Today a friend emailed this math problem to me.
What *is* the “right” way for math anyway? Is technology inherently less “right” than algebra? Solving it graphically by Desmos (or by TI-84) still solves the problem, but maybe that doesn’t feel as elegant or satisfying. I did want to share the joy of Desmos (since my non-math teacher peers aged mid- to late-thirties did not grow up with it), so I sent the following screenshot (before I eventually solved it algebraically).
“Ha ha, neat toy.
Since I forgot all the tricks to resolve mixes of square roots and variables, I looked at it as, it must be an integer since what awful brain teaser would have 4.87645372 as an answer, and it had to be a number with an integer square root, and that square root had to be less than half of 15, and the square of that number is 15 less than the square of (15 – that number). So I tried 7 first, 7 + 8 = 15, square of 7 is 49 which is 15 less than square of 8 (64) so that was it. 7 squared, 49. Had that not worked I would have tried 6, 5, 4 etc.
In the meantime, I’ve filled the backs of two envelopes with desperate attempts to solve it algebraically, going nowhere.”
Poor friend! Sent this to him:
I then sent it to my math colleagues (and my boss, who is a former math teacher).
Boss’ response, which I will ask to see in its original form, since email apparently translated it into gibberish.
Alternate Hint: Try putting the square roots on different sides of the equation and canceling 🙂
I took a pic of my work but don’t want to spoil it… email me if you want a look-y-loo. Thanks for the Thursday PM pick-me-up!
I emailed her to trade answers and she solved it this way. It made us both happy to solve it algebraically, but differently!
So there you have it:
1) logical way
2) graphical way
3) algebraic way #1
4) algebraic way #2
…how many more ways?
As much as I dislike Facebook, I do find value in the “On this Day” feature. From April 21, 2011, I wrote this note. Six years later, 3) through 6) are still so important for teaching (and now parenting). Six years later, we have Google Classroom, SeeSaw, Workplace, ClassDojo, Khan Academy and countless other technologies that increase our ability to access content or transmit content to our colleagues or students. Six years later, we have Amazon PrimeNow to get whatever baby product we need within two hours. We have similar access to “wisdom” via countless online mommy/baby forums, sleep consultants, and ScaryMommy/Pregnant Chicken-esque blogs. We can also transmit our content in those forums, in mommy Facebook groups, or on group iMessage threads during late-night feeding sessions.
Increasing access to or ability to transmit content doesn’t make teaching or parenting any easier if the emotional aspects aren’t addressed.
“From my roommate, who attended a talk about happiness by an HBS negotiation professor tonight. The HBS students voted for the three professors who they wanted to hear from, and these are the main points of the first talk.”
1) Quit early and often. Save up enough to make it monetarily possible for you to do so, and make your own choices.
2) Create value and worry about monetizing it later. The opposite is thievery (going where the money is and trying to create value).
3) Cultivate empathy. See the world through gentler eyes, because you will be better for it.
4) Learn humility. Either humility or arrogance is not enough; you must have a combination to succeed.
5) Learn from unlikely sources and don’t judge your teachers. Everyone around you can teach you something. Even if it’s harsh, if you are willing to take it, you can’t go wrong.
6) Make time for reflection. Ask questions about who you’ve become and who you were. Build in this time to keep reevaluating. You don’t need to aim for being stagnant and stable. Inevitably, things will change about you.
Via a fellow Mom of Camberville 2.0. #solidarity
I’ve been thinking a lot about how to better balance work and life so that teaching is sustainable for the long haul. Balancing the demands of parenting a toddler with the demands of teaching and IB coordinating has made year 9 of teaching much more challenging than the first few years. I have often told my senior students to make the most of college because “you will have the most free time you have ever experienced in your life, and that will be a blessing and a curse.” I wish I’d learned that lesson about teaching, because until my “free” time got cut by about 80%, I didn’t realize how important it is to find efficiencies versus just throwing more time at lesson planning. I take a lot less work home now, but I’d love to reclaim more night and weekend time (especially during end-of-term grading or around major IB events).
Here goes today:
4:40 a.m. Alarm goes off. Snooze when contemplating starting Day one of the Blogilates PIIT28 challenge.
