A few years ago the district I teach in moved semester exams from January to December. Not that the end of the semester actually changed, but the thought was that it would be good to have them before a two-week(ish) winter break.

I guess.

For my year-long classes, the change of weeks doesn't affect me much. But my colleagues who teach a semester-long class give their exam in December, have the break, then come back for 2 weeks before the class ends. Seems pretty awkward to me!

So this coming week is the last week of real classes we'll have before our (short!) winter break. Exams are Dec 19 - 22.

Anyway, every year I struggle with how to deal with the exam review days. I'm more of the mindset that I want the students to practice what they personally need to. I don't lead a whole-class review (unless they request it) and I like to give them time to work/ask questions. I give a packet of review problems and post the answers (or have them available).

And every year I wonder how to "grade" these problems.

1. I don't want to grade for correctness. It's practice for the exam. And besides, I'm posting the answers. And another besides, I don't want to take the time to do that.

2. I don't want to grade for completion.

a. If a student feels like they need to spend more time on a certain section than another, then I want them to go for it.

b. Copying is running rampant through my school right now. So the probability is great that students who aren't working on the problems during class are just going to leave my room and copy it from a friend who has actually done it. I refuse to reward the copy-ers.

3. If I choose not to grade anything at all, I feel like I'm babysitting in class for several days in a row. I can only imagine the number of Snapchats that will be sent around the school.

So I'm toying with the idea of just giving points to students who are actually working on the packet in my classroom. Basically, those kids not wasting the 3 days in class I'm giving them to review.

I don't want to give these points on their quarter grade (because what does it show they learned?) and am thinking about adding it as a portion of their exam grade. Because, really, it is showing if they worked on reviewing for the exam.

So my thought is checking to see if they are working for 3 days and add 3 - 5 points/day as part of their exam grade. If the students decide not to work then they know they are affecting their exam grade. And with these extra points built into the exam grade I wouldn't feel like I'd have to curve the grades.

# Foussinating

## Sunday, December 11, 2016

## Monday, November 21, 2016

### Polynomial Hand Turkeys

One of my students asked last week if we could just make hand turkeys in class tomorrow (our last day before Thanksgiving break). And first I was just like, "No."

But then I thought about it.

1. We have Grandparent's Day in the morning (students are pulled out of class) and a Student/Faculty basketball game during our last class.

2. We had a quiz today.

3. It's the day before a long break.

So hand turkeys it is!

But of course I'm going to make them do some math, too. Here's what I came up with:

But then I thought about it.

1. We have Grandparent's Day in the morning (students are pulled out of class) and a Student/Faculty basketball game during our last class.

2. We had a quiz today.

3. It's the day before a long break.

So hand turkeys it is!

But of course I'm going to make them do some math, too. Here's what I came up with:

I created a table of 24 different sets of polynomials for the kids to use. They're all cubics and linears, very similar but with some different signs and coefficients.

So hopefully this will be a fun little activity that will get the kids working, coloring, and enjoying the last day before a much-needed break.

## Tuesday, November 15, 2016

### Conics and the Super Moon

Earlier this year we talked about conics in Precalc. One day for a warm up I gave them this problem:

It was a fun little way to talk about a real-life ellipse.

And then last night, I saw this tweet from NASA:

So cool! My only complaint is that I didn't have this to show when we did the original warm up. (And someone asked in one class if the moon actually grew by 14%. Um, no.)

It was a fun little way to talk about a real-life ellipse.

And then last night, I saw this tweet from NASA:

Did you miss the #supermoon last night? Try again tonight because we won’t see another moon like this until 2034: https://t.co/TgZjkZquqy pic.twitter.com/6Lwkuf6Tm7— NASA (@NASA) November 14, 2016

## Wednesday, November 9, 2016

### Random Observations

A few things that are scattered throughout my brain today:

1. I used Plickers to review some content in both Math 3 and Precalc. I really like the site except when it freezes up. And then it annoys me. Luckily it wasn't something that I couldn't fix by restarting my phone, but who has time for that in the middle of class? And I really wish they'd include the possibility of mathtype in their answers. It's awkward to try and include square roots.

