4.1+Modeling+Real-Life+Events

Zareen K. Monday, September 15th, 2008 Block 8D: Advanced Math **__ Journal 4.1: Modeling Real-Life Events __** __ Notes: __ -Today he collected the investigation one and two journal assessments and the redone partner quizzes. ** Problem 4.1 ** // A. //// The graphs bellow model events described in the story. Tell which event each graph represents, and explain why you think the graph is a good model for the event. Copy each graph, and label the axes with the variable names. // 1. I think that this first graph best represent the experience that the lunch group had. This is because the story says that the temperature went down at a gradual (not constant) rate until it reached room temperature. The story also says that at first the temperature decreased rapidly, but then near the end slowed down. 2. I think this second graph best represents Paige's parachuting experience (the parasailing group,) because at first this graph is shown to increase and that could be Paige going up into the air and then gradually coming back down. // B. //// Identify other events in the story that involve relationships between two variables. For each event, sketch a graph that the models the relationship between the variables. Carefully label the axes so it is easy to see what the graph represents. // // C. //// For each graph that you sketched in part B, write a sentence or two explaining what the graph shows and how it fits the description in the story. // For the first picture, it was the graph that I got for the bicycling group. According to the story they rode at a steady rate the entire time, so I modeled a linear-horizontal line to show the relationship between time and distance. For the second picture, I showed the tour bus group on the bus slowing for the city's speed limit and then coming to a stop because they had finally arrived at their destination. I modeled this as a curve because there is so exact way of telling how fast or slow they were driving so I drew what the graph would roughly look like. For the third picture, I showed the tides rising up over time. This is because in the story it clearly states that they would have to wait till the tides rose before they went on any tour because the boat was grounded to the harbor. Later that day after the tour was over the tides dropped again (after they were done with dinner.) This is why I had the graph go up and then back down again. // D. //// Write a paragraph about a fourth group had while waiting for the tide to rise. Sketch a graph or graphs that show how the variable or variables in your story is related. // While the three other groups went out to their respective places, a fourth group decided that they wanted to take a bus tour of the rest of Charleston, South Carolina. Tough for the first half-hour the places they covered didn't take very much time to get to soon it was about lunch time and traffic began to pick up. They waited twenty minutes in one line before they saw two more places and decided to go back. On their way back they took a short cut and reduced the time that they would normally take returning in only fifteen minutes. ** Follow Up 4.1 ** // The following graphs show the relationship between the time and distance traveled by a cyclist. // // 1a. Describe the relationship shown in this graph. Make up a story about the cyclist that could be modeled by the graph. // Anthony decided that he hadn't been biking for a while and decided to start off slowly as a warm-up, but after about three minutes he began to pick up the face after speeding up for a few minutes he decided to stay at that pace because he found himself getting tired. The last five minutes before he finished he decided to test himself and go as fast as he could for the last leg of his journey. // 1b. Over what interval in the graph is the cyclist traveling the fastest? Explain how you know. // The last part of his journey, because that is at which point of the graph that the line is steepest (goes up the most quickly in the shortest area.) // 2a. Describe the relationship shown in this graph. Make up a story about the cyclist that could be modeled by the graph. // Anthony decided to go quickly for the first part of his journey but quickly tired out and went at a steady pace for a next while until he caught his breath. After resting her sped up again finishing his journey not quite as quickly as he started but satisfactorily. // 2b. Over what interval in the graph is the cyclist traveling the fastest? Explain how you know. // The first part of the graph, because that is where the line is the steepest. // 3a. Describe the relationship shown in this graph. Make up a story about the cyclist that could be modeled by the graph. // Anthony sped up at a regular pace but then decided to take a short cut to get to his destination quicker. But he forgot that it was about lunch time and got stuck in traffic for a good fifteen minutes before he started moving again, and ended up being late for his appointment.
 * Big Idea: ** Many real world ideas can be modeled and represented using mathematics.
 * Essential Questions: ** How can I model a non-linear relationship.