MTBoS Week 4: sharing a lesson

By Kristina


It feels good to be back at school! Here’s my 9th grade math lesson from day 2 (the first day of Coordinate Geometry), for the two 47-minute sections.

Day 1: 1-a Distance Formula
1) Name Graphs: Check off completion. [This assignment was to have students write their names on graph paper using only straight lines that begin and end at coordinate points on a grid.] Have 3 students draw a letter of their names on the board with points labeled.
2) Practice Quiet Coyote [my routine for getting attention–his ears are open but his mouth is shut]
3) Mini-Lesson: Distance Formula [taught using the 3 student examples]
– Look at how to solve for vertical and horizontal line distances.
– Look at diagonal distances to introduce the distance formula. Elicit the right triangle shape and Pythagorean Theorem.
4) Practice using Kuta worksheet (start with lines drawn on a grid, then ordered pairs). Introduce distance formula.
5) Formative Assessment: Plickers Exit Ticket (1 multiple problem with two ordered pairs) via Kuta multiple choice. Students turn their sheets and cards to the inbox.
6) HW: Haese & Harris Exercise 5A1 (answer key included)
7) Support for Math Enrichment: Extra WS practice. Give feedback on ET.

Section 1: Students were slow to take out paper for notes and turn in HW. We need to make this process more automatic. I noticed that many needed prompting to label the notes with the skill and the date, or even to use their binders (which seem to have grown into a pile in the back of my room over the semester I was out on maternity leave). Some students do have some excellent, organized notes from the past semester, so I might start having students volunteer to share their notes for my “absent work” binder to help absent kids catch up. I forgot to practice Quiet Coyote explicitly but the quieting was better today. For the practice, students really had enough time for the first four problems (mostly because they got stuck with simplifying radicals–the answer key had listed the square root of 8 as 2 square root of 2). I had to write more directions for the close of class on the board to clarify what I wanted for the exit ticket (for example, students didn’t realize they had to turn in their work as well as the Plickers cards). I need to label the Plickers cards with the student names for both sections and make sure they go into a separate bin.

Section 2: This lesson went smoother overall because of anticipating cueing of the HW checking process (in which I handed Plickers cards out to save time later), prepping them to segway from a picture to two ordered pairs, and completing the exit ticket. More students completed the ordered pairs questions, but we will still review. A principal intern came in to observe my class, and it was good to hear this feedback: “Thank you for allowing me to come observe your class today and welcome back!! I liked that you put the answers on the back of the sheet so that they could self check, it fostered more discussion than I would have thought. The students were so engaged. It was interesting to listen to a couple of conversations where the student answer didn’t match the back and so the next step was to ask a partner about what they had come to and why. Plus those Plicker cards were awesome – such a great way to use technology without the lag time. I had never seen that before but I will be sure to remember it for a high tech/low complication formative assessment measure.”

Super Bowl Recipe Exchange

By Kristina

Though the Pats won’t be playing in Super Bowl 50 and we’ll have to be home by 6:00 p.m. for baby’s bedtime, I’m still excited for Super Bowl food! I’m participating in a Super Bowl Recipe Exchange with fellow food bloggers, who’ve created the following delicious recipes:

  1. Slow Cooker Pulled BBQ from Eat.Live.Blog
  2. White Bean & Chorizo Stew from LivinLemon
  3. Buffalo Chicken Empanadas from yours truly
  4. DIY Snack Stadium from Wife in Progress
  5. Homemade Pimento Cheese Stuffed Sliders from Aimee Broussard
  6. Taco Dip from Anchors and Bows
  7. Corn “Tamale” with Black Beans and more from Good Cook Doris

Not only am I sharing with you these great recipes, but I am also excited to offer an opportunity to win a $100 gift card courtesy of Wayfair! You could choose from one of their MANY slow cookers, or any one of a million other things that will make your Super Bowl Party the biggest winner of the night!

The giveaway is open until the winner of the Super Bowl is crowned.

a Rafflecopter giveaway

first day of work

By Kristina


I’ve been looking forward to (and sometimes dreading) my return to teaching after maternity leave. It’s so exciting to get that part of my identity back, but it feels like getting a new job after I’ve been spending so much time learning how to be a mom. Becoming a mom has strengthened and subtly changed my relationship with my own mom. For instance, she recently shared a story about how she left the Philippines to start work at the World Bank. The story was for her baby apo (how you say grandson in Tagalog), but it meant a lot to me too.

