Posts Tagged ‘lesson’

popcorn challenge

By Kristina

You are trying to decide what popcorn containers to select for a school movie night.

For the four types, calculate:
1) Volume
2) Surface Area
3) Cost per Cup of Popcorn (hint: you’ll need to find out some more information).

The challenge: come up with new popcorn containers that hold the same volume but have less surface area (so they cost less to produce).

Screen shot 2013-03-05 at 9.18.13 AM

Authentic Movie Night: The small plastic tub costs $1.99. It measures 5.25″ across the top and is 5″ tall. The large plastic tub costs $2.99. It measures 7″ across the top and is 7.25″ tall.

Pop-open Popcorn: These cardboard tubs have dimensions 4″W x 8″H. They come in packages of 100 for $22.99.

Movie Time Red: This square plastic tub is 7” by 7” and costs $9.99.

The kids figured out that they had to find the number of cubic inches per cup, so I showed them how to do the conversion by typing it into Google.

photo (2)  photo (1)


Some kids figured out to take the second tub and turn it on its side so that the opening would be on the long side (holding the exact same volume but removing a bunch of the cardboard).

I liked this activity for having students manipulate real-world shapes and present their work in front of others. Some groups in one class didn’t get to this challenge activity because they needed more time practicing volume calculations, so they served as judges for choosing the best modifications to the popcorn boxes.


let them eat cake

By Kristina

The world is serendipitous. I ran into Hannah Lesk (grad student from HGSE who worked on Radix for a bit) at the LearnLaunch conference yesterday, and she gave me a cool idea for surface area and volume from Wayne Thiebaud’s Cakes.


Now pondering my design of problems relating to icing, pricing, and packaging. I’m thinking of having them calculate the cost of icing all the cakes in the picture (based on surface area), and then figuring out how many cakes they could store in a school store pantry before selling them for prom fundraising (using the cake caddy).


I’m also thinking of doing some pan conversions.

The Great Apartment Remodel of ’13 – Flooring

By Kristina

Here’s my first foray into the Great Apartment Remodel of ’13 – inspired by Everybody is a Genius.

You’ve been thinking about redoing your apartment’s floors. Your cat threw up in all the carpeted rooms, your friend Sally spilled nail polish all over the bathroom, your friend Jean spilled hair dye in the other bathroom, and your science project burned a hole in the kitchen floor.

However, it’s your lucky day. You won a raffle for a ₤500 gift card and your Grandma Sally has given you $100 for your birthday. 

What rooms will you choose to remodel? Why? Show your calculations for required flooring needed and how much it will cost. Assume 7% tax and ₤30 for shipping. Beware the unit conversion!

I also gave students the sample floor plan shown above as well as a printout of laminate flooring options from I wanted to have actual samples like Sarah’s project, but also wanted to include the currency conversion for practicing financial math and meters to feet conversions, so I went with a British company. When students heard that we were going to be designing dream houses as a culminating assessment, a few clamored to build theirs, so we might do that!

After introducing the assignment to students, I asked them to work independently and figured out if there were any clarification questions they wanted to ask me. Sure enough, there were:

How many euros are in a dollar?
I clarified that the symbol was for a British pound and told them how to google “pounds to dollars” and gave them the conversion “1 British pound = $1.60.”

How many centimeters are in an inch?
I picked up one of the class set of rulers and asked a student to read off the centimeters and inches, giving them “15 cm = 6 inches.”

Which rooms are carpeted?
Having lived in a house that had a carpeted bathroom, I gave the students the option to explain their own assumptions for carpeting.

How many cm^2 in one m^2?
We touched on this last year in unit conversions and SI units. I drew a square to represent 1 cm^2 on the board, labeling each side, then guided them to create a similar square that was one meter per side. Too many students think that 1 cm^2 = 100 m^2…but when they see it drawn out, they fix that error.

Many students also asked about the 2.13 sq. m pieces that were on sale on the website, and whether they could buy just one sq. m. They have to buy 2.13 sq. m units and cut them to specification (i.e., they can’t just buy part of a unit).

Non-sequitur reaction: “I don’t want a cat. Can I change it to a dog?”

Evaluating and Graphing Exponential Functions

By Kristina

I borrowed this from Sam Shah to use as the introduction to exponential functions.

