0 0 0 1 .1 .2 2 .2 .4 3 .3 .6 4 .4 .6 5 .5 .6 6 .6 .6 7 .7 .6 8 .8 .6 9 .9 .6 10 1 .6 11 1.1 .6 12 1.2 .6 13 1.3 .6 14 1.4 .6 15 1.5 .6 16 1.6 .9 17 1.7 1.2 18 1.8 1.5 19 1.9 1.7 20 2.0 1.85 21 2.0 1.95 22 2.0 2.0 23 2.0 2.0 24 2.0 2.0 0 0 1 .2 2 .4 3 .6 4 .6 5 .6 7 .6 8 .6 9 .6 10 .6 11 .6 12 .6 13 .6 14 .6 15 .6 16 .9 17 1.2 18 1.5 19 1.7 20 1.85 21 1.92 22 2.0 23 2.0 24 2.0 25 2.0
Activity 3: Interpreting Graphs
Focus for this activity
In this activity we are going to explore the relationship between graphs and stories.

First is a graph of a different kind of train trip, which you will answer questions about and then create a variation on.

Next is a graph that shows a race, which you will answer questions about and then tell a story of.

Last is an optional graph that you can invent a story about.


Reading another graph
A graph showing the position of a train on another trip is shown to the right. Station A is at position 1, Station B is at position 2, Station C is at position 2.5 Answer the following questions about the trip:












What was the position of the train at time = 3 seconds? What was the postion of the train at time = 5 seconds?
Was the train going faster or slower at 5 seconds compared to at 3 seconds?
Sketch what the graph would look like if the train went twice as fast.


-0.03797468 0.9809524 0.0 1.0 0.03797468 1.0 0.07594936 1.0 0.11392405 1.0 0.15189873 1.0 0.2278481 1.0 0.30379745 1.0 0.34177214 1.0 0.37974682 1.0 0.4177215 1.0 0.4556962 1.0 0.5316456 1.0 0.56962025 1.0 0.6075949 1.0 0.6455696 1.0 0.6835443 1.0 0.721519 1.0 0.75949365 1.0095239 0.79746836 1.0095239 0.87341774 1.0095239 0.98734176 1.0095239 1.0253165 1.0095239 1.1772152 1.0 1.2911392 1.0 1.4810127 0.9904762 1.556962 0.9904762 1.5949367 0.9904762 1.6329114 0.9904762 1.7088608 0.9904762 1.7848102 0.9904762 1.8227848 1.0 1.8607595 1.0 1.8987342 1.0285715 2.2405064 1.1904762 2.3544304 1.2380953 2.886076 1.4761904 3.379747 1.6952381 3.455696 1.7333333 3.5316455 1.7619047 3.5696204 1.7809523 3.6835444 1.8380952 3.835443 1.9047619 4.21519 2.0095239 4.253165 2.047619 4.291139 2.047619 4.329114 2.047619 4.518987 2.0666666 4.556962 2.0666666 4.746835 2.0761905 4.78481 2.0761905 4.898734 2.0761905 5.012658 2.0952382 5.088608 2.0952382 5.126582 2.1047618 5.240506 2.1047618 5.35443 2.1142857 5.392405 2.1238096 5.468354 2.1333334 5.506329 2.142857 5.5822783 2.1619048 5.658228 2.1714287 5.734177 2.1714287 5.772152 2.1714287 5.886076 2.1809523 5.924051 2.1904762 6.0 2.2 6.037975 2.209524 6.075949 2.2190475 6.113924 2.2190475 6.151899 2.2285714 6.189873 2.2285714 6.265823 2.2380953 6.341772 2.2380953 6.4177217 2.2476192 6.493671 2.2666667 6.531646 2.2666667 6.607595 2.2761905 6.721519 2.295238 6.759494 2.304762 6.835443 2.304762 6.873418 2.3142858 6.949367 2.3238096 6.987342 2.3333333 7.025316 2.3333333 7.063291 2.3428571 7.1392407 2.3428571 7.177215 2.352381 7.21519 2.352381 7.253165 2.3619049 7.291139 2.3714285 7.367089 2.3809524 7.405063 2.3904762 7.443038 2.3904762 7.481013 2.4 7.518987 2.4095237 7.670886 2.4285715 7.708861 2.4380953 7.746835 2.4380953 7.822785 2.447619 7.898734 2.4571428 7.936709 2.4571428 7.974684 2.4666667 8.012658 2.495238 8.35443 2.4857142 8.848102 2.504762 9.113924 2.5142858 9.227848 2.5142858 9.379746 2.5142858 9.455696 2.5142858 9.6075945 2.5238094 9.7215185 2.5238094 9.873418 2.5238094 9.987342 2.5238094 10.253164 2.5238094 10.670886 2.5142858 10.936708 2.5142858 12.037974 2.495238 12.07595 2.495238 12.151898 2.495238 12.227848 2.495238 12.265822 2.495238 12.341772 2.495238 12.417722 2.495238 12.531646 2.495238 12.56962 2.495238 12.683544 2.495238 12.759494 2.495238 12.987342 2.495238 13.025316 2.495238 13.556962 2.495238 13.898734 2.495238 14.012658 2.495238 14.088608 2.495238 14.2784815 2.495238 14.3924055 2.495238 14.886076 2.5238094
A race between T and H
At right is a graph that tells a story. Answer the following questions about it. T's graph











