January 2015 archive

logic on yikyak

By Kristina

Spotted on YikYak under the hashtag #ReclaimtheMirror2015. It reminds me of our IB Math Studies logic unit (which I won’t get to teach next year unless we can somehow swing one cohort of IB Math Studies and one cohort of IB Math SL for the Class of 2015).



1) Translate the two sentences into logical symbols.
2) Find the converse, inverse, and contrapositive of each sentence.
3) Are the two sentences logically equivalent? Create a truth table to check.



By Kristina

Sometimes it pays to get out of one’s comfort zone to find some lovely math problems. I watched an episode of Rob Dyrdek’s Fantasy Factory with my husband today. Cooking competitions and rom-coms are usually more my speed than their antics and adventures, but I do like their joyful attitudes about trying ludicrous things. This episode included a subplot in which Rob filmed Drama doing reckless activities to prove that he was “certified reckless.”

Activity 1: Ride his Harley up a ramp and into a pit filled with foam blocks
Activity 2: Get inside a wooden coffin which was then blown up
Activity 3: Get inside a cannon and get shot into a net

The Cannon Lady states in the show that Drama would shot from the cannon from 40 feet up and at 30 mph.

Questions for Math Students
1) What are the dimensions and height of the net? Where should it be placed?
2) At what angle should the cannon be pointed?

Screen Shot 2015-01-25 at 12.07.41 PM Source: Instagram

Screen Shot 2015-01-25 at 12.10.15 PM Source: Instagram

gratitude list

By Kristina

I have not yet figured out how to let down my guard about sharing the trials and tribulations of my school days. I’m going to try putting up lists of three things I’m grateful for on a given day instead and elaborating on those as I see fit.

1) I have been off Facebook and Instagram for two weeks. I miss sharing things like the funny signs on the Sav-Mor liquor store and looking at cute fat babies, but I am gradually freeing myself of the mentally poisonous cycle of looking at these sites on my downtime. I told my students this. One commented “but you’re missing so much!”

What *am* I missing?

a) Comparisons to the following people: the runner who humblebrags about her oh-so-badass polar vortex marathon training run, the mom who created a Pinterest-perfect party for her toddler, or the hashtag-addicted Top Chef who crafted three perfectly-lit, scrumptious Whole30-compliant feasts.

b) The negative energy of those who complain all the time about everything under the sun. From a teenager, this is understandable. From an adult in his/her late 30’s, the “woe is me” behavior is unfollow-worthy. From a supposedly educated liberal, ignorant comments about things like Ferguson are unfriend-worthy.

c) Clickbait from Buzzfeed, Quartz, Elite Daily, Clickhole, and ThoughtCatalog. No wonder I’m behind on reading real books…I’m just reading crap on my T rides and while waiting in lines!

2) Friends on Netflix makes me really happy. It makes me think of high school and college friendships that were more meaningful than Facebook-only ties.

3) My husband and I got to eat breakfast together because it’s a holiday. He’s usually not up when I leave for school, so it was nice to enjoy egg bagels over CNN with him.

Patriots Football Triangle

By Kristina

My husband knows I love finding math in everyday life. Last night we hung out with some of his college friends and their wives, which ended up becoming two gender-segregated gatherings in front of the playoff games on the tv and in the kitchen. When we were heading home from a friend’s house last night, he shared with me that the guys’ conversation ended up bringing right triangles into football. I want to give this problem to my students.

The guys were reminiscing about a 2005 AFC divisional game when Champ Bailey intercepted Tom Brady in the end zone and began running the ball back down the sideline. The announcer excitedly counts down how far Champ Bailey makes it (“30! 25! 15”) until Ben Watson comes flying in and knocks Champ Bailey out at the 1-yard line.

In the post-game analysis, Tedy Bruschi comments “Where did he come from? We didn’t know until replays. We saw Ben was on the other side of the field, so he basically had to run 120 yards or longer than that to get that.” They thought this number didn’t make sense, so they got to calculating.

