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.


First Day Back (well, on 8/7)… HOLY CHEEEZITS.

I wanna start this blog post with a request: STAY ON MY BEHIND if I don’t blog. I always say, “I’m gonna do better!” And then two weeks into school I just give up because it’s just too insane: coaching robotics (B.E.S.T. and F.I.R.S.T.), sponsoring Mu Alpha Theta, attending volleyball games (my son thinks the girls are hot… he’s nine… YEAH, pray for me), high school and college football season (#SECbaby), grading, etc. I can think of 1,000 excuses. Harass me. Yell at me. CURSE me if you have to. Just MAKE me blog. I will love you for it… eventually.

I should also warn you that my A.D.D. is in OVERDRIVE and I’m currently working on lesson plans, watching “How to Train Your Dragon”and “Restaurant: Impossible”, and blogging. So if I change tense or topics or tracks in mid-sentence… Surely if you’re reading this YOU KNOW ME and I don’t have to warn you what you’re getting into, right?

The first day back was crazy, but I got a “good luck!” text from my BFF @druinok to start my day (LOVE HER!!!). This wasn’t my first “First Day” rodeo (my 14th year), but when you switch administrators AND new ones come in, you just really don’t know what you’re gonna get. Our seniors were supposed to “parade” to school, eat breakfast as a group, then go to class. And we all know they follow directions, right?


They brought cowbells to school and RAN around school for at least 20 minutes. Wouldn’t be too bad if we had a senior class of 100 or 200… or even 300. But we have almost 400. It was CRAZY. How crazy? I ran out of band-aids from the blisters they had (I’m like “mom” to most of them) from ringing their cowbells. At one point, 15 of them burst into my classroom SWEATY and chased me around the room to hug me (I’ve known most of them since they were 12). I’m sure my sophomore Alg2 class was quite confused to see me running around them in heels trying to escape. But 10th graders are still kind of scared the first day, so that worked to my advantage.

Anyway, I have 2 classes of 10th grade Algebra 2 and one class of regular statistics. I know we’re “supposed” to teach rules and procedures on day one, but I’ve just never done that. If you do, I’m not judging you whatsoever. We all have our “jam” for what works for us, and “shocking their brains” works for me. I mean, let’s face it – I’m a shock to deal with on my own. I think the mix of that and being forced to think on the first day just works for me.

So Algebra 2 started class by filling out an index card that I store in a box on my desk. I keep their textbook checkout form, parent communication, and tardies in that box. On the card, I ask them for their 3 favorite songs – my way of creating their class playlist. I also like to shock them with my multiple-music-personality-disorder. They’re shocked at what lyrics I can quote.

Then we move to “the folders”.

Each folder is a different color, which represents the different groups in my classroom. Colors make sense for my brain, so that’s how I roll. The kids are in groups of 3-4 (desks are already in groups when they get there), introduce myself, the course (in case they’re in the wrong class – it happens), and we start. “I’m about to hand you a color folder that corresponds to your group. This is your group color for the rest of the 9-weeks. The first person from your group to get to class every day will come to the front of the room and grab the group folder, but there’s a catch: First rule about the folders? We DO NOT open them until Mrs. Hedge says so. Second rule about folders? We DO NOT open them until Ms. Hedge says so. And the third and FINAL rule about folders? WE DO NOT open them FOR ANY REASON until Ms. Hedge says so.” Yeah, it’s a throwback to “Fight Club“. (I love that movie – don’t judge me.)
So here’s the view once they do open the folder:

Left side of the folder comes first – I would love to say I know where I got this and I might figure it out eventually.

I did figure it out –>HERE they are. I’ve misplaced a page during the crazy, so all 20 aren’t there.

BUT basically it was a set of 20 relationships (ex: height of a candle vs. time, gas used vs. time, etc.). The trick was that the graph included 3 possible functions to represent the relationship.

In groups, students had to highlight the function that they felt best represented that relationship. The discussion in their groups was AHMAHZHANG!!

