Starting as early in the semester as possible you need to assign your students a problem to explore that will require them to find information, plot the information, and find a relationship between the 2 main components of the information. Then have requirements where your students must graph the information on an XY Axis, writing an equation for a line that represents the informational relationship, and make predictions about things that are not known but can be calculated using the information that is available.
An example I have done is centered on the concept of buoyancy. I gave each group pennies, representing treasure, and a sheet of aluminum foil. The students had to design a “boat” out of the aluminum foil (I recommended a rectangular prism shape but any shape was allowed). They then had to make a graph representing the volume of their boat and the mass of the boat plus the treasure and the buoyancy of their boat. And, they had to predict how much of the treasure they could carry in their boat. Then we had a day where they floated their boats in a kiddie pool and we “sank the boats” by adding pennies until the boats sank. They took pictures throughout and when it was presentation day they explained the math involved and whether they were successful in predicting how many pennies their boat could hold.
It’s important to remember that the students may not know how to plot the information. They may not know how to write an equation that represents the line for the information. They will be dependent upon you helping them learn how to manipulate the information and how to use algebraic symbols to represent the information. They are going to have questions. And that is exactly where you want them.
They know that they can’t be successful in the project without understanding the math that is required. You are one of the many resources available to them in their quest for success. PBL is a wonderful thing and, when done well, feels so good.