2. We're quizzing in Math 3 over solving quadratics tomorrow. Technically it's a Math 2 topic but the kids don't remember a lot (anything?) about factoring or solving and I feel like it's such an important thing to be able to do that I spend a good amount of time on it. Today I gave them a worksheet to practice solving equations (I emphasize the importance of choosing the best method to solve and not just the quadratic formula each time); the worked-out answers were on the back of the paper. My advice was to work through a problem then flip and check. I told them I wasn't going to collect the assignment tomorrow but to do what they felt they needed to do to prepare themselves for the quiz. In all 3 of my Math 3 classes I noted that the students who struggle immediately pulled out their phones once they heard the worksheet was optional. The students who do well immediately started working on it and checking their answers.

1. I used Plickers to review some content in both Math 3 and Precalc. I really like the site except when it freezes up. And then it annoys me. Luckily it wasn't something that I couldn't fix by restarting my phone, but who has time for that in the middle of class? And I really wish they'd include the possibility of mathtype in their answers. It's awkward to try and include square roots.

2. We're quizzing in Math 3 over solving quadratics tomorrow. Technically it's a Math 2 topic but the kids don't remember a lot (anything?) about factoring or solving and I feel like it's such an important thing to be able to do that I spend a good amount of time on it. Today I gave them a worksheet to practice solving equations (I emphasize the importance of choosing the best method to solve and not just the quadratic formula each time); the worked-out answers were on the back of the paper. My advice was to work through a problem then flip and check. I told them I wasn't going to collect the assignment tomorrow but to do what they felt they needed to do to prepare themselves for the quiz. In all 3 of my Math 3 classes I noted that the students who struggle immediately pulled out their phones once they heard the worksheet was optional. The students who do well immediately started working on it and checking their answers.

- Are the lower-performing students that way because they don't work? Or are they trying to avoid showing what they don't know and hoping it will go away? (My vote is a mixture of the two.)

3. In Precalc we're reviewing Rational Functions. We've spent a couple of days practicing finding the zeros, asymptotes, etc, and graphing and seemed to be doing ok with it. Today I gave them graphs and asked them to write the functions. It's amazing how much harder it is to work backwards through a problem. But it definitely shows what they know! Instead of a quiz I created a Desmos Activity that I'm going to have the kids work through tomorrow.

4. I stayed up way too late last night watching election results. Honestly, I think the election of either candidate would have created a scary situation. A few kids mentioned it in class today but it didn't seem to be a big deal but unfortunately that's not how a lot of the country is dealing with the president-elect. I feel so badly for those kids who will basically be viewing the new president as an enemy (and vice versa). The next 4 years are definitely going to be a roller coaster.

## Tuesday, October 25, 2016

### Desmos and Conics

I was sitting during a break in my parent conferences last Thursday evening trying to decide what to do the next day in Precalc. I had a review packet for polynomials ready (because I refuse to teach them

And what's more fun than Desmos?!

We just finished a unit on conics (added in this year because it got lost in the common core transition) and I thought it might be a good time to play with the equations. I remembered Bob Lochel doing something with conics and desmos, so I checked out his blog and found his conics project posted.

I read through his requirements and made a few changes. Here's what I came up with:

The students' task: Create a picture using conics

Requirements:

1. Use at least one of each type of conic (hyperbola, parabola, ellipse, circle)

2. Incorporate color

3. Turn in both a digital copy and a hard copy

That's it! I was a little nervous about not giving them more guidelines but I wanted the students to be able to really play and create on their own. The projects are due on Friday but I've already gotten a few submissions, and I am super impressed!

Some of the students are going above and beyond what I expected - my current favorite is an owl whose wings flap. It definitely took some learning on the student's part (and mine!) to figure out how to tilt the wings [ellipses] so that they weren't just vertical or horizontal. And then she figured out the animation.

I started creating a google slideshow with images of the kids' work... I'm going to post it below. Right now there are only a few images, but remember this isn't due for 3 more days! As I add to the slideshow it should update below.

**again**to a group of honors kids who learned it last year) but I wanted to take a little break to do something fun.And what's more fun than Desmos?!

We just finished a unit on conics (added in this year because it got lost in the common core transition) and I thought it might be a good time to play with the equations. I remembered Bob Lochel doing something with conics and desmos, so I checked out his blog and found his conics project posted.

