Movement In Linear Graphs Day 1 of 3
Lesson 8 of 23
Objective: STBAT conceptually understand that proportional movement creates linear graphs and proportional movement actually creates similar slope triangles.
You will need a large open space that is either tiled with square tiles or can be marked using markers or chalk (outside parking lots and sidewalk chalk work well sometimes). You want to mark the large space as a four quadrant grid complete with x an y axis numbered and spaced so that students can walk along the graph and stand without touching each other. (I like to use the tiled lobby of my school and colored ropes from Lowe’s for x and y axis. I number the axis with index cards and a permanent marker.).
You will need to plan the quick set up and transition to this open space during the activity. Another aspect of my school that helps this activity come to life is the availability of technology and a balcony. The lobby I use for the student activity is part of a two story entrance. I plan to set a camera on a tripod on the balcony of the second floor and take video and still shots of the students as they moved through the activity so I can use the aerial footage in class with students the next day. Allowing students to see the whole picture will be so beneficial to their learning.
Make sure you copy and cut the student cards before the lesson – keep group 1 separate from group 2. The average class size is 30 students; therefore, I had to use both positive and negative x values in order to fit and entire class within one reasonable open space. I urge you to think carefully about who to give the negative x-axis values. Make sure you pick strong students who will be able to reason through moving in the opposite direction on the x-axs and therefore moving down on the y-axis.
Tell the class that today the activity is all about movement and observing what happens when ratios are connected to movement. The idea of movement is so important that we will be leaving the classroom and moving ourselves as part of the activity. Set any ground rules and expectations about behavior while outside the classroom and be very explicit about consequences for poor choices.
Bring each student a card with group1 or group 2 and an individual x-axis number (students within the same group should not have the same x-axis number). Inform students that this card will describe how they move during the activity today. Pull up a four-quadrant grid on your projector board and show students that they will be given instructions in the activity page for how to walk. Clarify we are interested in the following:
- How each student walks
- Where they wind up (location)
- What they look like as a whole group after they move.
Beginning the New Activity
Bring students an activity sheet and allow them one minute to read the directions individually. Ask a student to summarize what the directions want them to do before leaving the classroom. (Decide how to walk and where to be when finished walking based on your group directions.) Have students write in the coordinates of their final destination and move about the room answering questions and checking papers for correct completion of directions. Hint: the students who have negative x-axis values tend to struggle with how to move along the y-axis, down instead of up. Make sure you give the negative numbers to your stronger math students and check with them before you leave the room to ensure they are thinking correctly.
Before you leave, make sure everyone is perfectly clear about what they should do during the activity. Show them using the projector board where to begin the activity. Group 1 always begins by standing on the origin and then walking across the x-axis and up the y-axis. Group 2 always begins by standing on (0,3) and then moving along the x-axis and up the y-axis. Ask for any final questions before you leave the room. For the purpose of taking turns, have the students walk in ascending order beginning with the students whose x value is 1. You could even as both students from group 1 and group 2 with the same x value to walk at the same time. It would save you time to ask 15 pairs of students to walk instead of 30 individual students.
Once outside, set up the tripod and camera to capture the magic (if you have one to use) and then begin directing students as they create the graph. While students are standing in their two lines you could ask them to look around and make observations about the graph. What do you look like? What do you see as some overall characteristics of your movement? They could jot down any ideas on their activity sheet first page. Making these observations about movement requires students to use math practice standard seven (MP7) looking for and making use of structure.
Next, clean up the space if you used ropes and cards and head back to the classroom. If you have time, ask students from each group to record the coordinates of their final destination in the table at the front of the room. (Making a table on paper such as sticky chart paper and markers works well when you need to keep the data for the next day. A dedicated space on your whiteboard also works well.
Your goal is to finish the walking and videoing section of the activity today by being well organized and thoughtful before moving students out of the classroom. If you have time to complete the class wide table, then that is a bonus for the following day.
If you choose to use the video and still pictures for the following lesson then you might want to spend time editing the video and pictures. It would be powerful to watch two students with the same x value begin at two different y-intercepts and walk the same ratio. If you select about three to four students to watch then the overall picture of parallel lines and what it means to be parallel would become very visual. If you edit the video with inserting a marker that highlights the walking path of each student as they walk right and up then, then the geometric shape of a triangle becomes more obvious (close to the slope triangle but opposite, run then rise). You could even take a still shot and add in different colors to show the different walking paths and multiple triangles (all similar) that are created. You could take a still shot or video and add the line across all students to high light the linear shape as well. All of these concepts should come to light during the discussion and questions on day 2 of the activity.