I don’t answer questions unless it’s with another question (drives them NUTS). They debated and I made sure I used @misscalcul8’s “Two Nice Things” (from #TMC12) as a baseline for being rude when you disagree. This only took about 20 minutes, and then I had pairs of groups debate their choices for functions. As a group, we talked about the “tricky” functions. The one that got them was choosing the function to represent the speed of a dog while it took a nap. They wanted to say that I messed up by not giving them enough information. I just ask, “What makes you think that?” Then they’d say, “Because you didn’t give us a constant function.” I’d ask, “What makes you think that?” “Because you didn’t give us a horizontal line.” “What’s YOUR speed when YOU are asleep?” “Duh, it’s ze… oooohhhhhhh…. I gotcha.” Wink and a fist bump when they figured it out.

So once we finished (i.e., I got bored) with that, we moved to the right side of the folder.

I decided to combine Algebra 1 Bootcamp with @rdkpickle’s “sum of the squares” idea from #TMC12. I set up 3 sets for the next few days: (A) evaluate numeric expressions, (B) simplify algebraic expressions and (C) solve equations in one variable. If you haven’t seen her idea, basically you have 4 problems in 4 blocks and students write the sum of their answers in the circle in the middle. Here’s a VERY BASIC template. I gave those goofy cheap foil stars for awards for groups that finished 1st, 2nd, and 3rd. They freaked out and fought over them (YES, high school kids LUV stickers!).

After they all finished sets A and B, I assigned each group a different problem and we talked about whiteboarding (shout out some love to my buddy, @fnoschese). They couldn’t process the idea at first. Them: “So you WANT us to work it WRONG?” Me: “Yes.” Them: “And it has to be a GOOD mistake?” Me: “I prefer GREAT ones, but we can start with good ones.” Them: “Is this a trick?” Me: “…..what makes you say that?” Them: “Geeeeez, Ms.Hedge… OK! OK! OK!” –>insert evil grin here<– They did a great job at creating the mistakes.

They were AWESOME presenting their work to the class as a collective group. However, the “audience” STRUGGLED at asking leading questions to get the presenters to discover their mistake. So many wanted to immediately point it out. Them: “So isn’t it true that negative three times negative three is POSITIVE nine?” Me: “Rephrase – you pointed out the mistake.” Them: “So when you learned to multiply negatives, did you not understand that squaring a negative makes a positive?” Me: “Nope – that was kinda rude. Rephrase.” Them: sigh. “Sooo, where you have negative three squared, can you help me understand how you got negative nine?” Me: “Sweet! Ok team – answer his question.”

Stats rocked it as usual (not ME, the kids). I love showing the Kristen Gilbert court case and going through that as a full class discussion, but I thought I’d change it up a little bit. I wanted more discussion. I treated it like a real court case and revealed a little of the evidence (or data) at a time to lead them into questioning her innocence. They really liked it (DUH – it’s an awesome case to do in stats if you haven’t ever tried it). Afterwards, we looked at Did You Know 3.0 – kids usually love watching that. Afterwards, I make them write down (in groups) the 3 stats that stood out to them. Not long after that, the bell rang. What’s good about this is that it’s my 3rd time to do this for stats (I do it in A.P. as well) and the kids always respond positively to it. So if you’re teaching stats for the first time, this will get them hooked. I will send you what I’ve got if you want it – just holla.

Tried to recover during my planning block. Let me say that wearing flip flops (if anything) all summer and then starting school in stiletto-heeled boots was NOT very smart. I get a call from the school secretary asking me to come to her office. I thought, “Dang it – WHAT have I done now?” No idea – I was cursing all the way to the office trying to figure out what the crap I’d possibly done to piss somebody off before noon on the first freakin’ day. Me: “Yes?” Secretary: “These are for you.”

OH. MY. GOSH. Flowers??? What the heck? Me: “Are you sure?” Secretary: “Yep – read the card.”

Ok – I shamefully admit that her desk is REALLY tall and those flowers were VERY high and I couldn’t reach, so I took her word for it and went back to my room. Thought they’d be from my mom or my son (via the hubs), but no.


Apparently she’d been scheming behind my back with @mesimmons5, but I can’t be mad because it was just so awesome and appreciated.

My 4th block Algebra 2 KICKS BUTT. I don’t know if it’s the end of the day or the fact that there are almost 30 of them in there or what, but I usually click best with my last class. They were SO into everything and just….. amazing.