Who won the race, T or H? 1. T 2. H How do you know? How long is the race in miles? How long did the winner take to run it? Did T pass H? If so, at what time did that occur? Who moved the quickest for a short period of time? How do you know?





What was T’s fastest speed? (in miles / minute) What was T’s slowest speed? What was H’s fastest speed? (in miles / minute) What was H’s slowest speed?





What is the story of the race?

13.608562 -0.20634921
Creating a story
A graph showing the position of a train on another trip is shown to the right. The distances are in miles, and the time is in minutes. Station A is at position 0, Station B is at position 10, Station C is at position 25. Create a story about a train trip that matches the graph. Feel free to invent characters and actions. What might have happened, for example, after 35 minutes?














-2.4630542 -0.0 -2.2167487 0.3809524 -1.4778326 0.50793654 -1.2315271 0.50793654 -0.7389163 0.50793654 -0.24630542 -0.0 0.49261084 -0.0 0.7389163 -0.12698413 0.9852217 -0.12698413 1.2315271 -0.12698413 1.4778326 -0.12698413 1.7241379 -0.12698413 1.9704434 -0.12698413 6.1576357 0.8888889 12.807881 5.3333335 13.054187 5.714286 13.300492 5.84127 13.546798 6.2222223 13.793103 6.6031747 14.039409 6.984127 14.285714 7.111111 14.53202 7.2380953 14.778325 7.3650794 15.024631 7.3650794 15.270936 7.4920635 15.5172415 7.873016 16.009851 8.0 16.256157 8.126985 16.502462 8.380953 16.748768 8.5079365 16.995073 8.634921 17.241379 8.761905 17.487684 8.761905 17.73399 8.888889 17.980295 9.142858 18.2266 9.269841 18.472906 9.396826 18.719212 9.523809 18.965517 9.650794 19.211823 9.777778 19.458128 9.904762 19.704433 9.904762 19.950739 10.031746 20.197044 10.031746 20.689655 10.031746 20.93596 10.031746 21.182266 10.031746 21.674877 10.031746 21.921183 10.031746 22.167488 10.031746 22.413794 10.031746 22.660099 10.031746 22.906404 10.031746 23.15271 10.1587305 23.399015 10.1587305 23.64532 10.1587305 23.891626 10.1587305 24.137932 10.1587305 24.384237 10.285714 24.630543 10.285714 24.876848 10.412699 25.123152 10.412699 25.369457 10.539682 26.108374 10.666667 26.35468 10.920635 27.093596 11.174603 27.832512 11.555555 28.325123 11.809524 29.06404 12.31746 29.55665 12.571428 29.802956 12.952381 30.049261 13.079365 30.295567 13.587301 30.541872 13.714286 30.788177 13.8412695 31.034483 13.968254 31.280788 13.968254 31.7734 14.095238 32.019703 14.222222 32.26601 14.222222 32.512314 14.222222 32.75862 14.349206 33.004925 14.476191 33.251232 14.476191 33.497536 14.476191 33.743843 14.476191 33.990147 14.476191 34.236454 14.476191 34.482758 14.476191 34.729065 14.349206 34.97537 14.222222 35.46798 14.095238 35.714287 13.968254 35.96059 13.968254 