I read through his requirements and made a few changes. Here's what I came up with:

The students' task: Create a picture using conics

Requirements:

1. Use at least one of each type of conic (hyperbola, parabola, ellipse, circle)

2. Incorporate color

3. Turn in both a digital copy and a hard copy

That's it! I was a little nervous about not giving them more guidelines but I wanted the students to be able to really play and create on their own. The projects are due on Friday but I've already gotten a few submissions, and I am super impressed!

Some of the students are going above and beyond what I expected - my current favorite is an owl whose wings flap. It definitely took some learning on the student's part (and mine!) to figure out how to tilt the wings [ellipses] so that they weren't just vertical or horizontal. And then she figured out the animation.

I started creating a google slideshow with images of the kids' work... I'm going to post it below. Right now there are only a few images, but remember this isn't due for 3 more days! As I add to the slideshow it should update below.

## Thursday, October 6, 2016

### Quadratics & Twitter: FTW

I won't see 2 of my 3 Math 3 classes tomorrow because all of the juniors are taking a practice ACT, so last night I was trying to think of something I could do with my last period class.

Now I just need to make a decision!

Today I showed them how to create a scatterplot and perform a linear regression using the TI calculator and I thought it might be fun to do a regression with data that we gather ourselves. I did a little googling and wasn't able to come up with any good ideas, so I went to twitter.

Anyone have good ideas to generate quadratic data? About to do some regressions. #mtbos— Kristen Fouss (@Fouss) October 5, 2016

And, oh, the responses:

.@Fouss Plot a point in @geogebra. Turn on Trace Point & Record to Spreadsheet. Then drag point in a parabolic path. https://t.co/IN9sMTRiUp— Jen Silverman (@jensilvermath) October 5, 2016

— Meg Craig (@mathymeg07) October 6, 2016

@Fouss anything in or nearly in free fall. Grab a video clip and Tracker Video Analysis free software. I can talk you in from there.— Megan Hayes-Golding (@mgolding) October 5, 2016

@Fouss There is an article in this months MT on using students airtime (height vs. time) from just jumping to generate regression data...— Bob Batty (@batty314) October 5, 2016

@Fouss they used vernier video physics to record videos and plot data, I used in calc a few times. It is kind of cool!!!— Bob Batty (@batty314) October 5, 2016

— Meg Craig (@mathymeg07) October 5, 2016

@Fouss barbie bungee?— dan bach (@dansmath) October 5, 2016

@Fouss I meant barbie's height as f of time in free fall…— dan bach (@dansmath) October 6, 2016

@Fouss had students toss tennis balls in front of a wall last year, members of the class placed sticky notes on the wall to note where the— Rose Roberts (@MsRobertsRoom) October 5, 2016

@Fouss ball passed by. Then did height/distance from start measurements.— Rose Roberts (@MsRobertsRoom) October 5, 2016

@Fouss random radii in circles. Random rectangles with fixed width.— Steve Phelps (@giohio) October 5, 2016

@Fouss I will see if I have something made up. Randomize radii and collect (radius,area) data.— Steve Phelps (@giohio) October 6, 2016

@Fouss Recollection of words; more people recall those at the start and end a word chain, versus the middle. (Credit @AlexOverwijk not me.)— Gregory Taylor (@mathtans) October 5, 2016

— Alex Overwijk (@AlexOverwijk) October 5, 2016

@Fouss Speedy Squares? https://t.co/6iGali5ppR— Dave Lanovaz (@DaveLanovaz) October 5, 2016

@mathymeg07 @Fouss @jensilvermath Yes, those, and the rubber band cannon also generates quadratic data ...— Beth Ferguson (@algebrasfriend) October 6, 2016

@mathymeg07 @Fouss @jensilvermath Here's a link that doesn't require the cannon itself ... https://t.co/eKcs3nhufK I haven't tried this.— Beth Ferguson (@algebrasfriend) October 6, 2016

— John Stevens (@Jstevens009) October 6, 2016I totally agree with Scott Leverentz:

@Fouss you got an awesome set of replies! So many ideas!— Scott Leverentz (@scottmlev) October 6, 2016

Now I just need to make a decision!