I was EXHAUSTED at the end of the day and THANK GOD I had the next day off (weird scheduling, I know).

Hope your first day is awesome, too!

Here are some random shots of my classroom – I’m not finished “decorating” but it’s a start:

Here’s the front wall of my classroom right by the door:

I have a box for each block to turn things in and pick up their folders for the day. I’m going to do @mgolding’s organization outline on the little table for spaces for stapler, hole punch, tape, etc.

This is MY motivation board. It reminds me why I do what I do. It’s not finished (I have to put TMC12 pics up), but it’s behind my desk. Things on it: buttons from TechSmith, an encouraging card from @troystein, pictures of students who have overcome A LOT and are inspirations to me, a postcard from a former student who now lives in Turkey who I am helping apply to colleges in the U.S. so she can come back, a newspaper pic of my kid, a newspaper pic of me and a student, my Harvard banner I got when I attended Project Zero, and a picture of me and my math BFF4EVA who passed away in 2007. If he were still alive, he’d be one of the most followed tweeps and bloggers around. Tragic end to someone I miss every day. Thankfully I teach his son, so I kind of get to see a glimpse of him.

This is my “score” board for kids to help me remember what games/events/performances they’re in every day. If they’re playing or performing, they write it on the board along with the time and location. Most days, I’ll take the kid and go watch. Means a lot to the kids to see you show up.

Going to try this little sucker I got from Target for kids to sign up for tutoring:

We’ll see how it goes.

And YES, it took me a whole WEEK to get the time to finish this blog. Arrrrrgggghhh.

Marshmallow guns (#made4math 7/16)

I know you think marshmallow guns aren’t EXACTLY #made4math because it’s one of my former middle school projects – kinda like my Shrinky Dink post.

The way it IS #made4math: it’s something you can use to teach statistics and probability and use for data collection with common core. But in order to get THAT stuff, you gotta come to TMC12 or wait until it’s over – this is one of my “Favorite Things”. ☺ The way it’s NOT #made4math: it’s just a really cool CHEAP thing to give a kid (or adult, like me) to keep them entertained for a while. My son and I have marshmallow wars all the time (outside, of course). And in true ApproxNorm fashion, I totally let my students make these (including the cutting) in class to teach measurement. So it might be a cool thing for middle school or higher if you’re brave.

Marshmallow Guns (ApproxNorm Style):

1. Go to your favorite home improvement store – head for the plumbing section. Look for the PVC pipe. You want ½’ inch pipe. It’s pretty cheap – $1.68 for 10 feet at my local Lowes. How much you need is determined by your design (tons of ideas on Pinterest) and how many guns you want. I usually use 20 inches per gun, so you can get about 6 out of one piece of PVC pipe.

**If you don’t have a saw at home, you can pick up a pair of PVC pipe cutters for about $10 – $12. This is what I use – more on that later.

2. Next you need to find the joint pieces. BE CAREFUL. You want the joint pieces the PVC pieces will SLIDE into. These are usually the cheapest ones. Make sure you get ½ inch joints! If you get ¾ inch joints you’re gonna have a problem!

Thankfully, Lowes has “contractor packs” of joints so you can save a few pennies (and some searching) by buying a bag of ten. You need two 90 degree elbows and one “T” (or “tee”) piece per gun. I was doing 10 guns, so I bought 2 packs of elbows and a pack of “T”’s. (Why 10 instead of 12? Think about it… you’ll figure it out.)

You’ll also need a cap to go under the handle so the marshmallow doesn’t fly out of the bottom. The caps are the most expensive part of the gun, so the bag of 10 cost me a little over $3.

(I’d have, um, shown you a picture of the caps bin like the other two, but uh, it was on the top shelf. I couldn’t reach it. **shocker**)

3. If you want to paint it, pick up a can of spray paint in your favorite color and head towards the checkout isle. Here’s my receipt for everything I needed to make 10 guns. See if you notice where they messed up:

Yep, they only charged me for ONE cap instead of a contractor bag. So my bill should be a few bucks more, but I chose to spray paint one for @druinok. So if you do the math, my bill should’ve been about $14.97 with tax JUST for the guns which comes to about $1.50 per gun. Not bad, huh?

