course Mth 151 }Ũ|ߖܽhxʳ assignment #006 006. Sequences and Patterns Liberal Arts Mathematics I 02-15-2009 ﳩRԽEgx assignment #007 007. Triangular, Square, Pentagonal Numbers Liberal Arts Mathematics I 02-15-2009
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11:13:27 `q001. Note that there are 7 questions in this assignment. Sketch three points A, B and C forming an equilateral triangle on a piece of paper, with point A at the lower left-hand corner, point B at the lower right-hand corner and point C at the top. Sketch the segments AB and AC. Now double the lengths of AB and AC, and place a point at each of the endpoints of these segments. Connect these new endpoints to form a new equilateral triangle. Two sides of this triangle will have three points marked while the new side will only have its two endpoints marked. Fix that by marking that middle point, so all three sides of your new triangle are marked the same. How many marked points were there in the original triangle, and how many are there in the new triangle?
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RESPONSE --> 3 in the first and 6 in the new triangle confidence assessment: 1
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11:15:16 The original triangle had the three points A, B and C. When you extended the two sides you marked the new endpoints, then you marked the point in the middle of the third side. So you've got 6 points marked. Click on 'Next Picture' to see the construction. The original points A, B and C are shown in red. The line segments from A to B and from A to C have been extended in green and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and an equally spaced point has been constructed at the midpoint of that side. Your figure should contain the three original points, plus the three points added when the new side was completed.
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RESPONSE --> ok self critique assessment: 3
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11:18:17 `q002. Extend the two sides that meet at A by distances equal to the distance original lengths AC and AB and mark the endpoints of the newly extended segments. Each of the newly extended sides will have 4 marked points. Now connect the new endpoints to form a new right triangle. Mark points along the new side at the same intervals that occur on the other two sides. How many marked points are on your new triangle, and how many in the whole figure?
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RESPONSE --> three new points in old triangle and 9 in the whole figure confidence assessment: 2
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11:19:48 You added the two new endpoints when you extended the sides. You then should have marked two new points on the new third side, so that each side contains 4 points including its endpoints. Your figure will now contain 10 marked points.
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RESPONSE --> so I was to extend it further to the right and I extended it to the left so my figure ended up being one point short self critique assessment: 3
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11:21:43 `q003. Continue the process for another step-extend each side by a distance equal to the original point-to-point distance. How many points do you have in the new triangle?
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RESPONSE --> 14 points confidence assessment: 3
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11:23:45 You will add an endpoint to each newly extended side, so each of the new sides will contain 5 points. You will then have to add 3 equally spaced points to the new side, giving you a total of 13 points on the new triangle. In addition there are two marked points inside the triangle, for a total of 15 points. Click on 'Next Picture' to see the construction. The line segments along two sides of the triangle have again been extended and points marked at the ends of these segments. The new endpoints have been connected to form the third side of a larger triangle, and equally spaced points have been constructed along that side.
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RESPONSE --> As I move further away from the 1 point(side A) I will add 1 point extra, so it was a 5 point line instead of a 4 point line self critique assessment: 3
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11:24:23 `q004. Continue the process for one more step. How many points do you have in the new triangle?
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RESPONSE --> 21 points confidence assessment: 3
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11:25:00 You will add an endpoint to each newly extended side, so each of the new sides will contain 6 points. You will then have to add 4 equally spaced points to the new side, giving you a total of 15 points on the new triangle. There are also 5 marked points inside the triangle for a total of 21 marked points.
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RESPONSE --> ok self critique assessment: 3
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11:29:30 `q005. The sequence of marked points is 3, 6, 10, 15, 21. What do expect will be the next number in this sequence?
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RESPONSE --> becuase the numbers are going up in sequence 3-6=3, 10-6=4, 15-10=5, 21-15=6 and this ssequence its going up by 1 the next number in the sequence will be 28 (21+7=28) confidence assessment: 3
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11:29:55 The differences between these numbers are 3, 4, 5, 6. The next difference, according to this pattern, should be 7, which would make the next number 28.
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RESPONSE --> ok, got it right self critique assessment: 3
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11:32:43 `q006. How can you tell, in terms of the process you used to construct these triangles, that the next number should be 7 greater?
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RESPONSE --> I drew lines in between the numbers to come up with the sequence in between and then I drew yet another line until a constant value was found, after that I worked upwards to find 7 and added to 21 confidence assessment: 3
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11:34:01 When you extend the triangle again, you will add two new endpoints and each side will now have 7 points. The 7 points on the new triangle will be all of the new points.
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RESPONSE --> I used the method shown on the video not the triangle, still came up with the correct answer self critique assessment: 3
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11:35:19 `q007. How do you know this sequence will continue in this manner?
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RESPONSE --> becuase it already has a set sequence confidence assessment: 3
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11:35:48 Each time you extend the triangle, each side increases by 1. All the new marked points are on the new side, so the total number of marked points will increase by 1 more than with the previous extension.
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RESPONSE --> ok self critique assessment: 3
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