Algebra I : Unit #1 - Thinking Like a Mathematician: Modeling with Functions : Lesson #8

Functions in Everyday Situations: A MAP Project Challenge

Objective: SWBAT describe everyday situations using functions. SWBAT interpret functions in context. SWBAT identify the domain of a function using information about its context.
Standards: HSF-IF.A.1 HSF-IF.A.2 MP1 MP2 MP4 MP5
Subject(s): Math
60 minutes
1 Pre-Assessment - 0 minutes

This lesson implements the Performance Task: Functions and Everyday Situations Math Assessment Project developed by the Math Assessment Project.

I have students complete the Pre-Assessment Functions and Everyday Situations either at the beginning of class or for homework the night before. The benefit of having students complete the Pre-Assessment prior to class is it provides me time to analyze student thinking and to make adjustments to the lesson to try and maximize student learning and benefit from today's performance task.

2 Introduction - 15 minutes

Prior to today's lesson my students completed the Pre-Assessment: Functions and Everyday Situations, so my plan for today is based on their current level of understanding. To begin, we'll take a few minutes to complete a whole-class introduction to today's activity. Using the Functions and Everyday Situations slides I will model the tasks that students will be completing. 

In Slide 2, for example, students are asked to create a graph comparing the number of painters and the time needed to paint a bridge. I will ask students to sketch a graph in their notebooks so that they have a model to refer to later in the lesson. Then, I will have several students demonstrate their graphs for the class. To close out the introduction, we will choose a likely graph and work as a class to generate a function that describes the situation and the graph. 

3 Collaborative Activity: Matching Situations to Graphs - 20 minutes

For this section students work on the Matching Activity: Functions and Everyday Situations. As I introduce the taskI will stress the importance of explaining one's reasoning to peers. The goal for this matching activity is for students to apply their mathematical knowledge and to develop their reasoning and communication skills (MP3). 

After setting expectations with my the students, I will ask them to work in groups of 2-3. While students work on matching the different situations to graphs, I will rotate among the groups and ask questions to help guide student learning. I will not be too directive, since this is a challenge for students and I want them to show what they can do (MP1). 


Teacher's Note: The lesson plan  for Functions and Everyday Situations Math Assessment Project prepared by the Math Assessment Project provides amazing examples and suggestions for specific questions teachers can ask students depending of how students are approaching the task. I highly recommend that teachers take the time to read through the Math Shell document prior to teaching the lesson.



Providing Opportunities for Justification and Explanation
Writing Across the Disciplines

For this section of the Math Shell Assessment lesson, students Matched Situations to Graphs

As an additional set of support, I developed a template to provide students with space to log which situation they matched with which graph and a space for students to explain their thinking. I try to have students engage in the four domains of language (listening, reading, speaking and writing) everyday. 

For this lesson, students were able to debate and discuss features of graphs and how well they match different situations. Having students Justify their Reasoning with Evidence helps students better organize their thoughts. I have also found that students ask better clarifying and follow-up questions after having time to process the work through a written response. 

4 Collaborative Activity: Matching Graphs and Situations to Formulas - 20 minutes

For the next section of the lesson, students work on the Matching Activity Resources Functions and Everyday Situations. In this section, students focus on matching the situations and graphs to formulas. My students tend to have more difficulty matching situations and graphs to formulas that are not linear. One way to help students overcome this challenge is to begin with matching the formulas they know (linear). Once they match the formulas they are most confident with, the task of matching the rest is more manageable. By looking at a smaller set of representations, students can look at pieces of information from different representations and work together to reason about the correct matches.

As the students are working, I like to give the class cues to time left, including a 10 minute and 2 minute warning to help students organize their time. I find that time cues help my students to make decisions when they are working on a task such as this one. 

5 Whole Class Discussion - 20 minutes

After matching the formulas to the situations and the graphs, the class reconvenes for a whole group discussion. During the discussion, the goal is to elicit participation from as many students as possible and dive deep into an analysis of a few of the cards (rather than explain all of the situations superficially). 

There are a number of conversation starters suggested in the lesson plan (see MAP_Whole_Class_Discussion_Topics). I plan to discuss with my students the situations that were easy to match. I will ask volunteers to explain why a situation was easy for them to match. This prompt gives students a chance to discuss one of the examples they feel more confident about. It also gives students a chance to listen to a peer who may have thought about one of the situations in a different light. 

It is important to monitor time during the group discussion as there are so many rich ideas that can come out of the discussion and it easily could continue to the end of class. 

6 Exit Ticket and Homework: Another Four Situations - 15 minutes

To conclude today's class, I will have my students work on the Another Four Situations: Functions and Everyday Situations.  The assignment is very similar to the pre-assessment task and asks students to match formulas, situations and graphs to each other. At this point, I will probably have my students work independently so that each can apply their current knowledge and skill at their own pace. They have been exposed to a lot of ideas today, so it is important for them to have some time to make sense of everything, and apply new ideas. 

I congratulate students on all of their hard work today! 

7 References - 0 minutes

Mathematics Assessment Project (2012). Functions and Everyday Situations: A Math Classroom Challenge. Shell Center: University of Nottingham. Accessed online on May 26, 2014 here.