Linear Function Stories

My 9th graders has been working through a unit on linear functions.  This co-taught class contains students who went through a traditional Algebra 1 class in semester 1, and are now in a course with me as preparation for the Pennsylvania Keystone Alegbra 1 Exam in May.  While developing core algebra skills is a goal for this course, the literacy skills are also a challenge.  The Keystone exam is language-heavy, and these students need as many opportunities as possible to read and communicate.

WHAT I DIDN’T WANT TO DO:

• Provide endless worksheets and textbook problems with no context
• Introduce technology tools after “traditional” mastery

WHAT I SET OUT TO DO:

• Provide multiple means to evaluate linear function scenarios
• Use technology from day 1 to evaluate data
• Allow an opportunity to peer-assess student works

 Wanting to stress contexts from day 1, I used the site Graphing Stories by Dan Meyer and BuzzMath, as an opener a few times within the first 2 weeks of class.  The site provides 15-seconds video of a scenario (such as time vs height on a rope swing), and students use pre-made graph paper to develop a graph which matches the scenario.  As an opener, I appreciate this site as a place to start conversations.  A document camera is used to display student works, which are randomly chosen from my handy popsicle stick collection.

In algebra class, students often learn slope as rise / run, and my students were able to recall this “definition”.  Almost all students were able to recall the slope formula, given two points, and could compute a correct slope (with some minor math errors).  But considering slope as a rate of change within a context was a mostly new experience.

For each of the last few days (after we had seen many of the Graphing Stories), I have given a similar opener.  A graph is given, and students must give the equation, AND a sentence which provides a possible scenario for the graph.  Sort of an inverse-Graphing Story.  Here was today’s opener:

After a few minutes, I collected the student responses, which were written on index cards.  In our review phase, I shuffled the cards, and chose random samples of student works to share under the document camera. The projector showed the original graph, along with the story:

 

“I had 200 baseball cards, every minute I unwrapped 30 more”

To check the student’s story, we looked at two criteria:

• Does the story have a correct starting point?
• Does the story have a correct rate of change?

Results are still mixed, ranging from responses which are on-point or emerging:

• “Tommy saw 200 bugs, every second 30 more bugs showed up” (I have a lot of critters in my room)
• “I start with $200 and I get $30 each week”
• “There are 200 people with car insurance every hour 20 people get car insurance when they see the Geico commercial”

To those who still need more practice:

• “Every 70 days 200 pizzas come to the pizza shop”
• “There were 30 spiders and every minute 200 more spiders come”
• “There are 30 toddlers each earn 200 pennies”

But the responses get better every day, and we celebrate the successes of those who improve, and learn to critique work appropriately!