Side note: Not only is this a great tool for data collection, middle school students could use the cost and receipt to calculate tax, total cost, unit price, percent of increase if you buy individual instead of in a pack, etc. MAN!!! I MISS MIDDLE SCHOOL!!!

4. Find a place to work. I like to be outside when I work on stuff (even when I blog), but that’s a personal thing. You need your PVC pipe, a pencil, a ruler, and your cutting method (for me, the PVC pipe cutters):

(ok, the beverage isn’t a necessity, but… you know me. *wink*)

5. Start by marking your PVC pipe. For each gun, my design requires: one 2 inch piece, two 3-inch pieces, one 5 inch piece and one 7-inch piece. How you mark and cut is up to you. Some people like to “mark and cut” as they go. Some people like to mark everything, THEN cut. Some people like to mark and cut what they need for each gun. I like to mark all my 7 inch pieces first, then all my 5 inch pieces, etc., and cut all at one time.

If you’re doing a lot with the cutter, you’re going to get sore so don’t say I didn’t warn you.

Side notes about the PVC pipe cutters:

I’ve heard SO many people turn down this project if they didn’t have a saw or with students because of the PVC pipe cutters. “You have to have muscle to use those cutters and I and/or my kids aren’t strong enough.” That’s just crazy talk. I am NOT photogenic like @Fouss and I hate having my picture taken. But I wanted to prove to you, sloppy ponytail and all, that I made these myself.

If I can cut PVC with my spaghetti arms:

then SO CAN YOU, so zip it.

If you’re considering this as a class activity, you need to make a few on your own FIRST to see how the PVC cutters work. The ones I use don’t cut much at a time and would be good for students. I would “train” one person in each group to be the cutter and make sure they could PROVE their abilities before allowing them to cut. This might be too scary for you and that’s fine. You could get some moms/dads to volunteer to come to class one day and assist with the cutting.

6. The entire process of marking and cutting the pipe for ten pieces took me a total of 30 minutes, but that included me talking to neighbors, yelling at the kid to stay off the roof, etc. Once you’re finished, the assembly is as followed:

See?? Easy breezy. And you can change it up to see if/how the rearrangement of the pipe gives you more/less distance.

7. Obviously you have to use the mini-marshmallows for the gun.

To launch one, there are several different ways but I usually put the marshmallow in the 2 inch piece (that’s the mouthpiece) and launch it IN the gun. Some people launch the marshmallow from their mouth/tongue, but that’s just a glorified spitball (EW). I also wouldn’t put my mouth ON the mouthpiece if I were you.

Hope you like it!

P.S. If you’re coming to TMC12, I’m giving away a few of them so be ready for a war!!
(You didn’t REALLY think I’d do a presentation on marshmallow guns and not try to start some trouble, did you???)

Cheap Shrinky Dinks (for math or just cool to do with your kid)

I used to teach middle school and I LOVED it. Something about kids who haven’t hardened their hearts about math was just really cool. This was one of the things I used to do with my students and, since most of us are stir crazy at home with our kids, I figured you could try it out on them and see what you think. Originally got it from an AIMS article back in the 90’s.

Before you give me excuses about why you can’t do it, let me say:
If your kid is old enough to DRAW, then he/she is old enough to do some of this.
So at least try it.

So the first thing you need is PLASTIC and not just ANY plastic. It needs to be “Grade 6” plastic. I used to use the salad plates from the school cafeteria. I’d pay the cafeteria manager ahead of time for them (ridiculously cheap), and she’d order what I needed or give me what she had.

You’re looking for a recycle triangle with a “6” in it AND you need to make sure that the plastic is completely CLEAR (not foggy or anything). Here’s an example of what I’m talking about:

Notice that there is a “1” in there instead of a “6”. So I would NOT use this.