I liked the self-guided aspect of this activity. I’m working on instilling more self-sufficiency in my students and learning to let go of the urge to have each minute of the class accounted for.  I would like to work on clearer directions, however. In the second section of class, I demonstrated the first few folds of the paper because many students in the first section just started trying to find the patterns without folding. Additionally, I would like to be able to guide discussions better on the “questions” and “properties” sections.

Unit 3, Lesson 2 (Evaluating and Graphing Exponential Functions)

Jeopardy: The Makeover Edition

By Kristina

I like Jeopardy as a review game, but have found that students get caught up in the idea of “winning” more than they retain knowledge from the review game aspect of it. I updated my Jeopardy plan to make it more about the review. Having explicit directions and clear expectations helped a lot. Cutting down on transition time also helped a lot (i.e., by having the teams pre-selected, having a plan to combine teams if students were absent, creating a graphic organizer so students wouldn’t have to write down the problem before solving).

– Jeopardy handout with problem “shells” – most of the structure there, but blanks for numbers
– Timer
– Whiteboards and markers
– Pre-made list of teams for each class


Each team will rotate in choosing the category and point value.

All teams have the ability to earn points in each round, as long as:
• The designated “answerer” provides the correct answer on the whiteboard within the time limit (set differently for each question). The “answerer” should cover the whiteboard with paper until the timer goes off and the teacher calls for all teams to show their work.
• All team members have the work shown on their papers.

Teams lose points for:
• Incorrect answers
• Having team members not showing the work on their papers
• Screaming out the answers before time is called
• Soliciting answers from other groups (not collaborating with own team)
• Changing their work after time is called

Because this is a test review, please do not ask the teacher for help* during this activity. You should be asking your teammates for help. You are not graded on how many points you receive. This is for helping you practice for the test!

*However, teachers are available to help you during lunch and after school. Please see us then.

**If we don’t finish all 25 questions, that is okay! We want to have about 40 minutes of review. We’ll give you the remaining questions to study with.

The graphic organizer also unexpectedly saved the day. I was originally planning to do this with a projector, but left my cabinet key at home by mistake, so my intern and I completed the lesson by creating a makeshift game “screen” on a large whiteboard and writing the categories + 100, 200, 300, … and writing the numbers to fill in the blanks for the selected problems. My intern also tallied the point totals for each table (replacing the automatic point counter from JeopardyLabs).

The students responded well to this game. I spent a good ten minutes going through the rules and making up fake scenarios (e.g., pretending that Little Sally peeked at Little Jimmy’s paper and asking what score Little Sally’s team would receive). I was also okay with not finishing the entire board–I’m working on “time on task” versus “get through this problem set.” Additionally, my overeager students who typically work ahead were kept with the class because the problems weren’t completely pre-printed.

The Cost of College

By Kristina

One of the syllabus topics in IB Math Studies is financial mathematics. I teach this unit in 12th grade (right around the time of college applications). This year I had the students research a college to which they are applying so that they could examine costs of college using the math they have learned (particularly inflation and compound interest). I wish I’d been able to include more of the topics (depreciation, currency conversion, simple interest, loan repayment tables).

How Much Will College Cost Me?

The goal of this project is to prepare you for the costs of college life. After high school graduation, it will be very important to keep track of your money. If your family is providing you with financial support or you are paying for your own college education, it is best to know what expenses to expect!

1) College Research
For a college to which you are applying, research the following and provide screenshots and URLs as evidence.
– Tuition
– Fees
– Housing

2) Loan Repayments
Calculate monthly repayments for tuition and fees for all your years of college. For instance, you might go to a college for four years or attend community college for two years and transfer. Assume inflation of 7% per year for tuition and fees to calculate the total amount owed. You can use the calculator at and provide a screenshot.

3) Housing
Is the college of your choice near your home? If so, would you consider living at home? List at least three reasons for why/why not.

If the college of your choice would not allow for living at home, compare two housing options (on-campus, off-campus). What are advantages and disadvantages of each?

4) Freshman Classes
Find four freshman classes that you are interested in taking. Explain why you chose these classes. Find the syllabi and what books are required, then find the prices of these books online (with screenshots and URLs).

5) Scholarships
Find three scholarships that you can apply to. Explain how much money they are awarding, why you chose them, and what the major requirements are (due dates, essays, etc.). Provide URLs.

