Multiple Representations - Linear Functions
Lesson 13 of 17
Objective: SWBAT to describe how to move from one representation of a linear function to another.
I begin class today by writing a linear equation on the board. For example, I might write something like y = 5x +10. I ask students, based on what they have learned so far in this unit, about different ways they can represent this equation. I want to elicit from students that they could graph it, represent it tabularly, or write a real world situation to describe the equation.
Next, I put up a table of values (that also represents a linear function). Again, I ask students different ways they could represent the data in the table. Students will likely begin to see the point I am trying to make: linear functions can be represented as tables, equations, graphs, and situations. I ask them about the characteristics of linear functions. What makes them linear? I want to be sure students hit on both the idea of a rate of change and a starting point. I ask them again, where they can see these characteristics in the equation I started class with.
I tell students that today they will be working in groups to write a guide about how to move from one representation to another. We read through the Multiple Representations Project together. I might assign, or let groups choose a starting point and then ask them to write instructions for all of the conversions from that starting representation. For example, one group might be assigned the starting point Situations. This group must write instructions for how to go from a Situation to a Graph, a Situation to a Table, and a Situation to an Equation. I ask each group to make a poster that they will eventually present to the class. It sometimes helps students to tell them to imagine they are writing a guide for future students who have yet to take this class. This places students in the role of "expert" and can help them with the tone of their writing.
Depending on my class, I might think through the groups of students and assignments (of a starting point) before class especially if I want certain groups to work on areas they struggle with or with more challenging conversions.
Next I let students get to work. I make sure they have access to all the tools they need: poster board, graph paper, markers, yard sticks, etc. As they work, here are some things I watch for:
- Some students will be more comfortable working with certain conversions. For example, if a group is starting with Situations, they might first generate a table (which is part of the assignment), but then create the graph based on the table. I press them to create a graph from the Situation, rather than using the table to graph instructions (which would be part of another group's work). This will encourage students to really think about how situations and graphs are related, rather than how tables and graphs are related.
- Students may find it helpful to come up with situations to make their instructions more relevant. They may need some help coming up with ideas. I make sure they know how to check to see if their situation is indeed a linear one.
- I try to encourage students to include decreasing rates of change as well as increasing rates of change.
- I make sure students are explicit in their writing. This is a good opportunity for students to practice writing about math, something they may not have done in the past. If I find a student who is having trouble turning thoughts into words, I sometimes ask the student to talk out loud while I scribe what s/he is saying.
Students may not finish their posters in today's class. Depending on the class, I will have to make a decision about when the assignment will be due and if we will dedicate more class time for students to work on it.
I also try to schedule a time for students to present their posters. This might happen in the next class, or I might consider scheduling something bigger in my school depending on what is happening in the community.
Students will need the bulk of class today to work on their posters. I leave some time at the end of class for students to think about the ways they are working with multiple representations. This is a key understanding for students in Algebra 1 and a good time to ask them to reflect on their learning. I might have them share their thoughts with the class by writing two different prompts on two white boards.
On one board, I write the prompt:
The representation of linear functions I like best is... because....
On the other board, I write the prompt:
The representation of linear functions I find most challenging to work with is.... because...
If there is time, I have students volunteer to talk about why they like the representation they do and why they struggle with the other one.