Once you get your plastic, just cut it up into whatever pieces you want. Here are the main supplies you’ll need:


  • plastic
  • sandpaper
  • pencil
  • ruler (if you want straight edges)
  • scissors
  • color pencils
  • hole punch (if you want to make it into a keychain, necklace, earrings, etc.)
  • a piece of paper (this is important)

Later you’ll need:

  • oven
  • spatula
  • tin foil

1. Go ahead and set your oven to 450 degrees. I’ve used toaster ovens in the past (about $20 from Wal-mart – VERY MUCH worth the cost if you’re doing this in your classroom) and I’m more familiar with that. Today’s the first time I ever tried it in an oven. It worked, but not as well as the toaster oven.

2. Take your sandpaper (cut into smaller squares), your first piece of plastic, and a piece of paper. SAND ON TOP OF THE PAPER. That piece of paper will keep you from sanding your desks, table, etc. (not that I’ve EVER done that before… *cough cough*)

3. Start sanding – we’re only going to do ONE side. Over the years, I’ve found a method for the madness. Sand your plastic top to bottom in one direction (ex: left and right). You gotta put your elbow into it, so don’t do this in a prissy manner. Imagine the face of someone you don’t like on that plastic and GO TO TOWN to scratch the crap out of it (not that I’ve ever done that before… *cough cough*). Then rotate the plastic so that your strokes are perpendicular to the ones you were doing before. Trust me, when you think you’re done, you’re NOT:

I can still see the clear plastic shine when I tilt it in the light. You’ve gotta make sure that sucker is completely sanded. It shouldn’t take that long, though. If you’ve spent more than 10 minutes sanding and it’s not finished, you’re not putting enough force into it. Once I’m sure that I’ve sanded every part of the plastic using those two strokes, I start sanding in a circle. This isn’t necessary, but if you look below, you can see that the difference between the perpendicular strokes (at the top) and the circular strokes (at the bottom). It’s easier for the color pencil to hold onto the plastic the better it’s sanded.

When you’re finished, it should look something like this:

Again, tilt your plastic in the light and see if it reflects. If it does, sand that part down. 4. If you’re doing this for math class or you’re just anal about it looking pretty (and I mean that in a non-judgemental sort of way), I use the notebook paper to help me line up my straight edges and I mark it in pencil:

5. Once that’s done, I cut it out. OPTIONAL: I always had my students trace the original on a piece of paper and measure it (I didn’t simplify one of the fractions, but if you wanna, go ahead – knock yourself out). I also made them do the diagonal, but that’s just an extension.

6. Now for the fun part. COLOR IT! I use color pencils. I haven’t tried markers (but I don’t really remember why right off the bat… oh well). I was in a hurry so I did this for my classroom keys:

NOTE: If you’re going to want to do this for a keychain or a necklace, punch a hole in your plastic BEFORE you cook it. I know that’s a “duh” thing, but afterwards you can’t do much about it so make sure you plan:

——-> Side note: after I baked it, I realized that one hole wasn’t big enough for the keychain I wanted to use. So for bigger keychains, be creative and make a slightly bigger hole.

7. So between me and the kid, we ended up with 2 each in about 15 minutes:

8. Now for the fun part! Transfer your plastic onto a cookie sheet COVERED IN ALUMINUM FOIL (you’ll thank me later).

See how they’re all spaced out? There’s a reason for that.

When they cook, they do this rolly-poly belly flop kind of thing and they, well, DANCE. Every time I do it, the dance is different. Some times it’s very fluid, and sometimes it’s really choppy. Sometimes they flip completely over, sometimes they roll completely up. Doesn’t matter, JUST WATCH. It is the coolest thing and kids will go CRAZY for it. You wanna make sure they have plenty of room to do their thing, though. If they “touch”, then those two pieces will probably bond together and you don’t want that. The cooking process doesn’t take long. I put the kid’s shrinky dinks in first to make sure the oven was at the right temperature. Here’s a video of mine going in (and YES, I burned myself – wouldn’t be ME if I didn’t):

9. When they come out, VOILA!! Mini-me’s!

Here’s the mini-version in the same rectangle as the original:

And in case you NEED to know, here are the measurements:

And here are the finished products:

It honestly took longer to blog about it than to do it. But you can do just about anything with this – gift labels, Christmas ornaments, keychain with your kid’s artwork on it, earrings, necklace, bracelet, etc. Be more creative than me. 🙂

One year my MathCounts crew set up a table for a fundraiser. Kids paid $1 to create one in assembly-line form OR up to $5 to have one custom made by our more artsy math nerds. We even mass created some with our school name in our school colors and sold those for $3. Just a thought.