6) Part-time Jobs
Find two potential part-time jobs near your college. Explain why you are interested in those jobs. What are the salaries? How much would you make, before taxes, if you worked up to 20 hours per week during the school year?

7) What If…
What if you had to put one semester’s worth of tuition on a credit card because of an emergency? Choose a credit card and provided screenshots and a URL of the interest rate and any late fees. What would your balance become if you could only pay $100 per month for a year? Show your calculations.

8) Ask a College Student
Ask a JQUS alumnus/alumna about their freshman year experience with college expenses. What expenses surprised them the most? How did they learn how to deal with finances on their own?

Unit 2 Project – College Expenses

In the project submissions, I found that the students had a hard time applying the math concepts in Questions 2 and 7. For Question 2, I should have said “leave the loan interest rate at 6.8% and compute it for 30 years of repayments.” Some students put 7% in because they thought inflation was the interest rate. Many students put in a short repayment (e.g., 4 years) and ended up with monthly payments over $3500. Many students put in only for one year’s worth of tuition rather than 4. For Question 7, some students found cards with 0% intro APR but put in the regular interest rate anyway. Many students calculated interest for a single month and assumed that it would be for the whole year of attempting to pay it off. Not a single one did the calculations that showed how $100 payments for each month would impact the compounding and what would happen to the balance at the end of a year. I’d like to expand more upon this question in future iterations of the project.


By Kristina

Photo Credit:

We started exponential functions today in IB Math Studies. The students attempted to guess the population of the U.S. and the population of the world. Surprisingly, most students guessed way over (about 2 billion). I showed them a clip of the Contagion movie trailer and had them write down the numbers spoken by Jude Law (so that they’d pay attention to the math rather than just the ominous nature of the movie), then see if the pattern matched up with his prediction of 1 billion deaths in 3 months, like in this MathsPig post. Some students asked “are you doing this to scare us away from bird flu?” I wish I had addressed the other factors that affect disease transmission at this point. Would 1 billion have been realistic for three months given geographic location (i.e., more time to transmit from continent to continent) and any slowing in disease transmission (i.e., if people were quarantined)?

We moved on to our Disease Detectives activity (based on this lesson from Georgia Southern University). I borrowed NaOH, phenolphthalein, graduated cylinders, and beakers from my science colleague in the room above mine.   During pre-class setup, I ended up rushing a bit because I had to fill the graduated cylinders with water from the cafeteria sink (the science sink water was cloudy ) and make handouts. I wouldn’t have been able to do this if I had a first period class.

The Setup

I handed out cups of clear solution to all the students, informing them that one student was “infected” (aka Gwyneth Paltrow in Contagion). I instructed the students to interact with two other students by mixing liquids and keep track of the students’ names. Then came the big test: who would be infected? I went around the room with a spray bottle of phenolphthalein to test each cup. The students waited in trepidation, and as soon as the first infected cup turned bright pink, they started screaming. I recommend using clear cups for this…it’s more exciting to see an infected one turn pink. During this round, four students were infected. I had them try to figure out who the original infected person was, but they couldn’t. Neither could I–I didn’t track the infected cup when handing it out.

Uh-oh…someone at this table was infected. Will the next person be too?

After round 1, we had the Great Spill of 2012 when trying to dispose of the liquids. I was hoping to carry them up to the science teacher’s classroom with a Halloween candy bucket, but the bucket started leaking all over the table. We lost about 10 minutes of instructional time sending students out for more paper towels, sacrificing a running trophy to catch the leak, mopping up the spill, and sending students out to wash their hands. However, the students were good sports and we still managed to do another round with three interactions. I forgot to have them estimate the number of students infected, so after we discovered 7 infectees (some of whom started screaming as soon as they realized they had traded with the first person whose cup turned pink), we looked at the theoretical numbers. In round 3, there should have been 8 infected people, but as my intern pointed out, the lower number could have been caused by two infected people trading.

Infected students in Round 2

I enjoyed doing this lesson because of the hands-on, visual aspect and the connection to real world issues. A few years ago, there was a swine flu outbreak at our school, so the issue of infectious disease transmission is very interesting to us.