Screen Shot 2015-01-11 at 7.03.27 PM

Given that the dimensions of a football field are 160 yards long (with 10 yard end zones) x 53 1/3 yards wide plus the screenshot above, how far did Ben Watson actually run? 

game of 49

By Kristina


We found out about the Game of 49 from some fellow runner/board game aficionados. After playing a few rounds with our friends, I immediately wanted to buy it for my students to play in class. It has elements of poker and bingo–you draw from a pile of number cards (1 – 48) plus wild cards (rings of numbers and 49), and bid for the cards. The highest bidder puts one of their tokens on the board. To win the game, you must get four in a row (horizontally, vertically, or diagonally). I also envisioned using the game for a probability unit after

Because the game wasn’t available to purchase at the time, I printed out five copies, laminated the boards and cards, bought bingo tokens from Amazon, and brought those to class. We played before Thanksgiving break, when many students were excused from class for running the annual Advisory Student Council potluck (two seatings for 9/10/11 and 8/12). The students got really into the game, and it was nice to see students who aren’t typically “good at math” excelling at it. We also played before Christmas break (when the probability unit had started). The kids who had played before were excited to teach their classmates how to play.

After they played, I asked the kids about their strategies. A lot tried to get on the board right away so that they’d get a lot of money when the payouts came. Some were concerned with wasting their money and therefore reluctant to make bids. Others drove up the prices in order to bankrupt their opponents and then be able to pick up number cards for $1.

I recently lent the Game of 49 sets to my coworker for her math enrichment class. It went over well, and they even sorted the game sets into Ziploc bags for me!

Game_of_49 (1)


52 week saving challenge

By Kristina

Spotted on my Facebook newsfeed: New Year’s resolution to save, based on this blog post, which shows a money challenge that results in an extra $1378 at the end of the year.

52-Week-Money-Saving-ChallengeSource: http://www.lifeasyouliveit.blogspot.ro/2013/07/52-week-money-challenge-update.html

52-Week-Money-Saving-Challenge-1Source: http://www.goodshomedesign.com/52-week-money-saving-challenge/

The original blog post comments have become a flame war of sorts. Folks call $1378 practically nothing and others pipe up to defend saving at all. There are arguments about luxuries versus necessities. Some say that putting money in bank accounts is stupid.

However, there are some comments that could spark a discussion related to arithmetic sequences and series and the feasibility of doing these savings challenges in real life:

1) “I’d think it would be easier to deposit $25 per week = $1300. I’d think the larger amounts would be more difficult for some people to cough up each week, and they’d give up. Now if they can add $2 more per week, that would give them $1404 in the end. Or give them several options just to show what they could end up with in different denominations, ie $50 and $100. $2600 and $5200….”
2) “yes, people living in poverty are not in a position to save for a ski holiday. the beauty of this idea is that
it makes it a bit more fun
in the first month or so, it helps form a painless (for most people) habit. the difficulty of putting in $25 per week (and more) is balanced by the difficulty in letting yourself down by abandoning the dream/ project. personally, I’d find putting $25 in a jar hard to start, but I’d also find giving up on my habit of the past 6 months hard.”
3) “We have done this the last few years but do it backwards, for us it was much more feasible to save the bigger amounts earlier in the year compared to during the holiday season.”
4) “So do it in different increments instead. You could do $0.25 or $0.50 increments. You won’t save as fast, but it’s better than nothing.”
5) Someone even suggested a geometric sequence: ““DOUBLE IT”
Starts off in cents so you may be able to do it day after day at first however when as the game gets further just do it when you budget and save to finish your game goal. Challenge yourself make it a great goal of money.
Day 1. -One little penny. “Double it” Day 2- two pennies
Day 3 – only four lousy pennies (it’s small now oh but wait there’ more.
Day 5 – 8 pennies (Don’t cheat now and put all of it in for the week this is where the game comes into play and you start building your discipline for when it starts getting difficult. It makes it so you want to participate all the way through starting with only a penny. you will want to be putting money aside for the days to come because it starts growing fast after we are on day 11.
Day 6 – 16 cents. Day lucky 7 – 32 cents
Day 8 – 64 cents Day 9 – $1.28
Day 10 – $2.56. Day 11 – $5.12
Day 12 or day of 12th deposit – $ 10.24 and so on”

if you give a math student a comic strip

By Kristina


When pondering logic projects, I found a lot of elementary school “create your own math books” based on If You Give a Mouse a Cookie plus some comic strip projects that incorporated other aspects of logical propositions (antecedent, consequent, inverse, converse, and contrapositive). I added a rubric for design, captions, and presentation.

Comic Strip Project

I used my coworker’s copy of If You Give a Mouse a Cookie to introduce the project to my 12th grade classes (many of whom remembered it fondly from childhood). Oddly enough, the students liked being read to! I also started a comic to explain how events could be linked in a logical chain.