I have the docs I used in my classes (7th grade math) SOMEWHERE around here, but it will take me a day or two to dig them up. Once I find them, I’ll post them. I used it to teach percent of change, but you could do just about anything with it. I suggest doing it as instruction and then again maybe the day after a state/standardized test as stress relief. Or maybe as a stats activity, you can have kids collect the data on the original and mini-me versions and see if they can create a regression equation to predict the length of the mini if given the length of the original piece. OR, even cooler, take that regression equation and have them use it in a “backwards” way. In other words, if they want the mini-version to be a specific length, what size original would they need?

If you DO this, I’d love for you to link to a picture in the comments or e-mail me (approximatelynormal dot stats at gmail dot com) and let me post it.

That’s all I’ve got for now, but I’m working on a post for mentor teachers with Chris Hill (@Hillby258) that should be ready today or tomorrow.

Until then….

BRAIN DUMP DAY: Building a regular stats course from scratch

This isn’t one of those blog posts where I disperse my profound insight on you so that you can share it with the world… Wait, I don’t do that anyway, do I?

This is more of a spur of the moment “brain dump” to let you see what’s going on in my brain so you can help me unscramble it (in a non-“Hannibal Lecter” sort of way… sorry for the visual). I do this a lot, but I figured it would better from now on to warn you in the title so you don’t waste your time on a post you think will be, um, “enlightening” (yeah, I can’t say it with a straight face either). I don’t edit, I don’t ponder how to say what I’m thinking, I just TYPE. Love me for it or GO AWAY.

Here’s the deal:

I’ve taught AP Stats for about 5 years and, while still a newbie, I’m now at the point where I’m refining my course and adding to it than the “WHAT THE HECK AM I DOING??” mindset. PROBLEM: once my AP Stats roster began to grow, people began signing up for the course with NO intention of taking the AP exam. In fact, they really thought (for some reason) the class would be easy and were dumbfounded to find out that (a) it’s HARD and (b) it’s not really like any math you’ve ever taken. So they started to complain and yadda yadda yadda. I think I’ve told you this story before… But I’m too lazy to go back and find the post.

So the counselors created a “regular statistics” course that would receive honors weight. That way the kids that wanted to take stats could get their “learn on” without the pressure of the AP exam and everything would be gravy, right? WRONG. My “regular stats” class became the dumping ground for students who fit into one of the following categories: those who (a) didn’t qualify for dual enrollment college algebra (b) didn’t qualify for the grade requirement for precalculus/trigonometry or had previously failed Algebra 2 once (or twice) (c) didn’t want to take AP Stats/Calculus because they didn’t want to have to work hard (d) were not likely to pass unless the teacher would bend over backwards and spend extra hours outside of class tutoring or (e) were about to graduate and, for some ungodly reason, wanted to have me for ONE more class because I’m THAT WEIRD.

Ok – dumping ground is harsh and I don’t want you to get the wrong idea if you’re relatively new to my blog. When I say “dumping ground”, I mean that counselors threw kids in the course without any consideration of the difficulty of the class and ASSUMED it would be “easy” because it wasn’t AP. None of my kids are “trash”. Even if they’re BAD kids (interpret that as you wish), I still like my kids a lot. But if a senior has failed Algebra 2 TWICE his jr year, finally passed it by ONE point (somehow) and can barely solve 2x + 5 = 8x – 4, he/she is likely to STRUGGLE in statistics (or at least the way I had it planned that year… more to come on that). There were other course options for these kids, but the counselors figured (correctly, I’m sorry to say – I must fix this somehow, but that’s a blog for another day) that I would bust my ass to make sure these kids passed so they plopped them in stats.

In a nutshell, I taught regular stats the same objectives that I taught AP, I just didn’t make the writing/proofs as structured/rigid as AP.

This bombed like a “quiet” fart from a defensive linebacker in study hall.