4:49 a.m. Alarm goes off again. Get dressed, put contacts in, and wander out to the living room. Look up “how to work out in the morning” and find a Parenting magazine 10 minute workout.
5:00 a.m. Warm up with some dynamic stretches. Start kettle for French press. Do the workout.
5:20 a.m. Pour coffee. Shower and get dressed. Cook breakfast (egg scramble for me and husband, milk, sliced banana, and peanut butter toast for toddler).
5:49 a.m. Toddler wakes up. Sing good morning song and change his diaper. Consider logging the wrestling holds used during the diaper change as part of my morning workout. Eat breakfast with toddler and husband. Clean up and pack daycare bag.
6:37 a.m. Leave for the T (husband is taking car into shop to repair a broken headlight). Sometimes the T is more enjoyable than driving–it’s fun to read and to walk vs. sitting in the car listening to Spotify or a podcast.
6:46 a.m. Barely miss a Braintree train, so spend some time writing down notes for this post.
6:56 a.m. Catch Ashmont train. Run into teacher friend on his way to his school and chat until Central Square. It’s good to chat about peer feedback and commiserate over the challenges of teaching before break.
7:11 a.m. Walk from Charles MGH to school via the Public Garden. Fun sights on this walk: gingerbread houses in the Hungry I restaurant and knitted hats and scarves on the Make Way for Ducklings statue.
7:31 a.m. Arrive at school. Make copies of reassessments, peer grading rubrics, and progress reports. Reserve Chromebooks. Start looking for teacher with backup key because the teacher who normally has the cart is out. Put up plans on the board.
7:50 – 8:37 a.m. 9th grade system of equations coffee project work day. Hand out progress reports and feedback to students. Think about how to revise this project for next year with Hacking Assessment and Strength in Numbers.
Revision ideas, from Hacking Assessment: Meet with groups to hear ideas. Help them ensure they stay on target and complete the systems of equations tasks on Google Slides and Desmos. Use feedback to troubleshoot, not provide answers. Help them discover knowledge on their own. When they work, discuss progress and observe group dynamics to see that all students are contributing. Try individual feedback (check out Grading and Group Work). When students are done, do a gallery walk on Chromebooks. As groups, to take notes, make questions and comments (on paper? on the docs themselves?) Provide feedback based on the IB Rubrics using a Google form. Have all students submit a reflection and self-evaluation about what he or she learned as compared against the standards so we can discuss growth. Students should reflect on what they had hoped to get out of the project and share what they learned.
8:40 a.m. – 9:00 a.m. Answer emails and make slight revisions to lessons.
9:00 a.m. – 10:17 a.m. Meet with other IB coordinator and leadership consultant to plan out our school leadership team meetings for January as well as some longer-term Diploma Programme and Middle Years Programme initiatives for Terms 3 and 4. It feels good to “backwards plan” our leadership work like we do to unit plans.
10:20 a.m. – 11:07 a.m. 12th Math Studies class. Students are to finish trig fairy tale work, but it turns out that four of the eight students are out for dance rehearsal. Turns out fine because of having to attend a parent meeting from 10:26 – 10:40 (with sub coverage from our office assistant).
11:10 a.m. – 11:57 a.m. 9th Math Enrichment. Groups finish up gingerbread house building and photography. They start reflections. Half the class came in late after dance even though rehearsal was only supposed to be from 8:40 – 10:17.
12:00 p.m. – 12:20 p.m. One group stays through lunch to finish their house.
12:23 p.m. – 1:10 p.m. Work on more school leadership team planning. Write emails. Make project adjustments for both 9th & 12th grade.Set up sub for two PD days in February. Add Sierpinski Christmas tree and Kirigami snowflakes to Math Enrichment plans for the week.
1:13 p.m. – 2:00 p.m. Repeat the 9th A-block plan from 7:50 a.m., but in a more energetic atmosphere. Afternoon and morning classes are so different in terms of motivation challenges.
2:03 p.m. – 2:50 p.m. Tidy up Chromebook cart and charge it. Check with headmasters if it is ok to build a Sierpinski tree. Change it to non-denominational tree. Obtain pink card stock from secretary and scrounge up some ecru card stock in my cabinet (at least it won’t look like a typical Christmas tree). Research Mandelbulb ornaments and log this idea for a potential 3-D printing project next year. Update coffee project progress in Jupiter Ed. Make copies of the snowflake patterns and Sierpinski nets.