36.206898 13.968254 36.4532 13.8412695 36.69951 13.8412695 36.945812 13.8412695 37.19212 13.714286 37.438423 13.587301 37.68473 13.460318 37.931034 13.333333 38.17734 13.079365 38.423645 12.952381 38.669952 12.571428 38.916256 12.571428 39.162563 12.190476 39.408867 12.063492 39.655174 11.936508 39.901478 11.809524 40.14778 11.68254 40.39409 11.555555 40.640392 11.428572 40.8867 11.428572 41.133003 11.428572 41.37931 11.301587 41.625614 11.174603 41.87192 10.920635 42.118225 10.793651 42.364532 10.666667 42.610836 10.539682 42.857143 10.412699 43.103447 10.285714 43.349754 10.1587305 43.596058 10.1587305 43.842365 9.904762 44.334976 9.650794 44.58128 9.523809 44.827587 9.396826 45.07389 9.269841 45.320198 8.634921 45.5665 7.873016 45.81281 7.7460318 46.059113 7.4920635 46.30542 7.4920635 46.551723 7.3650794 46.79803 7.2380953 47.044334 7.111111 47.29064 6.984127 47.536945 6.857143 47.783253 6.730159 48.029556 6.6031747 48.275864 6.3492064 48.522167 6.2222223 48.768475 6.2222223 49.01478 6.095238 49.261086 5.968254 49.50739 5.968254 49.753696 5.968254 50.0 5.2063494 50.246304 4.952381 50.49261 4.825397 50.738914 4.4444447 50.98522 4.1904764 51.477833 3.8095238 52.463055 3.5555556 52.70936 3.4285715 52.955666 3.4285715 53.69458 3.3015873 54.18719 3.047619 54.4335 2.920635 54.679802 2.7936509 54.92611 2.6666667 58.866997 1.2698413 59.1133 1.2698413 60.344826 1.0158731 62.561577 0.25396827 62.80788 0.25396827 63.30049 0.25396827 63.793102 0.25396827 64.28571 0.25396827 64.53202 0.25396827 64.77833 0.25396827 65.02463 0.25396827 65.270935 0.25396827 65.51724 0.25396827 65.76355 0.3809524 66.00985 0.50793654 66.25616 0.50793654 66.74877 0.7619048 66.99507 0.8888889 67.24138 1.0158731 67.487686 1.0158731 67.73399 1.2698413 68.47291 1.6507937 68.719215 1.9047619 69.21182 2.4126985 69.70444 3.4285715 70.197044 3.6825397 70.93596 4.571429 71.67487 6.4761906 71.92118 6.857143 72.16749 7.6190476 72.660095 8.5079365 73.64532 9.650794 74.63054 10.666667 75.36946 11.809524 76.60098 13.8412695 77.586205 14.857142 78.57143 15.873015 79.06404 16.126984 79.30174 16.977491 79.551125 17.10611 80.299255 17.749197 80.798004 18.135048 81.79551 18.906752 83.0424 19.807074 83.79053 20.321543 84.289276 20.707396 85.53616 22.122187 85.78554 22.379421 88.91626 24.761906 89.40887 24.88889 89.90148 25.015873 90.39409 25.142857 90.640396 25.269842 90.886696 25.269842 91.133 25.269842 91.37931 25.269842 91.62562 25.269842 91.87192 25.269842 92.36453 25.269842 92.85714 25.269842 94.33498 25.269842 95.07389 25.269842 95.812805 25.269842 96.55173 25.269842 97.53695 25.269842 99.01478 25.269842 99.261086 25.269842 99.75369 25.142857
END OF ACTIVITY
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