January 2016 archive
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-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.
I 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!
One of the best things about my husband is that he loves creating curriculum ideas with me. He helped me develop SAM animation math stories years ago, and recently had his high school interns make some of their own.
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
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.
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 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 http://www.readwritethink.org)
– 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
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.
“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…
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?
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!
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!
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.
I’m researching blackout shades for our nursery and started my design process by polling a few mom groups. One mom suggested Pottery Barn Kids.
These Harper shades are lovely, on sale, and have been positively reviewed at Embrace My Space. However I realized that they wouldn’t work for our nursery upon seeing that all variations were 64″ long. Our windows are almost floor-to-ceiling.
I went in to measure the window widths to see if curtains might work. A friend recommended these Koala Baby curtains, but they would be too short. These Harper curtains come in varying lengths that could potentially be tall enough. However, the smaller windows are approximately 22″ and the large window is approximately 58″. We’d need three 44″ panels to cover the span of the windows without leaving gaps.
Perhaps wider curtains would work? My friend Heidi at This Bold Home recommended these, which are 52″ across. Two of those panels could work! The nursery foiled me again though. This weird ceiling dip also prevents a curtain rod from going all the away across the windows.
Based on all of these constraints, I’m eyeing custom cordless cellular blackout shades that can be installed by the company.Blinds to Go cordless cellular thermal shades seem the most promising right now because the former owners of the unit two floors above ours also used these for their baby’s nursery (same room as Parker’s and same dimensions), so their shades would likely work well in our space. I feel like I *should* DIY and self-install, but I’m neither interested in nor good at it. I feel hypocritical saying “I’m not good at it” because I really dislike it when people say “I’m just not good at math” and give up on it. But, in comparison to something like cooking (which I enjoy and can do without lots of struggle), the time and effort spent on self-installation would far outweigh the cost. I recently had an Elfa closet installed, and the fee was well worth it. It only took the installer an hour to do (while it would have taken my husband or me much longer, and we would have had to have the other person watch Parker).
Other recommendations from fellow moms:
– The Shade Store
– Lowe’s – from the former owner of our unit, who installed plantation shutters in the living room and cellular shades in both bedrooms
– Bed, Bath, and Beyond curtains
– JC Penney cordless cellular blackout shades (install yourself) (though one mom pointed out that
– Home Depot cordless cellular blackout shades