## Tuesday, September 27, 2016

### Better Warm Ups

I'm trying to do a better job of keeping warm-ups more interesting this year. Instead of just throwing a question up that mirrored the previous day's work, I'm mixing it up a bit.

In Ohio, every junior will be taking the ACT in the spring. And since I spend my day with (mostly) juniors, I thought incorporating some ACT prep would be a good thing to do. So every Wednesday-ish we do some ACT questions (which were so generously donated by Meg Craig!). I used Plickers for the first several weeks; tomorrow I'm going to switch it up and do Socrative.

Last Friday my 4th grader came home from school with a 3x3 grid and asked me if I could put the numbers 1 - 9 in them so that every row, column, and diagonal had a sum of 15. (Using every number once.) She said it was a problem given to them in math that day and no one, including their substitute, could solve it. That was a great one for yesterday! Some of my students worked and got it in a timely manner, some did better once they had the middle square, and some never got there at all. But they all worked on it!

Some students asked me to give puzzles more often, so I'll have to add that to my list.

Last Thursday my 4th grader (she's a wealth of questions) came home from school and told me that she'd read a book that day. She loves to read and does so very quickly, so I wasn't surprised. She'd told me that before. But then I asked what book and she answered, "Harry Potter." Um, what?! I thought maybe it was an abridged junior version or something until she pulled out that 800-page monster out of her backpack (it was book #5 if you're wondering). She claims to have read at the babysitter's in the morning for about an hour, on the bus on the way home for almost an hour, and then walking up the driveway (we have a long driveway but it's not

This actually segued into the thought of the world's fastest reader Howard Berg (which I searched an found a YouTube clip of)

and then the next clip on YouTube was a 13-year old girl on Johnny Carson back in the day. Of course the kids had never heard of Johnny Carson, but whatever. It was a fun discussion.

My Precalc warm up wasn't as fun today - I asked the kids to find the intersection of a line and a circle (we'd just discussed the equation of a circle yesterday). I loved how it incorporated writing equations of circles, solving a system of equations, and the quadratic formula all in one fun problem. But they didn't agree with the fun thing.

I pulled in desmos to show how they could've used it and skipped all the algebra...

In Ohio, every junior will be taking the ACT in the spring. And since I spend my day with (mostly) juniors, I thought incorporating some ACT prep would be a good thing to do. So every Wednesday-ish we do some ACT questions (which were so generously donated by Meg Craig!). I used Plickers for the first several weeks; tomorrow I'm going to switch it up and do Socrative.

Last Friday my 4th grader came home from school with a 3x3 grid and asked me if I could put the numbers 1 - 9 in them so that every row, column, and diagonal had a sum of 15. (Using every number once.) She said it was a problem given to them in math that day and no one, including their substitute, could solve it. That was a great one for yesterday! Some of my students worked and got it in a timely manner, some did better once they had the middle square, and some never got there at all. But they all worked on it!

Some students asked me to give puzzles more often, so I'll have to add that to my list.

Last Thursday my 4th grader (she's a wealth of questions) came home from school and told me that she'd read a book that day. She loves to read and does so very quickly, so I wasn't surprised. She'd told me that before. But then I asked what book and she answered, "Harry Potter." Um, what?! I thought maybe it was an abridged junior version or something until she pulled out that 800-page monster out of her backpack (it was book #5 if you're wondering). She claims to have read at the babysitter's in the morning for about an hour, on the bus on the way home for almost an hour, and then walking up the driveway (we have a long driveway but it's not

**that**long). So that was today's warm up: How many words per minute would she have had to read? We even gave her the whole 10 hours that she was gone from the house.This actually segued into the thought of the world's fastest reader Howard Berg (which I searched an found a YouTube clip of)

and then the next clip on YouTube was a 13-year old girl on Johnny Carson back in the day. Of course the kids had never heard of Johnny Carson, but whatever. It was a fun discussion.

My Precalc warm up wasn't as fun today - I asked the kids to find the intersection of a line and a circle (we'd just discussed the equation of a circle yesterday). I loved how it incorporated writing equations of circles, solving a system of equations, and the quadratic formula all in one fun problem. But they didn't agree with the fun thing.

I pulled in desmos to show how they could've used it and skipped all the algebra...

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