Link to the lesson: Unit 3, Lesson 1 _Intro to Exponential Functions – Infectious Disease

first day reflections

By Kristina

Even though the first week of school in BPS is only two days long (we start the Thursday after Labor Day), this one felt longer than a typical five-day week! We spent a lot of time preparing for the welcome back assembly, in meetings, and setting up the classroom. I also did a lot for after-school programs (scheduling, student recruitment, presentation for assembly, handouts, bulletin board, guest speakers from community organizations in advisory). I’m glad to be back in and in the school routine again though.

Greet and Seat – I had my intern create the seating groups for each class since he’d gotten to know them in pre-practicum, then made a few changes based on whether students would need more attention, needed to see the board, or would get along better with a different group. I also had him create index cards of fraction pairs for the seat-finding challenge (since the Tarsia card samples I found would take longer for the students to solve than I wanted). The fractions worked well, timing-wise, and having the seating chart as a reference helped us check their “work.” However, our first section was right after the welcome back assembly, where we were given the student IDs to hand out in class. The big rush of students and extra items to hand out made a big backlog at the door. Next time, I may let the students sit (to see where they choose to go) and then have them get up to find their actual seats.

Welcome Back – The short welcome back went fine.

Weekly Seating Change – I forgot to mention this in both classes! I’d forgotten to put it in the agenda on the board. All of the students should know how to handle the seating change on Monday (except those who were in my 9-person class and the one who transferred in from a different teacher’s class), so I will see how it goes.

Respect Exercise – This did not go well. I initially chose a Wikipedia article about Josiah Quincy and an ESPN article about the Patriots’ acquisition of Michael Hoomanawanui. Both articles were too long, at first the students I chose to read did not understand that they were supposed to read at the same time. The length of the reading caused the class to get antsy. For Section 2, I changed the reading material to the syllabus and to a short Onion article about the Cowboys and Giants. That class is a bit rowdier so the activity still did not go well.

Quiet Coyote – I tied this in with respect and an explanation about how yelling to get attention = not good. I think it made sense to the students. I did have to use this a lot more in Section 2.

31 Game – Using the 31 game as a way to assess learning styles was so helpful. The game was engaging and didn’t require the teacher to tell students whether they were right or not. My unexpected takeaway was the need for helping students deal with the feeling of “rage quitting.” To “rage quit” is to give up on something in a huff, often accompanied by an exclamation of frustration or a sulking expression. I noticed that some students kept at the 31 problem the whole time while others rage quit. I would like to work on fighting the urge to quit. I think this will go a long way in getting SBG to work better this year because the urge to quit prevents students from taking the steps for reassessment.

Survey – I moved the survey up rather than making it homework. I focused on computer, calculator, Internet, study habits, and concerns. My intern and I read through all the results after class, taking note of patterns and surprises. I will revisit the math attitudes survey next week.

3-2-1 Exit Slip – Give the students the following 3-2-1 writing activity: 3 goals for the year, 2 challenges, and 1 wish. Some students wrote much more than others, and a bunch of students forgot to do the 3-2-1 activity. I had put the directions on the board and explained them verbally

Homework – I sent home parent homework and the syllabus. I only had Section 2 on Day 2, and all of them brought back the syllabus. Several brought in parent homework (some for parents who did not use email, and some who did but chose to return the paper rather than emailing me).

Advisory – We combined with the other advisory section. We ended up doing a Four Corners activity with statements from the syllabus and the 31 Game. Four Corners is a debate activity in which students listen to statements such as “I feel confident about the PSAT” or “I understand what the school requires me to do for Creativity, Action, Service (CAS)” and then go to the corner of the room that is labeled with Strongly Agree, Somewhat Agree, Somewhat Disagree, or Strongly Disagree. I thought the Four Corners was great for getting a sense of where the group is with respect to college/career and for setting the tone that students will be working in Advisory this year (rather than having study halls or free time). I will bring out the detective activity later on in the semester.

First Day of School

By Kristina

This year I am a grade team leader, so I have a reduced class load. I’m teaching all of the 12th grade (~50 students split into two sections) and two sections of 11th grade advisory. Last year I had three sections of 11th grade, one section of 12th grade, and two sections of 11th grade advisory. The combining of the three class of 2013 cohorts into two cohorts will be a little bit odd. The smaller class sizes (9, 17, and 19) were great. Having a maximum class size of 24 is not bad at all, but I’ll have to scrounge for two more tables and four more chairs before classes start.

