**Here is a sample problem I’m supposed to do for my class:**

You are standing on the edge of the roof of a building. 8.0 m from the base of the building is the wall of a 5.0-m tall garage with a flat roof. You throw a ball with an initial speed of 8.3 m/s at a direction that is 42o above the horizontal. You release the ball 11 m above the base of the building.

**Here is the problem I’ve decided to do instead.**

You are standing on the edge of the roof of a building. 26 m from the base of the building is the wall of a 5.0-m tall garage with a flat roof. You throw a ball with an initial speed of 16.5 m/s at a direction that is 37° above the horizontal. You release the ball 20m above the base of the building.

*Why these changes?*

(1) So, The 16.5 m/s at 37° gets me an initial vertical speed of ~10 m/s, which is convenient for discussing change in velocity when the acceleration due to gravity is ~10 m/s/s. It also gets me an integer horizontal speed of ~13 m/s, which makes it convenient for talking about how far the ball will go each second.

(2) The 26 meters is used because the question of whether the ball get far enough to land on the adjacent roof is easier to think through with resorting to equations. The questions becomes “Does the ball stay in the air for at least 2 seconds (before it drops 15 meters)?” Well, the ball lose it’s 10 m/s up in the first second, and gains back that 10 m/s (going down now) in the next second. So horizontally, the ball has gone the 26m by the time it’s at the same vertical height it started (now going down) leaving time to land further into the adjacent roof.

Now that’s we’ve made sense of what’s happening without equations, we can figure the rest out the way I’m supposed to model the situation (even though reasoning it through is still really easy at this point). We really just need to figure out how much more time it spends in the air (1 seconds here), and then add 13m for ever additional second it gets to go (13 extra meters here)

**What do people think? Is it worth it? Am I doing my students any disservice by trying to give them workable numbers?**

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I don’t think you’re doing them a disservice by trying to give them workable numbers for their first few problems, as long as they get to practice (and be assessed) on problems with uglier numbers. I have students who think they must have done something wrong if they get an answer that isn’t an integer, because all of their previous teachers have made all of their numbers pretty…

The problems they work after I model the sample problem are usually with numbers that are not designed to work out as easily as my examples. I hope to use the easy numbers in order to have a discussion about the concepts, and to reason through the problem (semi)-quantitatively. And since I don’t write assessments, students are pretty much given random numbers.

I really like this idea. It’s sort of like looking inside the procedural “black box” that the traditional approach would take, and really trying to make sense of what is happening –which gets ignored too often, in my opinion. Whether or not your students appreciate this inside look, especially if they don’t see this approach as useful on the rest of the activities that they do, is another issue. I can certainly see a potential for benefit, though, and no cause to think that you might be doing them a disservice.

I too really like this idea. It is a very useful tool in their problem solving toolkit to be able to think/estimate their way to a realistic solution and then apply the equations to find the exact answer.