3:19 p.m. Sign out. Walk to Charles MGH.
3:39 p.m. Catch train, respond to emails, and read Glamour.
4:06 p.m. Arrive at home. Check mail, put away laundry and dishes, and prep French press while listening to Dinner Party Download podcast.
4:45 p.m. Walk to daycare. Toddler’s face lights up when he sees me at the window. He runs over to his cubby to get his jacket. Talk to the teachers about his day while trying to get him into his vest and jacket. Get toddler into stroller and walk home.
5:19 p.m. Get home. Feed toddler mac and cheese, one small avocado, an applesauce pouch, and water. Play with toys, read books, and chase him around the house.
6:20 p.m. Start bedtime routine.
6:42 p.m. Toddler is asleep. Make pizza. Watch three episodes of Happy Endings. Do dishes. Prep toddler lunch and put quinoa out to cook in the morning for part of our lunches.
8:17 p.m. Write this post.
9:00 p.m. Read a little and go to sleep.
Last Sunday, I ran the Cambridge Fall Classic 5K with the Fit Flock team of chefs and bloggers.The Fit Flock is a joint effort between the American Lamb Board and BostonChefs.com to celebrate lamb as a nutritional and flavorful protein option. Fit Flock provided us with race bibs, shirts, a team tent, and an after-party at the Smoke Shop.
The Cambridge Fall Classic is part of a seasonal 5K series along with the Winter Classic, Spring Classic, and Summer Classic. It follows the same course as the An Ras Mor 5K and is easy to get to by T (Red Line to Central Square) or by car (because Cambridge parking permits aren’t needed on Sundays). The course is also easy for spectators to navigate. My husband and toddler cheered for me on Mass Ave at the start of the race and again near the end of the race.
Bib and shirt pickup went smoothly. I appreciated that the race staff allowed separate day-of pickup with teams. We spotted a Fit Flock member dressed in a full lamb suit on Main Street as we were looking for parking, and he was right next to the pickup table. Parker was a bit befuddled by the lamb though!
I headed over to the start, where I spotted Nicco, Ellie, and Lexi from Commonwealth sporting their Fit Flock shirts. It was Nicco and Ellie’s first ever race! We chatted for a bit, and then we were off!
The weather was surprisingly humid for mid-September, so the gradual uphill for the first 1.5 miles felt difficult. Seeing Ethan and Parker gave me a much-needed energy boost there!
Finishing felt great! I ran this race over a minute faster than I did the An Ras Mor 5K, so I was happy to see that improvement.
Post-race, we headed back home so Parker could eat and nap. Parker loves the lamb tagine from the Baby Led Weaning cookbook (pictured below from meals earlier this month), and we look forward to making more lamb dishes for him (starting with the LEON Naturally Fast Food lamb and apricot balls!).
Thank ewe, Fit Flock!
In the past 13 months of motherhood, nights out have become a scarce commodity. When Leah invited me to a Parents’ Night Out at Trade, I jumped at the chance to enjoy delicious food and drinks with Dave, Debbie, Leah (and her daughter), Kim, Kimberly, Nancy, Phyllis, and Sharon. Bonus: no one threw their food on the floor, shrieked at the top of their lungs, or played peekaboo–though a toy fish did appear in one of the beverages!
Being out so late (7:30) on a school night made me feel like I did in the days before teaching and motherhood! So did the lively conversation, which was as full of sassiness as it was full of useful parent advice. My biggest takeaway: blogs, Twitter, and Instagram aren’t awesome just because of the information and pictures–they’re awesome because they help enable interpersonal connections to people with common interests (when you finally get to meet them!).
