Something to do with your kids this summer.

This came highly recommended from Peggy Orenstein, a well-know author.

She wrote:
Daisy (my daughter) and I are taking a 6-part online course by math guru Jo Boaler and it is truly life-changing. It is not only changing our relationship to math but to learning as a whole. Only 10-20 minutes per lesson, you can do it any time between now and December and it's FREE. I HIGHLY HIGHLY HIGHLY recommend it for students of any age and their parents!


I haven't tried this yet but plan on doing together with my 11-year old daughter this summer.

Standard heights for your kitchen counter, bar, dining table and other household items.

We are a tall family and over the years and few hellish renovations I gradually learn that we have to stand up for ourselves while convincing architects or Home depot employees in necessity of an extra height for our kitchen counters, vanities and toilets. A few cm do make a big difference for your comfort.

What are the standard household heights a how much freedom do you have?
  • Kitchen countertops: 36" standard. Tall people may prefer 37-38". Short people 32-35". To find the ideal countertop height, hold your elbows out at a 45-degree angle as if you were placing your hands on a counter. The distance from your hands to the floor is the ideal countertop height for you. However, beware that most appliances designed for 36" counter height.
  • Counter stools: 24".
  • Kitchen bar: 42-43".
  • Bar stools: 30".
  • Pendant lights should be hang 40-43" above the kitchen island.
  • Dining tables: 30".
  • Dining chairs: 17-19".
  • Bathroom vanity: 34-35".
  • Standard toilet: 16-17" height. Comfort height toilets for tall people or people with disabilities: 17-19" height.
Find more details in this Houzz article: Easy reference: Standard height for 10 household details.

Top image by Lynn Friendman, distributed under CCL.

Mother's Day Quiz

Life is a puzzle and we - moms - are experts at solving it with logic, humor, and numbers. This quiz by The Math Mom is celebrating moms who are wise, glamorous, efficient, and funny. Motherhood experience is required to answer. The Quiz was originally posted on boston.com

Puzzle #1: Handbag Mania


Mothers, daughters, grandmothers - we all have our passions. One mother could not go to the store without buying a handbag. Leather, plastic, cloth - she loved them all. When asked after a recent shopping expedition "How many did you buy?" she answered: "Three quarters of their number plus three quarters of a bag." How many did she purchase?
Choices: 
  • 30 
  • 13 
  • None
Think a bit, then scroll down to see the answer.









Correct answer is 3. 
Three quarters of their number plus three quarters of a bag is:  3/4 times 3 + 3/4 = 3



Puzzle #2: Mom vs Dad Race.


Mom and Dad are running on a high school track, but in opposite directions. They notice that their meeting point keeps shifting by three steps in the direction Mom is running. Who is a faster runner?

Choices: 
  • Mom
  • Dad
Image by Ed Yourdon, distributed under CCL.











Correct answer: Mom, she does the whole track distance plus three steps while dad is running the track distance minus three steps in between their meeting times around the track.



Puzzle #3: Speedy Breakfast



You are making grilled cheese sandwiches on a pan that is just wide enough for two slices of bread. It takes 1 minute to grill one side of each sandwich. Can you make three of those sandwiches in just 3 minutes and send your kids out of the door just in time for the school bus?


Choices: 
  • Sure you can; 
  • No, you need at least 4 minutes. Gotta drive the kids yourself.









Correct answer: Sure you can. This is tricky. Name the sandwiches A, B, and C. 
Minute 1: Grill one side of sandwiches A and B. 
Minute 2: Grill the second side of sandwich A and the first side of sandwich C. Sandwich A is ready. 
Minute 3: Grill the second sides of sandwiches B and C. All three sandwiches are ready.





Puzzle #4: Cookies Heaven


Twelve mothers from a kids' activity class decide to get acquainted through a baking party. They agree that each will bring homemade or store-bought cookies to share and each will try one cookie from everyone else. While tasting each other's cookies, each pair will have a little chat getting to know each other. How many cookies are consumed altogether at this party?

Choices: 
  • 12
  • 63
  • 132
  • 144









Correct answer: 132. 
Each of the 12 moms tried 11 cookies that the other moms brought: 12 x 11 = 132



Puzzle #5: Eggs for Breakfast


To make breakfast for yourself, you bring a big pot of water to a boil and then boil one egg for 4 minutes. How long would it take you to boil five eggs to feed your whole family?

Choices: 
  • 4 minutes 
  • 8 minutes 
  • 20 minutes








Correct answer: 4 minutes. 
The boiling time is the same if you put all the eggs in the pot at the same time.




Puzzle #6: Sport for Moms


You are a soccer mom, a swim mom, a lacrosse mom, a runner's wife, a Shape Magazine subscriber, and have a family gym membership. Does this guarantee that you can look your family physician in the eye and say that you get enough exercise?

Choices: 
  • Sure: Soccer, swimming, lacrosse, running, gym - you are obviously well aware of the importance of physical activity!
  • Absolutely not: Just because you make time for others to play sports doesn't mean you have time to do it yourself!









Correct answer is: Absolutely not!