She sent these two pictures from January 1971, when she flew to the U.S. with two other women also starting jobs at the World Bank from a group of eight who were recruited from the Asian Development Bank (ADB). She had no idea at all where I was going except the knowledge that she was going to work at the World Bank. Since she was traveling with two friends she just went with the flow. The picture on the left is from her airport sendoff with family (she’s in the fabulous ’70s yellow/orange/green outfit). The other picture was from a stopover in Hong Kong, which was followed by San Francisco, L.A., and then Disneyland. In L.A., she marveled at the amazing things she had never seen before. She had a very enjoyable time because all expenses were paid by the Bank (she had left home with only about $100 in pocket money). On January 31, she and her friends flew to Dulles airport and were met by a World Bank car and driver. They stayed at the YMCA on 16th Street for about four days until they found an apartment where two other ADB girls lived (at 2430 Pennsylvania Ave NW).

Her first day of work was February 1 (I find that symbolic because of today’s date). She recalled being very sleepy at 5 p.m. during orientation and pinching her arm to keep herself awake. She didn’t know what fate awaited her in D.C…only that a certain Florido Buenafe lived on the same apartment floor as her and her roommate Cora. And the rest was history (helped along by my dad trying to woo her by bringing her a watermelon and sabotaging any would-be suitors by telling them that she moved away 🙂

MTBoS Blogging Initiative Week 3: Better Questions

By Kristina

You’re planning a lesson and you try to come up with super good question to ask to get kids to think about something. What is that question? Why did you phrase it the way you did? Why do you think it will prompt discussion/thinking?

I’m returning to work at my International Baccalaureate school on Monday after seven months of maternity leave, and teaching Middle Years Programme (MYP) Math 9 for the first time. I’d written a few MYP-style units before in spite of teaching only Diploma Programme (DP) classes. I’m trying to be more thoughtful and intentional about unit planning now to create more effective assessments that tie into the MYP global contexts, key concepts, and approaches to learning. I felt that my previous MYP units tried to fit those IB components versus having the assessments arise organically from them. I also didn’t want to plan in the disorganized way that I’d done before–thinking by day or by week rather than backwards from assessments. That leads to more daily work in spite of being less work up front. I also didn’t want to develop a creative project as a summative assessment rather than weaving it into formative assessments. I’ve often done end-of-term projects in the past, but this stressed students and me out because the projects were stand-alone and not designed before the unit started.

I listed out the skills for the first unit I will teach (Coordinate Geometry) and brainstormed project ideas that would assess those skills.
1-a Distance Between Two Points
1-b Midpoints
1-c Gradient
1-d Using Coordinate Geometry
1-e Equations of Straight Lines
1-f Distance from a Point to a Line (though after the fact I realized that systems of equations are an embedded skill; not sure how my students are with this)

I thought about trying a water park project like this, but realized that the types of skills I wanted to assess didn’t fit quite right with the way my students would likely design their water parks, so I’d end up making up some artificial constraints that limited their creativity. I was intrigued by the idea of placing benches at the midpoints of walking paths or by designing slides with constraints on the slope, so I tried to explore urban planning projects. Urban planning seemed so perfect for the MYP global context of globalization and sustainability, in which students “explore the interconnectedness of human-made systems and communities; the relationship between local and global processes; how local experiences mediate the global; the opportunities and tensions provided by world-interconnectedness; the impact of decision-making on humankind and the environment.” However, I couldn’t come up with an urban planning project whose scope would be appropriate for this particular 9th grade unit.

I kept coming back to the idea of having students draw pictures with lines of given slopes. I first experienced this in 7th grade (the 1992-1993 school year, eek) when my Algebra 1 teacher gave us an art project in which we had to create a picture using a given number of linear equations (our choice on the equations). I still remember my friend Gwen’s for its clever name. She made a kaleidoscope pattern named “Kaleidoslope.” Mine was “Starry Night on the Slopes”–my take on Vincent Van Gogh’s Starry Night. There are lots of slope picture projects and cool ideas out there (like this from Math Equals Love).

After I impulse-bought this magazine at Whole Foods, I began to explore the idea of artistic expression more.

