Performance+Task+Assignment+2

Click here to see Assignment #1, which includes the Objective, Essential Questions, and Standards.

//Problem:// Chris likes to go hiking. He doesn't have a very good sense of direction though, and can only remember how far he went and what directions he turned. In order to find his way back, he leaves a trail of breadcrumbs behind. After walking for a while, Chris trips over a branch and winds up in a snake pit. Chris hates snakes, but knows that if he stays still, they won't eat him just yet. He radios back to his friend Tina and asks her to rescue him. She asks him where he is, but he can only tell her how he traveled. For each of the following scenarios, your job is to tell Tina what the shortest distance would be to reach Chris at the bottom of his snake pit.

Here is what he said:

"I walked for a mile north, then turned right and walked another 2 miles. After that, I turned left and walked another 2 miles before turning right again and walking for a mile. If you follow the breadcrumbs, you'll find me."
 * Scenario 1:**

"I walked for a mile north, then turned right and walked another 2 miles. After that, I turned right again, and walked for 2 miles before turning right one more time and walking for a mile."
 * Scenario 2:**

"I walked east for a mile, then turned 30 degrees to my left to walk for 2 miles. After that, I turned another 30 degrees to my left to walk for another 2 miles before turning yet another 30 degrees to my left to walk for a mile."
 * Scenario 3:**

"I walked north for a mile, then turned 30 degrees to my left to walk for 2 miles. After that, I turned 60 degrees to my right to walk for another 2 miles before turning another 30 degrees to my right to walk for a mile."
 * Scenario 4:**

Assume that a turn is 90 degrees if no angle is given. Now, Tina knows that breadcrumbs left out in the woods will be eaten long before she gets there, so she needs to come up with a way to find him from that information. She can either follow his footsteps, knowing how far he walked and in which directions, or she can ignore him and swing through the trees to go straight to where he ended up.


 * For each scenario, answer the following questions:**
 * 1) If she follows his footsteps, how far will Tina have to travel to reach Chris?
 * 2) If she ignores his footsteps and goes directly to him by swinging from the trees, how far will Tina have to travel to reach Chris?
 * 3) What is the direction of Tina's straight-line trip? Give your answer as an angle relative to a direction (i.e. 30 degrees north of east). Check your answer by drawing the path traveled with a ruler and protractor, then measure the distance.
 * 4) Assuming both methods move at the same speed, would it ever be faster to follow the turn-by-turn directions? What conclusions can you then draw about traveling?


 * //Materials Required://**
 * Protractor
 * Ruler

__**4:**__
 * //Grading Rubric://**
 * Student draws an accurate representation of each path traveled.
 * Student recognizes that each path is the same distance when traveled by foot.
 * Student recognizes that each path can be broken up into horizontal and vertical components which can be added individually and is able to do so.
 * In scenario 2, student recognizes that components in opposite directions must be subtracted instead of added.
 * In scenarios 3 and 4, student recognizes that each angle is relative to the last. He/she then either uses trigonometry to determine components at each step, or finds the absolute angles relative to the horizontal.


 * __3:__**
 * Student draws an accurate representation of each path traveled.
 * Student recognizes that each path is the same distance when traveled by foot.
 * Student recognizes that each path can be broken up into horizontal and vertical components which can be added individually and is able to do so.
 * In scenario 2, student recognizes that components in opposite directions must be subtracted instead of added.
 * Student does not realize that each angle is relative to the last in scenarios 3 and 4. He/she either assumes they are all absolute or is not able to find the correct component lengths.

__**2:**__
 * Student draws an accurate representation of each path traveled.
 * Student recognizes that each path is the same distance when traveled by foot.
 * Student recognizes that each path can be broken up into horizontal and vertical components which can be added individually and is able to do so.
 * In scenario 2, student is unable to recognize that components in opposite directions must be subtracted instead of added.
 * Student does not realize that each angle is relative to the last in scenarios 3 and 4. He/she either assumes they are all absolute or is not able to find the correct component lengths.


 * __1:__**
 * Student draws an accurate representation of each path traveled.
 * Student fails to recognize that each path is the same distance when traveled by foot.
 * Student fails to recognize that each path can be broken up into horizontal and vertical components which can be added individually or is able to do so.
 * In scenario 2, student is unable to recognize that components in opposite directions must be subtracted instead of added.
 * Student does not realize that each angle is relative to the last in scenarios 3 and 4. He/she either assumes they are all absolute or is not able to find the correct component lengths.


 * __0:__**
 * Student provides an answer which is not based on any mathematical measurements or fails to provide any answer at all.