Puzzle #7: Your Good Night Sleep


What are your chances of a good night sleep if there is 30 percent probability that your baby will cry in the middle of the night, a 20 percent probability that your son will have nightmares and come into your room, and a 10 percent chance that your husband will be snoring after the giant steak he consumed at dinner?

Choices: 
  • Zero
  • 50 percent
  • 70 percent
Image by Micah Taylor, distributed under CCL.











Correct answer: 50 percent. For you to have a good night sleep none of these events should occur. No crying AND no nightmares AND no snoring = 0.7 times 0.8 times 0.9 = 0.504 or about 50 percent.



Puzzle #8: A Working Holiday


This may have happened to you. Take Veterans Day, Martin Luther King Day, Presidents Day - or any other holiday observed by your child's day care but not observed by some private companies. If both you and your spouse work and you have not lined up a babysitter, you are facing a puzzling day. Assuming you have flexible hours, can you arrange the day so that you and your spouse will each work an 8-hour day and split childcare?


Choices: 
  • Yes
  • No








Correct answer: Yes. All three go to sleep at the same time. Mom and Dad wake up after 8 hours of sleep. There are 16 hours are left in the day. Mom watches the child for 8 hours while Dad works for 8 hours. Then, dad watches the child for the remaining 8 hours while Mom works for 8 hours.




Puzzle #9: A Rotten Egg


You buy a dozen eggs. After a few days, you notice that just a few are left and you buy a dozen more. You fill up all the empty egg spots in your refrigerator, then refill and buy more as necessary. But if you don't keep track properly, some will get rotten before you eat them. Which practice will leave you with some rotten eggs?


Choices: 
  • Pick eggs for use from the right side of the refrigerator, shift eggs to empty spots to the right, refill egg on the left.
  • Leave eggs in the cartoon. When you buy a new cartoon, put it under the old one.
  • Mark eggs with numbers using a pencil.
  • Just pick eggs randomly, refill empty spots when you buy new eggs.







Correct answer: Random picking. If you pick eggs randomly and refill empty spots with new eggs, there may be a stinking rotten egg that never got picked.





Puzzle #10: I'm a mother, I'm a sinner, I'm a saint. 


Remember the song by Alanis Morissette? You are a professional woman (20 percent of the time), a mother (20 percent of the time), a wife (10 percent of the time), a daughter (5 percent of the time), a sleeping angel (25 percent of the time), a good friend (3 percent of the time), a line cook (4 percent of the time), a house maid (5 percent of the time), a self-indulging queen (3 percent of the time), a neurotic guilt-ridden mess (2 percent of the time), and a driver (3 percent of the time). Is this all possible?

Choices: 
  • Yes
  • No



Correct answer: Yes. Of course the answer is yes! We all do it, somehow.

Happy Mother's Day!

Fair Split of the Rent


Do you know Joe, Jay and Jim? They are renting a 3-bedroom apartment in Cambridge and have to split the $3,000 monthly rent.
$1,000 each?
But the trouble is that all 3 bedrooms are of a different size.
Divide the rent based on a room size?
Good idea! However one room has two windows, second has only one and the third one has a fire escape in front of its window. Joe really wants the last one for his cigarette breaks but he is wiling to pay no more than $900 for it.
Apparently math could help them!

Recent New York times article describes an algorithm that could be used in such situations. Take an equal-sided triangle where every vertex represents a totally unfair situation when one person pays for one room only the whole $3,000 rent. Subdivide this triangle into smaller ones and interpolate rent linearly into every new vertex. See below:


Now go over all the vertices and for each vertex ask either one of the roommates which room he prefers at such rent split. Apparently there always will be a triangle where every roommate has picked a different room. The fair rent subdivision lies somewhere in this triangle. Read more about the algorithm in the New York Times article: To divide the rent, start with a triangle.


And try the New York Times interactive rent division calculator: Rent Division Calculator.

Top image from Rentcafe.

Best Time For Lunch

No matter where you work, at some point during the day you have to gobble something to refuel your energy. Most of us at least occasionally leave our desks for a lunch in a cafeteria or a restaurant. Frequently accompanied by coworkers or friends.
What's the best time to go out for lunch?
When one is hungry?
Probably.
When a majority of the people in the lunching group are hungry?
Perhaps.
But what if 5 minute of waiting till your colleague will finish his non-urgent email may cost you 20 extra minutes of waiting at the salad bar, or leave you without the daily special or a table to sit at.


People that are very particular about what they eat and when usually develop mathematical theories that define when they need to start heading towards food. Below are a few of the theories I heard. 
  1. Most of the people decide to go out for lunch at round hours or half-past an hour: 12:00, 12:30, 13:00, 13:00. This results in "waves" of crowding a few minutes past these times. To avoid the crowds try to come a bit ahead of either wave: 12:20 or 12:50.
  2. To guarantee the specials, the seat and the fresh salad bar come ahead of the crowds: leave your desk at 11:53 so that you could be among the first customers at noon.
  3. Do not follow your instincts.  Most of the people seek salad on Mondays recovering after the weekend feast, soup on a rainy or cold day, light fare in warm weather, turkey in October-November. Avoid these trends to guarantee a quick lunch.
When do you head for lunch? Share your thoughts or theories.