It didn’t work. **face palm** There, I said it and yes, I’m embarrassed. I honestly ASSUMED that I would get honors-level kids since the course was designated with honors weight. Well, there goes that “ass-u-me” joke that I ABSOLUTELY proved with my regular stats course (I actually now consider myself the poster child of that joke). I had kids with high math abilities (making 34 on math part of ACT and finishing precalc/trig with A’s) and low math abilities (you already know about those). My grades were ALWAYS bimodal in distribution (insert crude joke here) with the high ability kids easily making A’s and being bored, while the lower ability kids were bombing and not making connections. I could blame it on the reason you may have read about in the #secretblog OR I could just own it and say I DIDN’T PLAN THE COURSE LIKE I SHOULD HAVE to account for the possibility of such extreme differences in mathematical backgrounds.

But at least NOW I know what to expect for next year. I don’t want to be “that” teacher that sets requirements for this course. I think every kid should have the opportunity to take statistics because it’s something they’re going to come across as adults (and it’s FREAKIN’ COOL!!). I get to design this course from scratch and do whatever I want with it. That’s exciting and scary as hell at the same time. I want it to be something that the lower-level kids can do and find interesting. Yet at the same time, those upper-level kids will find it challenging so it’s not “underwater basket weaving” and they’ll actually have to THINK.

How would you design a class like that to be engaging and challenging for such extreme abilities? Where would you start? What would you include? What would you leave out (or make optional for kids who need to be challenged)? Would you start with something that EVERYBODY could do so that your lower-level kids could start out feeling successful? Or would you start with something a little different so that the upper-level kids would be knocked on their ass just a little and the lower-level kids would see those kids struggle (which might backfire as, “if THEY can’t do it, how do you expect ME to do it”)?

I don’t really know.

Honestly, I don’t really know where to even START. Stats isn’t exactly like algebra where you need to layer and build on prior knowledge. There are different areas that don’t seem to be related until you get to inference and tie it all together. So really I could start almost anywhere: univariate data, sampling, experimental design, simulations, probability… You name it.

The election will be the same semester that I’m teaching this course. And while that’s interesting to ME, is it something that the kids really care about? Or would they rather learn how statistics is important in sports, crazy legal cases, taste tests, bias in the media/advertisements, etc.

I DON’T KNOW. I HAVE TOO MANY OPTIONS. This is NOT good for my attention-deficit disorder brain… But I gotta figure it out ASAP. I have to present my course to my administrators (with pre/post tests, common assessments, pacing guide, academic vocabulary, etc.) by August 1st.

Anyway, that’s what’s going on in my brain today – hope you could follow because I’m NOT going back to edit this post. It’s brain dump day, like it or not.

If you have any suggestions/advice, I am always open to that so comment away.


Holy crap, I’m exhausted… But happy!

I wish I’d had time to blog about this earlier, but there was NO time. It’s about 10:35 p.m. and I’m watching the Cotton Bowl. I just got home from a basketball game where the ref warned me he was about to give me a technical foul – evidently he didn’t hear me say, “Bite Me” after that (and THANK GOD my son didn’t either).

We started a new semester, so I finally got what I always wanted – MORE AP STATS!
My stats scores always sucked in the past because I taught it in the fall and apparently I don’t review well in the spring. I know the kids understood it in the fall, no doubt. So my school moved stats to spring – it’s now time to “put up or shut up” with my scores. But there’s more time pressure than before, too and my classes are almost full (27 in one class, 28 in the other).

So I wanted to really hook kids the first day and get them excited about stats. Most people I talk to hated statistics in college. But stats is so amazing – I wanted my students to feel that same “wow” factor. So what do you do on the first day to hook them? This is only my 3rd year of teaching, so I had NO idea. These are the biggest classes I’ve ever had AND I’ve got TWO!

My first thought was that I was going to drown in paper work if I did not get them to help me. I decided to put the students into groups and call them “research teams” (RTs). The idea is to teach them to peer edit each other and hopefully, in the process, it would help them become better writers on free response questions.

