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Activity 1:  Vector Treasure Hunt 

The first questions students respond to is, "Was Bluebeard just lucky or would a different order of the vector arrows lead to the same spot?" 

Teachers will not have time to read each student's response.  Rather, it would be better to ask a two part question: 
Was Bluebeard just lucky or would a different order of vector arrows lead to the same spot?

            ?  Just Lucky

?  A different order of vectors would lead him to a different spot

?  A different order of these vectors would lead him to the same spot each time

Explain why you chose the answer above.
 
 

After finding the treasure the third time, students should use the numbers given for each vector to determine that the total displacement to the right was 4 units and the total displacement up was three units.   

Ask students to count the number of "blocks" Bluebeard traveled to the right (east?) each time. 

Students enter the number in a box. 

Ask students to count the number of "blocks" Bluebeard traveled up (north?) each time. 

            Students enter the number in a box. 

Students should refer to the number assigned to each vector that they saw on the third path followed and compare these numbers to the ones they just entered.  Regardless of which path Bluebeard traveled, he always traveled 4 units to the right and 3 units up. 
 

After Bluebeard walks through a new set of displacement vectors (different starting location with different vectors) one time, students should be asked if a different order of the four vectors would lead to a different location.  Students should select an answer, as in the example above and explain the reasoning.  Teachers should be able to quickly get feedback from the yes/no part of the question.

?  No, a different order of vectors would lead him to a different spot

?  Yes, a different order of these vectors would lead him to the same spot each time

After sending Bluebeard along three different paths to end up at the same location, students are asked (question #7), "The two sums displayed below the map are the same. Why is this?" 

I would also want my students to answer, "What do the 3 and 0 represent?" 

Once students are creating their own treasure maps, students are asked in question 8, "Will a negative X or Y component be necessary to find the treasure? Explain your reasoning." 

Again, even though students will explain their answer, it would benefit the teacher to see immediately if students understand what negative displacements are by submitting part of the answer in a box (checking a box or something like it). 

A negative x component will be necessary

A negative x component will not be necessary

A negative y component will be necessary.

A negative y component will not be necessary. 

Explain.   

I'd expect most student to answer the above questions quickly and correctly, but if students do not respond correctly, then that is information the teacher can use right away to correct a problem. 

Question #9 reads, "Do you think there is more than one path that uses 2 sets of components to reach the same treasure? Explain your reasoning." 

Instead, I'd ask: 

Do you think there is more than one path that uses 2 sets of components to reach the same treasure?

????            No, there can only be way to get to the treasure using 2 vectors.

????            Yes, there are two different paths Bluebeard could follow to get to the treasure.  We have already seen that it does not matter which order you follow, one will end up at the same destination each way.

????            Yes, there are many different paths using 2 sets of components to reach the same treasure. 

When students must make up three different displacement to locate the treasure, I'd like to know how many attempts each student had. 
Another possible component: 

Are distance and displacement the same thing? 

Have Bluebeard follow 5 paths to get to a treasure; avoid angles (diagonals) for this part.  For instance (5,0), (0,4), (-8,0), (0,-2), and (3,0).  This will land Bluebeard two units above where he started with no horizontal displacement.  Students should be asked to calculate the total distance Bluebeard had to walk to find the treasure (22 units) and what his overall displacement is (2 units, up).   

Students are asked a question similar to this in the summary, but not in a single activity. 
 
 

Overall, this is a great introduction to vectors.   
 
 
 
Hanging with Friends 

I think it is too soon to ask about velocity in step 2 of activity 1.  Students have just completed the vector treasure hunt, which deals only with distance and displacement.  Activity one should build upon and review the work completed in Vector Treasure Hunt, focusing mostly on displacement.  It seems disjointed to me that we ask students immediately about velocity then have the students answer questions about displacement. 

In step 4, students are told to complete table A by entering the distance and direction each person needs to travel to reach the cinema.  First, I could not easily find table A.  Second, this data needs to be entered in a way that immediately shows the teacher who can successfully complete this task, which is a recap of the Vector Treasure Hunt.