# Hoisting the Flag 2

Alignments to Content Standards: F-IF.B.4

Every morning at summer camp, one of the campers has to hoist the camp flag to the top of the flagpole.

For each graph below, describe the action of the flag raiser that might have led to this graph that shows the height of the flag as a function of time.

## IM Commentary

In this task, students are given a scenario and different graphs that could describe the relationship of the quantities in the situation, the height of a flag as a function of time. The scenario is open ended enough, so that most of the graphs could fit the situation. Therefore, the task is much richer than simply a matching problem. Students have to realize how different features of the graph connect to the physical situation.

Attached to this task are student work samples collected from a test as well as a summary from the teacher.

## Solutions

Solution: 1

1. In this scenario, the flag is raised at a constant rate, and then the flag raiser pauses. The flag is raised at a constant rate again, and then the flag raiser pauses. The flag is raised at a constant rate again, and then the flag raiser stops, as the flag is now at the top of the pole.
2. Here the flag is raised in spurts, quickly and then more slowly, and then the flag goes down a bit. Then another spurt – quickly and then more slowly, and then the flag goes down bit. Then the flag raiser gives one last spurt to get it to the top.
3. In this scenario, the flag is raised at a constant rate and left for a while (perhaps throughout a day), lowered at a constant rate and left for a while (perhaps for a night), raised again and left, lowered again and left, and then raised to half-mast and left.

Solution: Student solution samples and teacher summary

Teacher summary:

These students had not done the first raising flag task. We used the second task on their summative assessment. Many students were able to describe the motion of the flag in terms of raising or lowering - the context obviously made sense to them. More than half of them talked about how fast and how slow the flag was being raised, even through we didn't have a huge focus on rates of change during the unit - our focus was more on increasing and decreasing, constant,  etc. A lot told a story to go with the graph, which was interesting to me. They had been asked to create stories during the unit, but I didn't predict that would carry over to the summative task. For example, some named the flag raiser. Some noted why there was a pause in the action (he stopped to answer his phone). Very few put in units for both time and height.

We recognize that is important to decide what information you want to assess, and we wonder whether we should be more clear about what we except them to describe. The directions say "describe the action of the flag raiser that might have led to this graph". Should we be more specific as to indicate that we want them to talk about up, down, fast, slow? If not, and if they only talk about up and down, then do we deduct points for not talking about how fast and how slow?

Kate

Devin started raising the flag, stopped (5 ft), raised it more at the same pace he did the first time, stopped again (10 ft), raised it to the top (15 ft), then he left it on top.

Devin started raising the flag at a rapid pace but slowed down a little before making it fall a little (6 ft) without stopping he lifted it up again, slowed down a little, then dropped it again. Then without stopping he raised it to the top.

Devin raised the flag to the top at a rapid pace, let it wave for a few moments, then dropped it to the ground. He kept it there for 6 seconds then raised it again in 4 seconds, let it wave for 6 seconds at 15 ft, then dropped it to the ground for 2 sec. He waited for 6 sec then raised it 7 ft in 2 sec where it stayed.

Josh

he moved the flag fastly then stopped to grab more rope then he pulled the flag up fast then had to grab more rope then again pulled it up higher then tied the bottom of the rope to the bottom of the pole.

at decent pace he pulled the flag up then he slowed down to get more rope then he pulled on the rope at decent pace and then he again stopped and the flag was almost at the top and he pulled the flag at a slower pace but it was at the top.

the first day he moved the flag all the way to the top in a few seconds then he left it down after school then the next day he put it all the way to the top again in a few seconds, let it down after school then on the third day he only pulled it half way to the top because he was tired.

Laney

The camper went to raised the flag. He raised it a bit then stopped. He raised it a bit more and stopped. Then he raised it the rest of the way to the top.

The camper started raising the flag and stopped for a second and it fell back down a bit. He did this another time.

The camper raised the flag all the way. A little while later he lowered it back down. He did this again and then raised the flag half way.

Jacquelyn

The camper pulls the rope w/ the same force each pull. In between each pull he/she stops for a few seconds before pulling again.

The camper pulls the rope w/ the same force for the first 2 pulls then the force lowers at the last pull. In between each pull he/she lets the flag fall a little before pulling the rope again.

The first 2 times, he/she pulls the flag up all the way to the top, then the last one, they only pull it halfway up. In between each time, he/she stops for a couple seconds before pulling again.

Jason

He was raising it up slowly.

He was raising it up very quickly.

He lowered it very slowly.

Jordan

He raised the flag, took a break, raised it again, took a break, raised it for the last time until it reached the top and then left.

He raised the flag and it fell down a little bit, raised the flag, the flag fell a little. The last time he raised it he had a little more trouble than the first time, and then once he got the flag to the top he left.

He raised the flag all the way up on his first try, it stayed there for just a little bit and then fell all the way down. The next time the same thing happened. The last time he got it half way but eventually fell back down.

Kate

Up, takes a break. Up, stops to answer the phone. Goes again and then stays when its at the top.

Goes up some, then goes down a little. Goes up more, stops to check a text then goes again and puts the pin on it when he’s done.

Goes up all the way, stops, and then brings it down. Then puts it back up then bringing it back down again. Because he forgot something. Then goes halfway and pins it there.

Andrew

The flag raiser heightened the flag at a normal pace got tired rested started again and then finished putting it up.

Brought the flag up and slowly slowed from being tired drop the rope for a second catch it make it go up but started going slow and dropped it again then he started and finished.

Pulled the flag all the way to the top forgot to tie it and then it dropped then he repulled it to the top and forgot to tie it again and it dropped and then made it go up half way because he was tired and tied it off.

Brook

The flag elevated rapidly, stayed at that elevation, elevated again, stayed at that elevation, elevated again, and stayed at that elevation.

The flag elevated rapidly, slowed down, decreased half of the elevation, rapidly elevated, slowed down, decreased half of the elevation rapidly; increased the elevation rapidly, slowed down.

The flag elevated rapidly, stayed at that elevation, decreased elevation rapidly, didn’t move, increased the same elevation as before rapidly, stayed at that elevation, decreased elevation rapidly, didn’t move, increased half of the elevation rapidly, stayed at that elevation.

Grayson

The raiser raised the flag soft and rests then again 1 more time before the flat is at the top of the 30 ft pole.

The raiser fast pace and decreases and the flag drops the flag and repeat 2 more times.

The raiser raises the flag at a constant rate and it stays at a constant rate and it stays at the top and falls and it repeats the same way. The raiser raises the flag to half mass and leaves.