I already stole the idea from @druinok to give free response problems every week to be due Friday. Then the thought of grading almost 60 FRs a weekend gave me the shivers. So I’ve already set aside one day each week that they will peer edit their free response problems for 15 minutes in their RTs. The goal is so that when I get it on Friday, it should be their best possible work (and hopefully will be very close to correct). This may bomb, but we’ll see.

Anyway, back to the first day. I didn’t want to bore them with syllabus or classroom procedure talk (I know, I know – that’s what you’re supposed to do). But by the end of the class Friday/today (I won’t bore you with the details), they figured out the following ideas:
1) When we’re in a group, we understand better.
2) Our group has a pocket folder in the back of the room – the first person in class needs to get it.
3) We don’t pull anything out of the folder until she tells us to get it (and no peeking).
4) When we finish things as a group, those materials go back in the pocket folder on the other side.
5) Before class is over, someone puts the folder in the class bin back in the back of the room.

That’s not much, but they figured all that out without me listing off the procedures.
I know at least half of these kids already, so I pre-assigned them into their RTs. A lot of my kids are in forensics/debate/drama and will get off topic at the drop of a hat, so I wanted to try and fix that on the front end. I may let them change groups at the end of the 9-weeks, I’m not sure.

I showed the students the original version of “Did You Know/Shift Happens“. I wasn’t sure which version to go with, but this one worked great (thanks @mrhodotnet!). I told the students that most of the stats were from 2006, so we talked about how extrapolation can be wrong sometimes.

To kick off stats, I did the case of Kristen Gilbert. I started by trying to make the kids think it was a case of false imprisonment. I used a lot of the graphs from where the story appeared in “The Numbers Behind NUMB3RS”. I think all teachers have to posess some acting skills, don’t you? I put mine into use that day and tried my best to be as convincing as possible to make the kids think Gilbert was sitting in prison rotting over this horrible crime that she did not commit. By the end, they were arguing with me that there’s NO WAY she was innocent. Without technical vocabulary or getting into the “meat” of the class, they used what they aready knew to figure out I was completely full of crap. It was “wicked awesome” to see them shout with delight when I told them that they were all right – Gilbert was guilty. And when the bell rang, I said, “Welcome to Statistics.” (If you want a copy of my PPT, just let me know – it’s not great, but I’ll share.)

On their way out the door, I had them write their first impressions of the class and any concerns/questions they may have had. Overwhelmingly, the general response was “I’m so excited about this class and I have NEVER said that about math before.”

So it was amazing, but now I’ve realized that although this type of teaching works, it comes with a LOT of planning on my part. And I’m going to have my timing down to the minute if I’m going to teach this way for the AP test and hope that they do well. (If you have any suggestions, hit me up because I’m freaking the BLEEP out over it.)

My formal evaluation is Monday and I don’t do the “dog and pony show” for my administration. I want them to see me for exactly what I am so that if I’m screwing something up or could make an improvement in my daily plan, they can help me. But what my administrator DOESN’T know is that I’m putting him in one of my research teams and he’s going to be a student for the day. Maybe it won’t get me fired. 🙂

And So It Begins

So the two people that actually READ this blog know that I pretty much quit posting a while ago. Honestly, I was SO overwhelmed my first year with stats that I dropped it.

But now I’m out for the summer and prepping for my 2nd year of AP Stats. BIG thanks to MizT (see link to “Teaching Statistics” on the right) for taking me under her wing. She’s allowing me to harass her daily for advice and ideas (and believe me – “daily” is not an exaggeration). My preps have narrowed from 4 to 2. My other prep is SO easy to teach that I won’t have to spend much time stressing over it.

Still feeling the pain from falling on my face, I now have a better understanding of my teaching weaknesses. But I’m EXCITED about my stats class next year (instead of terrified).

I’m still having trouble wrapping my head around our “higher ups” and the way things work at this school. Like the fact that our handbook says the kids don’t get the AP weight unless they have an 85 or above (but in secret they give EVERYBODY the AP weight if they’re in an AP class). And they seem to resent how tough our AP Calc teacher is because parents complain so much (nevermind that she’s AMAZING but has zero tolerance for laziness). And we have teachers who seem to mirror the females from the movie “Mean Girls”. Really immature.

Do any of you teach stats on the semester block schedule?

Hope you all have a great summer!!