We toasted to our night out with the Beets by Trade, then sampled the following from the dinner menu:
Raw Bar and Small Plates
Salmon Poke with serrano, red onion, avocado and plantain chips
Buttermilk Fried Quail with harissa aioli and pickled root vegetables
Falafel Pancakes with tzatziki, serrano and scallion
Chicken Meatballs with tomato vinaigrette, garlic cream and pine nuts
Fried Sweet Potatoes with salsa verde and orange
Tasso Ham and Smoked Gouda Flatbread with roasted corn, pickled pepper and onion
Mushroom and Fig Flatbread with gorgonzola, sage pesto and walnuts
Lamb Sausage Flatbread with eggplant, Manchego, peppers and garlic yogurt
Seared Salmon with shredded kale salad, lemon-tahini vinaigrette and pistachio
Oven Roasted Half Chicken with fried potatoes, lemon aioli and charred romaine
Painted Hills Bavette Steak with arugula, french fries and 540 steak sauce
Baked Rigatoni with spicy lamb ragu and provolone
Just when we thought we couldn’t eat any more, out came a Not a Cloud in the Sky cocktail and dessert:
Milk and Cookies: chocolate shortbread, buttercream and crema spressa
Ginger Ice Cream and TRADE Brownie with chili-chocolate sauce, candied ginger, and dukkah
Thank you, Trade for the amazing parents’ night out! Looking forward to visiting again on a girls’ night out or a date night!
540 Atlantic Ave, Boston MA 02110
T: South Station
Parking: Atlantic Wharf Garage at 280 Congress Street or valet
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A- Age: 35
B- Biggest fear: Heights/falling or ghosts
C- Current time: 2:46 p.m.
D- Drink you last had: decaf soy latte from Nine Bar Espresso
E- Every day starts with: the song “What Is Love” blaring from my iPhone alarm
F- Favorite song: whatever parody we are making up for snoop’s lullabies
G- Ghosts, are they real? yes
H- Hometown: Arlington, Virginia
I- In love with: husband and baby (aka snoop)
J- Jealous of: teachers who have figured out how to leave the job at work and keep the worry out of home
K- killed someone?: no, but why would I admit that in one of these surveys?
L- Last time you cried?: a few weeks ago
M- Middle name: Quimson
N- Number of siblings: 2
O- One wish: win ridiculous PowerBall jackpot for the purposes for paying off (and procuring new) family real estate as well as buying whatever I wanted for my school
P- Person you last called: mom and dad (on FaceTime with snoop)
Q- Question you’re always asked: why are we doing this?
R- Reason to smile: husband and snoop
S- Song last sang: the “good morning song”
T- Time you woke up: 7:02
U- Underwear color: striped
V- Vacation destination: next one is cabin with husband and snoop
W- Worst habit: procrastinating and impulse shopping
Y- Your favorite food: today, chicken pho
X- X-Rays you’ve had: teeth
Z- Zodiac sign: Scorpio
While my students were working independently in math enrichment recently, I overheard some non-math-sounding talk.
Student 1: “I’m going to the mall later.”
Student 2: “Oh what are you getting? I want to get her candy and earrings.”
Student 3: “I can’t get Granny anything this year.”
Student 1: “You just spent all your money on food!”
Realizing that they were talking about Mother’s Day gifts, I thought about what I’d want now that I’m a new mom. Since you can’t box up “8 hours of continuous sleep a night + a magic genie that cleans the house while crafting impeccable lesson plans,” this is what I’d want:
1) Things that are Pretty and Relaxing
Pampering-related stuff like this True Moringa Mother’s Day Gift Box would be awesome because it’s pretty, relaxing, and socially conscious. I received a sample of the all purpose body oil to try. It’s great for moisturizing especially since the weather’s stayed cold and gloomy this year. Theo dark chocolate is one of my faves to snag at Whole Foods while passing through the chocolate section. Prosperity candles are soy-blend, hand-poured by women refugees, and come in a variety of scents and styles.
I bought the bridesmaid versions as wedding favor gifts almost two years ago, and I think this Kate Spade Mom Idiom Bangle would be pretty sweet to wear now.
Starbucks and Dunkin Donuts gift cards might seem impersonal, but they still help SO much in terms of caffeination and saving time. In spite of being an avid French press and cold brew coffee maker and knowing how much making coffee at home saves, sometimes I’d rather spend a little more time chilling with my son now than cleaning up all the coffee grounds and equipment.
3) Cute Things Made By My Child
I can’t wait for the cards with backwards R’s and the macaroni necklaces spray-painted gold (if kids even still make those)…look for me sporting those in a few years!