Screen Shot 2016-01-30 at 8.13.18 PMI started to focus on the global context of personal and cultural expression, in which students “explore the ways in which we discover and express ideas, feelings, nature, culture, beliefs and values; the ways in which we reflect on, extend and enjoy our creativity; our appreciation of the aesthetic” the key concept of form (the “shape and underlying structure of an entity or piece of work, including its organization, essential nature and external appearance. Form in MYP mathematics refers to the understanding that the underlying structure and shape of an entity is distinguished by its properties. Form provides opportunities for students to appreciate the aesthetic nature of the constructs used in a discipline.”), and the approach to learning of communication.

My unit inquiry question will be: How does math influence personal artistic expression? I’ll weave in drawing activities throughout the unit and tie in the current trend of adult coloring books (like this, this, and this). For the final assessment, I’ll have them design their own quilt panel to represent themselves for a hypothetical time capsule that would get buried to commemorate their class (perhaps in a new building) and explore the mathematical properties of the quilt design. Maybe I’ll even get to tie in the history of quilts in the Underground Railroad. I’m psyched about trying these lesson and assessment ideas with my students and to see what they will come up with!

buffalo chicken empanadas

By Kristina

2016-01-30 14.11.20

I enjoy putting a twist on Filipino recipes such as my mom’s empanadas and pancit. Now that I’m a new mom, I’ve started to streamline my cooking by minimizing chopping and using my slow cooker more. Pulled chicken has become quite a staple in our household. For the Super Bowl, I’ve always loved eating buffalo wings or buffalo dip, so my Filipino mom adaptation will be…slow cooker buffalo chicken empanadas! This makes ~20 depending on how big you roll them.

Dough (2 batches of my mom’s recipe)
6 cups all-purpose flour
0.5 cup sugar
1.5 cups water
1 cup butter (cut into small cubes)

2 pounds boneless skinless chicken breast
1 cup buffalo sauce, divided into two 1/2 cup portions
2 cloves garlic, minced
1/2 onion, diced
1 tsp smoked paprika
1 tsp Penzeys roasted garlic
1 tsp salt
1 tsp black pepper

Other Ingredients
2 cups blue cheese crumbles
1 bunch scallions, chopped
3 carrots, diced
1 beaten egg (for egg wash)
Blue cheese dressing and more buffalo sauce for dipping

These pre-chopped onions from Whole Foods worked great, and I might try the mirepoix in filling next time I make it!


1. Put buffalo chicken ingredients (one of the half cups of sauce) into slow cooker and cook for 8 hours on low. Shred with forks. Add the other 1/2 cup of sauce. I realized that this makes a lot of extra filling–it turns out great in lettuce wraps, tacos, salads, and egg scrambles though!


2. Mix dough ingredients in food processor (I do two batches to make sure it fits and mixes evenly) and form into a large ball. Cover with plastic wrap and let sit for about 30 minutes.
3. Roll out dough circles about 6 inches in diameter (from small handfuls of dough).
4. Place 1 or 2 heaping tablespoons of chicken onto the rolled-out dough. Top with blue cheese, scallions, and carrots.
5. Fold the dough circle over to start forming the empanada. Press fork along the curved edge to create a border.


6. Bake at 375 degrees for 30 to 35 minutes on pans lined with parchment paper. After 15 minutes, brush empanadas with beaten egg for coloring, then put them back in the oven to finish baking.


my favorite: trig tale

By Kristina


I originally chose to teach math because I thought that it’d be so cut-and-dry, with one right answer for everything. Eight years later, I find myself looking for ways to assess that have multiple right answers. A recent conversation with two of my best college friends reminded me of that, and led me to pick trig tale for my favorite. One of those friends is a German teacher, and she likes to give open-ended quiz questions that are unlike the typical matching ones. In a recent class, some students got quite agitated at the question “How was your last report card of freshman year?” One student said “but what do you want me to say? that the report card was good?” because she hadn’t studied for that (and probably couldn’t ask fellow students “so what’d you get for number 5?” after class). My friend could tell if they knew the vocabulary if the response made sense, and would have been fine with multiple answers. Another best (but non-teacher friend) piped up and said that in one of her favorite high school English classes, you could get 100% on any paper as long as you could justify your reasoning.