Logic_comic_strip_on_StripGenerator.I crowdsourced for comic book generators on Facebook because the only comic strip generator I know is Bitstrips. One friend suggested StripGenerator. I’m glad he did, because Bitstrips was not accessible on our school’s computers, and the iPhone app didn’t easily lend itself to creating multiple-frame comics. A student did use the iPhone app, but she ended up having to put six frames into a collage with another app. StripGenerator also allowed students to save their comics as image files and easily upload them to JupiterGrades.


peetakatnissSome students wanted to make their comics by hand, and I allowed them to do this provided that they took a picture of their comics as backup.


Most Common Mistakes:
1) Forgetting to turn in design sheets
2) Not creating a circular chain
3) Missing transitions between panels (not having the next frame’s antecedent be the consequent of the previous)

speed dating – two versions

By Kristina

A few months ago, I started using f(t)’s speed dating as a review activity in both 11th and 12th grade classes. Even now, many students seem to crave the passivity of copying down notes from lectures. I’m trying to make class as active as possible for them as I can–if I’m solving problems, then they’re not experiencing the work.

Take 1

My first attempt was with function transformation in 11th grade, using the cards from Cheesemonkey SF. My classroom is crammed full of mismatched tables rather than desks, so I asked my 12th advisory to create a long table setup at the end of their class. I made these directions based on the original blog post and went through them with the students ahead of time.


1) Find a seat.
2) Get a transformations problem. Solve and become the expert on that problem for the day.
3) Raise your hand to check your answer with Ms. Danahy.
4) When ready, trade problems with the person across from you and work it. If you have a question, ask your speed dating partner.
5) When ready, get your original problem back.
6) One row stands up and shifts in the same direction. The student on the end that gets bumped off circles around to the other end.
7) Now everyone should have a new partner and trade problems.
8) Repeat ☺

The whole process proceeded somewhat awkwardly. I ended up with an odd number of students, so I pulled one student who had been flying through the topic to be an answer-checker with me for step 2. Some similarly bright students finished their problems before I even finished reading the directions out loud, while others had to be prodded multiple times to start. Having the answer-checker helped, but we had trouble maneuvering around the huge table formation and keeping track of whom we had checked. The timing difference between the slowest students and the fastest students on step 2 caused a huge delay, so we didn’t get to do that many problems. I would like my students to be self-sufficient enough to do well with this structure, but we have some work to do.

Take 2


I tried this again with my 12th grade math classes a few days later. I pre-divided each class into groups of three students of mixed ability level and put these groups on the direction papers.

1) Divide into the following groups [groups listed here].
2) Get a truth table problem. Solve and become the expert on that problem. All group members should solve the problem before trading.
3) Raise your hand to check your answer with Ms. Danahy.
4) Trade. At the end of each round,
all groups get their original problem back.

Round 1 Round 2 Round 3 Round 4
1 trades with 5

2 trades with 6

3 trades with 7

4 trades with 8

4 trades with 5

1 trades with 6

2 trades with 7

3 trades with 8

3 trades with 5

4 trades with 6

1 trades with 7

2 trades with 8

2 trades with 5

3 trades with 6

4 trades with 7

1 trades with 8


In the initial solving round, I drew a diagram of the room on the board and labeled each table with their number. I put check marks on the board diagram when the group had found the answers and continued to do this in subsequent rounds so that we could keep track of when to move on. I liked that the mixed abilities and group support kept the class moving at an even pace and encouraged the students to teach each other (something that has been hard for some of the brighter students to do).

happy 2015

By Kristina

In the past, I’ve made tons of New Year’s resolutions. These resolutions often include blogging more, and I haven’t been able to get the habit to stick. My habits often fizzle out because I make too many goals and set myself up to fail by making the standards for success unreasonable (much like a resolution exerciser who claims she’ll go to the gym every day for two hours, convert to a Paleo diet, and quit coffee cold-turkey).

I admire Relearning to Teach for sharing daily reflections on his teaching and putting it all out there–not just the lessons that go well. I share snapshots of my lesson ideas on Instagram a lot because it’s quick and easy, but it doesn’t help me improve if I don’t thoughtfully reflect on how things went. I also get a lot of good ideas from other bloggers and appreciate when other folks share how these ideas went for them or what modifications they made, so it’s time to start doing that too.