# Granny s Balloon Trip

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1 Granny s Balloon Trip This problem gives you the chance to: represent data using tables and graphs On her eightieth birthday, Sarah s granny went for a trip in a hot air balloon. This table shows the schedule of the trip. Time 2:30 3:00 3:30 4:00 4:30 5:00 5:30 6:00 Height above the ground in yards Finish labeling the axes and draw a line graph to show the balloon trip. Height above the ground in yards :30 3:00 Time Copyright 2007 by Mathematics Assessment Page 76 Granny s Balloon Trip Test 5

2 2. For about how long did the balloon stay above 250 yards? 3. At about what time do you think the balloon rose to 400 yards? Explain how you figured this out. 4. At about what height do you think the balloon was at 5:50? Explain how you figured this out. Copyright 2007 by Mathematics Assessment Page 77 Granny s Balloon Trip Test 5 8

3 Task 4: Granny s Balloon Trip Rubric The core elements of performance required by this task are: represent data using tables and graphs Based on these, credit for specific aspects of performance should be assigned as follows 1. Completes both axes correctly Completes the line graph correctly Partial credit. One point for a partly correct graph such as: Correct points marked but line not drawn. or Line drawn but one or two incorrect points marked. points 1 2ft (1) section points 3 2. Gives correct answer: One and a half hours 1ft 1 3. Gives correct answer: accept 4:05 through 4:15 1ft Gives a correct explanation such as: If you follow the line for 400 yards on the vertical axis and look down the horizontal axis it is about half way between 4:00. and 4: Gives correct answer: accept 5 through 35 yards above the ground Gives a correct explanation such as: It was less than 50 yards and more than 0 yards 1ft 1ft 1ft 2 2 Total Points 8 Copyright 2007 by Mathematics Assessment Page 78 Granny s Balloon Trip Test 5

6 Looking at Student Work on Granny s Balloon Student A is able to label the axes in appropriate, equal size intervals matching the scale already being used. The student shows visually how he used estimation to answer questions 3 and 4. Notice that the student labeled ten-minute intervals to find the 5:50 and then work backwards to find the correct number of yards. Student A 5th grade

7 Student A, part 2 Student B has 7 out of the 8 points on the task. The student has difficulty thinking about the time the balloon is above 250 yds. The student only considers the time the balloon is still rising, forgetting that part of the descent is also above 250 yd. What question could you pose to the class to push their thinking about this issue? What other questions could you ask to have students think about a range of values on the graph? Student B 5th grade

8 Estimating values between grid marks was challenging for many students. Student C has a reasonable strategy for estimating the distance in part 3 (although the ten minutes should have been added to 4:00). However this same strategy does not work for finding the value in part 4. Can you explain why it no longer works? Student C Why is dividing by 2 incorrect for finding the distance for 5:50 Is there way to divide 100 to get a good estimate? Look at the work of Student D. 5th grade

9 While Student E s estimate for part 3 is within the allowable range, what is the student not understanding about proportional thinking? Student E Student F is able to label the axes in equal intervals and graph the data points. The student does not show the line for a line graph, which may have made it more difficult to estimate values for other parts of the graph. Student F 5th grade

10 Student F, part 2 Student G makes a bar graph instead of line graph. The student seems to want the vertical scale to be between lines, which would imply that there aren t values in between ( the whole row would be 150 or 300). The same is true for the horizontal scale. Something is either at 3:30 or 4:00, but there are no values in between. It s not possible with this graph to estimate a height for the balloon at 3:45. Student G 5th grade

11 Some students think all line graphs are linear. Student H scales the vertical axes in equal intervals, but doesn t use the data in the table to plot the graph. The student does seem to look at the line in attempting to answer parts 3 and 4. Why do you think a student might have this type of misconception about graphing? What questions might you pose to the class? Student H 5th grade

12 Student I also makes a linear graph. However this student does not divide the horizontal scale into equal intervals or even ascending values. Notice the student skips from 3:00 to 4:30 on the horizontal axis. Both students just end the graph at the highest value 500. In contrast to Student H, Student J does not seem to use either the table or the graph in answering questions about the trip. What kinds of experiences does this student need? What might be logical next steps? Student I 5th grade

13 Understanding how to scale the axes was quite challenging for many students. While Student K has values at unequal intervals on the vertical axis and numbers that return to 0, the student ignores the top of the scale to at least graph the points appropriately for the incorrect scale. Student L has unequal intervals and 250 is listed twice. Student M has listed the data values instead of providing intervals on the vertical axis. Student N has 2 zeroes on the vertical axis and skips from 3:00 to 5:30 on the horizontal axis. The line on the graph does not match the action of the data table. Student K 5th grade

14 Student L Student M 5th grade

16 5 th Grade Task 4 Granny s Balloon Trip Student Task Core Idea 5 Data Analysis Represent data using tables and graphs. Interpret information on a line graph and estimate values between grid lines. Display, analyze, compare and interpret different data sets. Organize and display data in appropriate graphs and representations (e.g., histograms and line graphs). Based on teacher observations, this is what fifth graders knew and were able to do: Label the axes Estimate the time when the balloon reached 400 ft. Graph points on a graph from a data table Areas of difficulty for fifth graders: Making a scale with equal intervals Determining when to use a point, line, or bar graph. Scaling between intervals to find the distance at 5:50. Thinking about a range of values, finding how long the balloon was above 250 yards. 5th grade

17 The maximum score available for this task is 8 points. The minimum score for a level 3 response, meeting standards, is 4 points. Most students, 76%, were able to label the axes in equal intervals (students with a score of 1 or 3 were able to do this, but not students with a score of 2). Many students, 76%, could estimate a reasonable time for the balloon reaching a height of 400 yards by using their graph or the table. More than half the students, 54%, could label the axes, graph most of the points, and make an estimate about time for reaching 400 yd. Some students, 20%, could make the graph and estimate the time to reach 400 yd. and the height of the balloon at 5:50. Almost 9% of the students could meet all the demands of the task, including finding how long in total the balloon was above 250 yd. 13% of the students scored no points on the task. 83% of the students with this score attempted the task. 5th grade

19 Implications for Instruction Students at this grade level should have many opportunities to make their own graphs. The thinking involved in planning the scale, labeling the axes, and setting up the graph is quite different from that required to just read information off a graph. Students at this grade level should be comfortable with a variety of graphs besides just bar graphs, including line graphs, pie graphs, and histograms. Students should start to be able to reason about which one to choose for different situations or why a particular type of graph would be inappropriate for the situation. They need to learn about attributes of graphs. Students should also be able to think about scale in increments other than one; e.g. like 10, 50, 100, 30, etc. They should also realize the difference between the scale, marking off equal size groups, and the data points, the information graphed or plotted in the interior of the grid. Many students don t realize that the scale should increase in size. The action of increasing and decreasing takes place with the data points. Understanding that the scale is a framework and the plotted points tell the action of the information is difficult for students. Some students want to draw lines going back to the origin if something goes back to zero. There are so many things to consider when making a time and distance graph. For example, take some information about a walk to school or a bicycle trip. Have students graph the information as distance from home. Then take the same information and graph it as total distance traveled. Have them discuss how the same information can look so different. (See MARS task Sixth Grade- Bike Ride) Ideas for Action Research 5th grade

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