That’s why I like to do these projects in spite of the bigger grading effort that they require. Sometimes students protest the open-ended nature of this and claim they want to just do math problems instead, but they end up getting really into the story lines and figuring how to use the trig in ways that advance the story well. My mentor teacher used this during my student teaching year, and I find that creativity and fairy tales stand the test of time even as technology permeates ever more of the classroom. Though I do appreciate the many ways this could be done on the computer, sometimes it’s just fun to kick it old-school with construction paper and crayons.


The Description

The goal of this project is to have you develop a creative fairy tale that shows your understanding of the trigonometry skills from this unit. You may work with 1 or 2 classmates to outline the story, draft it, and illustrate it in class.

1) Unit Skills (32 points)

Your trig tale must demonstrate the following skills (4 points each, similar to quiz rubric).

Right Triangle Word Problems:
1. Find Missing Angle in Right Triangle
2. Find Missing Side in Right Triangle
3. Find Missing Angle in 3-D Figure
4. Find Missing Side in 3-D Figure

Oblique Triangle Word Problems
5. Apply Sine Rule to Find Missing Angle
6. Apply Sine Rule to Find Missing Side
7. Apply Cosine Rule to Find Missing Angle
8. Apply Cosine Rule to Find Missing Side

2) Writing, Illustrations, and Organization (22 points)

Elements of Fairy Tales (from
– Set in the past—usually significantly long ago. May be presented as historical fact from the past.
– Include fantasy, supernatural or make-believe aspects.
– Typically incorporate clearly defined good characters and evil characters.
– May include objects, people, or events in threes.
– Focus the plot on a problem or conflict that needs to be solved.
– Often have happy endings, based on the resolution of the conflict or problem.
– Usually teach a lesson or demonstrate values important to one’s culture.

The Rubric: TrigTaleRubric


By Kristina

Powerball is all the rage right now. Despite knowing that I could have spent my $6 on something useful, I still gave in to the hype.


Screen Shot 2016-01-13 at 7.52.26 PM

“An Annuity Option means winners can choose to be paid in 30 graduated annuity payments made over a twenty-nine (29) year period. A Cash Option means winners can choose a one-time cash payment which will be (approximately) the cost of the annuity divided by the number of winning tickets. Note: If a winner fails to claim the jackpot and select a jackpot payment option within 60 days, the prize will be automatically paid as an annuity. All prizes must be claimed within one year of the drawing.”

My Facebook newsfeed has been hopping with erroneous applications of dividing the jackpot by the U.S. population as a “solution for poverty,” people making fun of the incorrect math, fun math discussion, and fun speculation of “what would you do if you won?” My friend Heather pointed out “So I tried to figure out a scam to win: if you need 292M permutations to win, at $2 a ticket you need a bankroll of $584M – the lump sum pay out is 62%, and that definitely puts you in the 39.6% income tax bracket… The take home is $487M (not counting the cost of the team of lawyers you now need to employ). Back to the drawing board.” Likewise, my friend Jonathan said “Also, isn’t the $1.3 billion mythical? In the sense that, if one elects a one-time payment, the payout is substantially less, and the $1.3 B number is only achieved by adding together 30 years of nominal payments of 1/30th of $1.3B. Of course, in 30 years, the last payment will be worth less than half its value in today’s dollars. In a real-life conversation, my friend Ashley said that she’d rather take the lump sum and invest it because she could get a better interest rate than with the annuity. I would love to examine the concepts of probability, expected value, inflation, annuity, and taxes with students (not to mention the social aspects of lottery winning). It would make good fodder for a math debate…

Screen Shot 2016-01-13 at 7.40.00 PM

I would also be interested in having students analyze the changes in the Powerball game structure:
“Powerball® Enriched: Starting Jackpots Double to $40 Million
In January 2012, Powerball® was redesigned to bring even more excitement and value to its players. Jackpots in the multi-state game now start at $40 million and grow faster overall. There are more chances to win a prize of at least $1 million cash and the overall odds of winning any prize in the game are also better. Beginning with the January 15, 2012 drawing, game tickets increased from $1 to $2 per wager.
The Power Play® add-on feature is also available for an extra $1 per play. For that extra $1, players have the chance to multiply their prize by as much as ten times. Just before each Powerball drawing, a multiplier number (2X, 3X, 4X, 5X and 10X) is randomly drawn. If a player purchased the Power Play option for an extra $1 per play, that randomly selected number is used to multiply any prizes won, with the exception the JACKPOT and the Match 5 prize (which increases from $1 million to a set $2 million with Power Play).