The Plan: 

Greet and Seat – Shake students’ hands as they walk in the door. Hand them a Tarsia number match card (inspired by Math in the Middle) to help them find their seat (pre-grouped based on how I knew them last year, mixing the sections). I’m a little miffed that the Tarsia formulator is only for Windows…will have to do that when I get my school laptop back. My intern can help students find their seats as I greet students. We will also check to see if all students seated themselves correctly. Instead of calling out students for being wrong, we will tell a table if one or more students at the table is incorrect (without saying who it is).

Welcome Back – Introduce myself and my intern. Explain that he will be taking over Section 2 for part of the fall/winter. Give an overview of the year (major units and projects, preparation for the IB Math Studies exam, the exam, and the alternative project that non-diploma candidates will complete). Note: I’m not going through a By the Numbers introduction with my students because they all had me for math and advisory last year.

Weekly Seating Change – I started this about midway through last year. I noticed that students worked with the same students every single time we had small group work or a group project. Given that most of them have been together since kindergarten, I thought that we were due for some shaking up. I put the students in different tables each week so they would experience working with new people and different learning styles. They appreciated it (compared to what they may have felt had I simply decreed a completely new seating chart with no friends sitting next to one another and with no explanation), and some found new “school-friendships.”

Respect Exercise – Modify Take it to the Limit‘s respect exercise with the Patriots.

Quiet Coyote – Introduce the Quiet Coyote. I haven’t gotten my “everyone get quiet and focus” routine down immediately in past years, and this year that is going to change. I liked  the “Can I get your eyes up here, please?” routine that I learned in Classroom Management class in grad school, but it didn’t feel authentic when I did it, so it didn’t work for me. I did not like the Zenergy Chime that was so popular in BPS new teacher professional development (PD) classes. Becoming dependent on an external tool to get students quiet seems very inauthentic to me. I definitely do not like plain ol’ yelling. When this is done to me in any sort of class (PD, workout, etc.) I cringe at how students must feel.

Hence, the return to quiet coyote: “his ears are open and his mouth is shut.” Put your middle and ring fingers on your thumb to create the coyote’s shut mouth, and stick your index and pinky fingers up to create the coyote’s ears. If you feel like adding a judging element to your coyote, push the ears forward to create “judging jaguar.” I used this when I was a Brownie Girl Scout troop leader, and it turns out that my 12th graders experienced it in elementary school too. When I debuted the quiet coyote in the middle of the year last year, they waxed nostalgic over it. I like the quiet coyote because it’s calm and allows me to practice “wait time” as well.

Math Challenge – I like the 31 game over at Everybody is a Genius and the observation questions from Coefficients of Determination (listed below and modified for the 31 game versus the diagram ).

1. Are all the students involved? Who is looking around the class or out the window (or whatever) instead of participating in the activity?
2. Who is very focused and studying the game intently?
3. Who simply HAS to talk with his or her neighbor as they process what to do or process how many he or she got correct?
4. Who has to check in with me to see if they’re doing it correctly?
5. Who seems to want to sit back and observe what everyone else is doing before they jump in?
6. Who calls out comments as they’re working?
7. Which students simply can’t concentrate for the short time period you give them to study the diagram? What are they doing? Getting up? Beginning conversations? Fiddling with their “stuff”?
8. As I walk by to see how the students are doing, who wants to talk with me or show me something? Who wants to simply work without interruption?
9. As we discuss our findings, who wants to share? Who seems to want to add their comments more than expected?
10. Which students try to steer the discussion off topic?
11. Which students don’t share at all?

3-2-1 Exit Slip – Give the students the following 3-2-1 writing activity: 3 goals for the year, 2 challenges, and 1 wish.

From Coefficients of Determination: Check the writing the students do for the exit slip.

1. Which students write well? Poorly? Who struggles to communicate their thoughts?
2. Which students invested themselves in the writing task? Who sort of blew it off?
3. Were students able to stay on topic or did they meander all over the place?
4. Who didn’t write anything at all?

Homework – Read syllabus and bring it back the next day for us to go over (practicing organizational skills). Fill out this survey (courtesy Sam Shah and Bowman Dickson).

For advisory, I’ll do Peter Pappasdetective story…would love to fit this into the math class first day, but periods are only 53 minutes long!