Graphing: Input VS Output
Lesson 19 of 22
Objective: Students will be able to interpret a graph consisting of coordinates in the first quadrant.
The focus for this lesson is on looking for patterns in graphs, and determining what information we can summarize from a graph. I’m exposing my students to the concept of input and output, using a real world situation to have the students create a table and graph then using it to make observations. The graph will show how much time is spent on homework in class.
One of the common core shifts is using real world contexts for mathematical tasks.
This graphing activity is my approach to the introduction of coordinate grids. I am using graphing - a concept my students know and have used - to introduce a new concept, coordinate grids.
Think about when you did their homework last night. Describe to your neighbor what your surroundings were like and how much time you spent on your homework.
I ask a few students to share out their partner’s response of how much time it took and include one detail of the surroundings. Although the surroundings of the student while completing their homework is not part of the data collection, it does provide interesting information on work and study habits. The data shows the majority of my students report they spent about 20 minutes on their homework last night.
Now that we have collected some data, we should be able to create a table and graph. Let’s start creating a table together. What should the headings of the columns be for this table?
It is important that the students do the thinking (the work). My role, in modeling, is prompts to develop the visual model. I work on setting up the table with the students and together we complete the first few rows. I have students work with their groups to complete the remaining portion of the table representing the 30 students in our class. Although they are working with their groups, I require each student to create their own table. I create my own table but do not display it until the end. It has a purpose. Students are expected to check their own work, in comparison to my table.
Now that we have created a table, let’s move on to creating a the graph. What would be the first data point we would need to plot? Think of this as a list of points we need to plot in the coordinate grid.
I facilitate the discussion and listen for students to talk about the data as points on the grid. I supply the students with a piece of graph paper and ask them to create a graph based on this information.
Before I let you go back to working with your groups, let’s set up each axis for this graph/grid together. Who has some ideas for what we can put on the x-axis? What about the y-axis?
After the graph/grid is set up, I let the students go back to conferring with their group while creating the graph. I circulate the room and assist students as they begin graphing.
During the closer of this lesson I have the students work with their groups to create a summary of their graph. I use questions to guide their prewriting preparation.
How could you use this graph and table to figure out how much time would be spent on homework per night if we had 30 students? 50? 100?
After allowing some time for the small group discussion I bring the class back and have a class discussion in the campfire about input vs output. Up until this point in the lesson students have created a context for input vs output. Now, I will continue the scaffolding by adding the mathematical vocabulary of input and output.
Let’s share some of the summaries we came up with our groups. What conclusions did you make about trying to determine how much time would be spent for 50 students?
I am looking for students to recognize a pattern in the data. I continue fostering the conversation to get to the point where the pattern is identified.
So what I hear you saying is that if I input 10 into the grid, I will get 200 minutes of homework time. How did I get from 10 to 200 mathematically? So my input is 10 students and my output is 200 minutes. If my input was 50 students what would be my output?
I wrap up the discussion by asking students to create definitions for input and output orally.