I recently received a copy of The Perfect Portion Cookbook to review. The Perfect Portion Cookbook includes 150 healthy, easy-to-prepare recipes with a 100-calorie portion system for counting calories and managing portion sizes. The website also offers helpful tips and videos.
As a new mom, I’m not into the “must immediately get pre-baby body back” attitude, but I really appreciate the simple, healthy takes on comfort food in this cookbook. It’s so refreshing to see mostly real, unprocessed food versus something like “three-ingredient protein pancakes” or a healthified version of rich food that uses non-fat, sugar-free “diet” ingredients. The familiar comfort food nature of the recipes offers a good base for making small tweaks or customization. The recipes don’t involve a ton of prep work or active cooking time either, which is great for getting back into cooking as a new mom. I made four of the recipes: blackened cod, 100 calorie biscuits, tuna melts, and cheese crackers.
I’ve been finding great cod at Market Basket lately, so I was excited to try this out. My usual go-to cod recipes involve mayonnaise + sriracha + panko bread crumbs or butter + panko bread crumbs, so the blackening spice in this recipe was a much lighter alternative. On the first attempt at this, I served it with some pasta on the side and topped it with a squeeze of lemon and some chives. Overall, the flavor was good (though my husband found it a bit spicy). I wish I’d adjusted the spice amounts more better because the filets were pretty large. The second time I made it, I added some paprika and decreased the cayenne. I also tried to get a better sear on the fish and served it alongside jasmine rice with kale, garlic, and shallots. I will definitely keep this in my repertoire.
100 Calorie Biscuits
I’ve had yogurt biscuits on my to-make list for a while, so I was glad that The Perfect Portion Cookbook included them. I used a mix of whole wheat flour and all-purpose flour and Fage 0% yogurt, and served them with butter and strawberry jam. They didn’t turn out as well as the biscuits I have made with grated frozen butter and buttermilk lately, but I’ll give them at least another try to see if I can improve my dough-making or biscuit shaping or tweak the baking time.
I really liked these. I used Cabot 3 year aged cheddar, Hellmann’s mayonnaise, whole grain bread, and Bumble Bee light tuna in olive oil. I subbed celery for tomato. The bread I bought was small, so there ended up being enough to make one more tuna melt each the next day. If only I had a toaster oven at work…I’d be making these every day!
I’ve been intrigued by Smitten Kitchen’s goldfish recipe, so I used a goldfish cutter on The Perfect Portion Cookbook’s recipe. I used a screwdriver for the eyes and a 1/4 tsp spoon for the smiles. I also added some Old Bay seasoning to the crackers. I took them to school with me and gave some to my students. Some said they were too salty (too much Old Bay?) but one commented that they tasted “just like pizza goldfish.”
Looking forward to making more recipes from this cookbook!
When getting ready to start maternity leave, I created a Google Calendar called “Parker” and promptly filled it with every single potential support group or maternity leave activity that I heard about from friends, my pediatrician, and Mt. Auburn Hospital. For example, I had bookmarked this post (from exactly three years ago!) and thought that I needed to attend multiple activities every single day of the week. Though Parker behaved better and I felt a lot happier on outings, I soon realized that having a few consistent activities and room for flexibility worked the best for us.
Class & Free Drop-In Groups
Having spent most of my teaching life in very structured time blocks, I longed for the familiar comfort of school when faced with the prospect of unstructured maternity leave. I signed up for the JCC New Arrivals (0-3 Months) and Getting to Know You (3-6 Months) classes at Ready, Set, Kids! in Arlington thinking that parenting classes would help me figure out how to be a mom. Early on, we did check-ins and had a group discussion/lesson about pertinent developmental topics such as sleep, breastfeeding, or preparing for the return to work. As the babies got older, we got to do more activities with them (such as parachute play or the ball pit). I appreciated getting to learn in a small group setting from an experienced teacher and in the company of mothers who were facing similar challenges. Each week, our teacher Liz did an amazing job of focusing each week’s discussions so that we could make progress without getting overwhelmed by the sheer multitude of parenting information that’s out there. I’m sure a lot of the information could have been found via Google, but the filtering definitely helped me focus on Parker’s development. Similarly, the strong personal connections in our small group were worth so much more than the class tuition. Even though I’d come into the class not even thinking about creating a support network, I left with a lot of wonderful mom friends. We spent many a fall afternoon relaxing at Kickstand Cafe or Common Ground, and now we’ll meet up for small “reunions” when there’s a holiday such as Presidents Day.