Powerball with Powerplay gets bigger!
October 4, 2015 – The multi-state Powerball lottery game changed the matrix which is designed to produce larger jackpots and add more winning experiences. In the new matrix, players will select 5 out of 69 white-ball numbers and 1 of 26 Powerball numbers. The overall odds of winning a prize in the game improves from 1 in 31.8 to 1 in 24.9.”

1) How would you approach this with your students?
2) What would you do first if you won the jackpot?

one good thing: friends and puzzles

By Kristina

Today I’m grateful for a fellow mom-friend who said “want to come over and hang out?” when I mentioned that my husband was in Denmark for a business trip. Though interacting with folks via Facebook, Twitter, and text message does offer some solace when at home with an infant, it doesn’t replace the calming effect of in-person time. We chatted a bunch while playing with our babies (who have known each other since ~6-8 weeks of age but only recently recognized each other’s existence). She mentioned that she would be doing Mystery Hunt this weekend and explained it to me when I got intrigued. She shared a few of the past puzzles with me so I could get a sense of what it was like, and then I got hooked. We got to chatting more about riddles we’d enjoyed as kids and spent a while trading ones back and forth about people found dead in various places and having to figure out why. It felt nice to kick it old-school style with just puzzles and human interaction!

2016 Blogging Initiative, Week 1

By Kristina


Option 1: We rarely take the time to stop and smell the roses. Even on the most disastrous of days, good things happen. And these good things, when you’re on the lookout for them, pop up. All. The. Time. So for one day (heck, do it for many days), keep a lookout for the small good moments during your day and blog about them. We bet that by keeping an eye out for the good, your whole day will be even better!

2016-01-12 19.08.39 My one good thing! He’s overseeing my blogging from his “office.”

I’m in the home stretch of maternity leave with my son Parker, so as much as I wanted to share what a day looks like for me teaching math and being an IB coordinator, it feels weird trying to recreate that when I haven’t been in the classroom since June 25, 2015. In the throes of the newborn stage, I quickly realized that there is no “leave” in maternity leave. I missed school–not only the familiar faces and routines but also the feeling of being competent. As a student and as a runner, I’ve previously been able to achieve good grades and better race times. With a known input comes a known output.

But with motherhood, like teaching before it, I have felt so deskilled in that putting hard work in doesn’t necessarily yield a desired result. It’s been a humbling journey, and though each day brings new challenges, I’m starting to find my footing. Over the past few months, I have grown by leaps and bounds since that first day home with Parker (when my husband and I put the car seat down on our floor for the very first time and wondered “how did the hospital let us out when we know *nothing*?”). I feel more confident with taking him out, with soothing him, with feeling like a mom, and with knowing him and his quirks. I cherish our snuggles, outings to baby lapsit, long walks, and co-cooking sessions (when he oversees me from his lion seat). Watching him grow and learn is amazing. Laughs, rolling, grasping, and getting closer to sitting up are all so cool to see.

That leads me to the overall “one good thing” of this post. Being at home with Parker and enjoying these small moments is helping me be patient with where I am rather than always worrying about not doing enough. When I got pregnant, I knew that teaching would become very different as I took on the new role of mom. However, I kept up my old habits and work style right up until the summer because I just wasn’t ready to let go of them and change. Throughout maternity leave, I’ve worried about forgetting how to teach, about my school not needing me anymore, and about how I was going to handle work if Parker still woke up multiple times a night to feed. Recently, I finally started to change my mindset about the onset of work. My brain sometimes still thinks it needs to go into panicky worry mode before every start of school, even though it doesn’t need to do it anymore.

Life will be okay if I’m reasonable about setting my bars for success. For instance, I recently ran without RunKeeper or music and just set out to enjoy the run without setting a pace goal. I could have gone into it saying “well, you *already* failed because you also didn’t double up and do a barre class today” or “if you don’t go faster than your last run, you’ve failed” or “you’re not running five miles at a time yet? FAILED!” Instead I just enjoyed the balmy weather, quiet Tufts campus, and feeling happy for having gone on a run at all. Teaching is going to be fine. It’ll be a tough adjustment, much as getting used to maternity leave was, but I’ll be able to handle it.

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