Mental Math Application: Archery, believe it or not

Confession: I drank too much coffee around 8:30 pm or so and my brain is going 90 to nothin’. So this isn’t like a “profound blog post” or anything, just a “you might be able to work this in somehow (or maybe not) but if you do, holla and let me know how it goes”.


You should be. You’re reading MY blog and you know how my brain works (or doesn’t work – I know you’re thinking it, I’m sayin’ it). Basically, I know what I MEAN, but it might not come out of my brain that way. But if I don’t blog it NOW, I’ll forget later and then I won’t do it at all and…. Anyway.

Here we go:

Archery in a nutshell = shoot 5 arrows at the target. Quickly calculate your score, remove your arrows.

Lemme show you what the target looks like with scoring points:

So, if you’re shooting 5 arrows, the highest you can score in one round is 50 points.

Let’s say Billy Bob Joe Mack (BBJM, from now on) shoots 5 arrows and goes to the target line to score. He may see something like this:

You can see that BBJM, has two 9 point shots, a 7 point shot, a 6 point shot, and the last one (far right) is also technically a 6 point shot (because it hit the border, so you take the higher one). Figuring out what each arrow scored isn’t the issue – IT’S THE SUM (yes, that’s in all caps, if you don’t like it, STOP READING MY BLOG) that takes forever during practice. Students try to take their phones to the target line to use as calculators. I’m like, “No, sweetie. Your coach is also a math teacher. You’re gonna need to do this in your head quickly.” Another reason: at some tournaments, they make students put their phones in a secure location so they don’t accidentally get shot while texting (because they didn’t realize they walked right into the live range).

So BBJM has 18 + 7 + 12, so here’s where you can show students where commutative property is beneficial by mentally adding 18 + 12 + 7 to get 37. Or your students might think a quicker way to calculate this round would be to use negatives. So instead of 9 + 9 + 7 + 6 + 6, it could be thought of as (-1) + (-1) + (-3) + (-4) + (-4) because of the loss from the bullseye. Therefore it’s -13 + 50 or 37. You could also get them to calculate their percent score (out of 50). There are several extensions to this, and you could even do some more advanced questions: What percent of the circle is yellow? Blue? Red? Concentric circles are pretty freakin’ cool. 🙂

Anyway, I’m getting off track (as usual).

When BBJM competes at a meet or tournament, he shoots 6 total rounds: three at 10 meters and three at 15 meters. So you could ask your students to figure out what the total possible score would be for BBJM (and it is, of course, 300).

So each time BBJM shoots and scores, he must fill out an official scoring card. His card at a local meet looks like this:

Problem: most schools don’t have a scanner yet. Coaches have to score them all quickly by hand. The way I score and the way Coach Birdbrain scores may be completely different but, because it works for us individually, we can score at approximately the same rate*. So you might give your students a sample score card in groups and ask them to come up with strategies to quickly calculate the total score for BBJM. Coaches are allowed use of a calculator, but efficiency and accuracy are a must. If you have 3 schools competing, you may have 72 student scores to do by hand before the schools can leave competition so you gotta BOOK IT and it has to be LEGIT. 🙂

*Possible rate problem: If Coach Hedge can score 8 students in 5 minutes and Coach Birdbrain can only score 6 students in 8 minutes, how long will it take them to score 72 students if they’re working together? (By the way, none of the coaches I’ve met are dumb – they’ve all been awesome. I’m just making stuff up.)

However, BBJM is just one student on the team. Your team’s score is determined by calculating the scores for all students and then taking the sum of the top 12.
There’s another nice mental math question: what’s the total possible team score?

Here’s a real problem I deal with every day at practice:
“Hedge has ______ students come to practice. She only has 9 targets, so only 9 students can shoot at a time. Each student needs to be able to shoot at least 3 times before the end of practice, which only lasts 50 minutes. How many groups will she have? How much time should each group be allowed to shoot?”
I have anywhere from 20 to 32 kids of my FIFTY FIVE show up for practice every day. Ermahghersh – it’s crazy sometimes.

If you teach AP Stats, that might be a cool random variable problem with an application to normal distributions… Hmmmm. That’s a good idea for my quiz. Sorry – A.D.D. brain. Refocus, Hedge – refocus.

Where was I going with that…. I dunno. There are probably several dozen other applications of math to archery, BUT it’s 12:20 a.m. and I need to sleep… at some point. If you use any of these ideas or have more, please let me know. That would be cool – I miss teaching middle school a lot, and this would be one of those things I know my kids would love to use. And you could tie in the Marshmallow Guns with this and make your own targets.

For those interested, the “official” score cards (to use in your classroom) are HERE.

If you’d like to start a competitive archery team at your school (hint hint), you can check out more information HERE.