I don’t have pictures of the Medford group because phones aren’t allowed…this is Parker at a pre-group lunch at Colleen’s.
Two of the women in my JCC classes recommended the Medford New Parents Group as well. This free group meets at Medford High School on Tuesdays, and it’s for parents of children up to 1 year old. Each week, members will check in with their highs and lows for the week and then have an open discussion (one conversation for the entire group). A few folks often meet up at Colleen’s for lunch and some social time before group. Though this group’s facilitator is just as excellent as the JCC one, it has a completely different feel than the JCC classes. It’s drop-in, so it’s a lot bigger with less consistent attendance. There are dads as well as moms (no dads allowed at the JCC classes), second-time parents, and working parents. The discussion topics don’t follow a developmental timeline–for instance, they often arise out of circumstances such as wanting advice for holiday travel. I really enjoyed learning from parents with older babies in this group. Even though they weren’t struggling with the same challenges I was, they often had great advice from having gone through those experiences already. Another bonus: seeing their babies sitting up, crawling, and walking gave me stuff to look forward to for Parker. I also really appreciated that Aine, the facilitator, has a way of making everyone feel welcome and like they can move forward from even the most frustrating of circumstances.
The Library: Cambridge Public Library Lapsit
The library was always one of my favorite spots as a child, so I’d always planned to take Parker there for storytime and crafts. A few friends recommended the baby lapsit (with the caveat that the competition for tickets got so fierce that you’d have to arrive an hour beforehand). At first I thought that was crazy, and didn’t even attempt to go until Parker was 9 weeks old. I took a friend’s advice to go at 9:00 a.m. to pick up a ticket for the 10:00 a.m. lapsit and then go across the street to Darwin’s for a coffee. Parking in the library garage is cheap and easy to find on Monday mornings, which helps with early arrival. When the weather was nice, I’d stroll Parker around the neighborhood and check out the corgis playing in the nearby dog park. Sometimes I’d pick up books for myself in the new fiction section, read board books to Parker in the children’s room. I liked that the children’s room was so welcoming–it’s super clean, has ample bathrooms and changing tables, and lots of couches to sit on and nurse. It’s always hopping with parents, caregivers, and kids.
The lapsit itself lasts about 20 minutes. Julie the librarian (and her model baby Jake, a Curious George doll) leads the group in singalongs and finishes with reading a board book. The “good morning” song always starts, followed by introductions of the babies. The songs are consistent from week to week (to help the babies with language development). The lineup usually includes Pattycake, The Wheels on the Bus, Tony Chestnut, Kissing Frogs, Open Shut Them, Dump Truck, The Noble Duke of York, Trot Trot to Boston, Let’s Go Riding on the Elevator, Jumping Frogs, and Twinkle Twinkle. Even when Parker was going through fussy stages, he was always enraptured by all of the singing and the other babies. I grew to love it as a way to kick off the week.
Other Fun Stuff
We also liked:
– hanging out in coffee shops or restaurants (especially Diesel, Dwelltime–now Barismo, and Bagelsaurus)
– walking on the Minuteman Trail, Somerville Community Path, Alewife Greenway, Fresh Pond, and the Fells
– Capitol Theatre Baby Matinee: only went twice, and realized that this is best for really young babies…at six months, Parker would want to be entertained constantly rather than just sleeping through the movie.
– O2 Mommy Baby Yoga: only went once, and now I wish I’d been able to go once he hit six months because he doesn’t need to be held as much and would probably be happy exploring toys on the mat.
Stuff I Wish I’d Tried
I know it’s impossible to do everything, but I do wish I’d tried the following:
– Little Fox Library Singalong
– Jeff Jam Singalong
– Museum of Science (esp. because I could go for free as a K-12 teacher)
– Trustees of Reservations hikes
– Hike It Baby