All About Anne

As customary on TheMathMom's website we are honoring each of our 50-puzzle points winner with an exclusive interview. This week it is Anne.


Q: Dear Anne. Does your work have anything to do with math?

I am recently retired and after working in a hospital I spent most of my career as a visiting nurse for my county.  Of course I had to use math for medication administration and proper dosage.  When going into a home there was much problem solving and creativity involved which I enjoyed.  The home environment, especially on a new visit, does not have all the health amenities of a hospital and you must figure out how to proceed with what is there, which can be very little and/or not as hygienic as you need or would prefer.  You must also problem solve to assist the patient in following instructions and adapting them to a sometimes challenging household environment or because of personal reservations.

Q:If you could go back, what profession would you choose and why.

I love the basis of the healthcare field (forget about the insurance, politics, etc!).  It is based on science, something new is always being discovered, it is challenging and it helps people.  If I could choose again I would definitely choose a scientific field, maybe healthcare again or something in astronomy or physics or medical research, and I think it would be fun to be a detective or someone who can crack sophisticated codes!

Q: Is there a childhood mentor who infused your interest in math?

I would have to say my parents.  My father was an engineer and my mother was a science major in college so their interest in things math/science related was always there.  I guess you take for granted your father's tinkering, contraptions and the lack of repairmen coming to the house!  They definitely supported and encouraged a full math/science curriculum for me when it was not the usual way for a girl.  I loved the subject matter but not the fact that I could be the only, or one of a few, girls in the class ...... but I continued and was a math major in college.

Q: Do you think math helps you in your daily life?

I definitely think math helps in your daily life, from simple things like cooking, sewing, smart shopping to home repairs and financial decisions to a certain way of thinking that solves problems.

And may I add that my children are grown and my days as a Math Mom are over.  Neither child avoided math and, in fact, took many advanced mathematics courses.  My son in an engineer with an MBA and my daughter is a neuropsychologist,  both professions where math is used.  I have two grandchildren now and, while I know their parents will raise them with an appreciation for math, I have moved on to Math (Grand)Mom!

Anne is the 8th person to reach such a celebrity status on our pages. Before her there were: Kim, Tom, Jerome, Ilya, TracyZ, Anne-Marie, and Wang. 

A Holiday Greeting for You from You

My mom is our family poet and a writer who has been composing little humorous personalized sonnets for almost every birthday, wedding, anniversary or other significant events in our family and her work clusters.  Last weekend she worked on a non-rhymed New Year greeting, and the fact that the year 2014 is a year of the Horse in Chinese calendar gave her a lot of ideas to write about. Here it is, loosely translated from the Russian;

We already work hard as a workhorse; pull the plow as peasant horse; strive to come to the finish line first , like a racehorse; fear losing our jobs as an old horse; easily bought by sweets like a circus horse;  devoted to our owner (employer , children, friends ) as domestic horse.
Therefore we are ready to welcome the 2014 NEW YEAR!
And let every home and every heart find a place for a small horseshoe, which will bring us a little luck and much happiness!
Be healthy, as a young horse, racing all year long.
and so long....

She sent the greeting by email to me and seven of her closest friends from Israel and Russia on December 30th. A day later she received an email with her own greeting from one of my dad's friends who resides in Florida. Interestingly the text was edited to exclude parts about life in Israel that were not so applicable to the Florida retirees. What are the chances for an email to go around the globe (at least once) and among millions of potential recipients, and come back to the original writer!

Actually, this is not so rare.  Something similar may have likely happened to you.
While our world is inconceivably large, our circle of friends is rather small and typically based around age, interests, education, socio-economic status. And some of our friends' friends are likely to know each other. Moreover, there are those of us who serve as "network hubs", social butterflies with extremely large circle of friends and acquaintances that goes outside of their age, interests, education and socio-economic status, which allows to connect people from different networks together.

In Hollywood this paradigm is known as 6-degrees of separation from Kevin Bacon, stating that any actor could be linked to the well-known Kevin Bacon with up to 6 steps.  Mathematicians are counting their "proximity" to  Paul Erdős in Erdős numbers.  This prolific Hungarian mathematician apparently spent large portion of his life travelling around and writing papers with those who would give him room and board. He published more than any other mathematician in history. LinkedIn has used this chain-of-connections concept to help anyone reach almost everyone for a professional contact.

Going back to our New Year week, let's contemplate our enormous world being tightly connected and inter-dependent, and how anything good we do could spread around bringing so much happiness and ricocheting back to us just when we need it. Happy New 2014, the Year of the Horse.


Happy Holidays! Next year challenge - think outside of a box.

Happy holidays to all my dear readers!
Thank you so much for your loyalty, comments and ideas. Please keep them coming.
Wishing you a healthy and successful year.
Today I would like to tell you a story and give you and myself a New year challenge: Lets try thinking outside of a box.


the story:
You have likely heard of a field of cryptography that is dealing with secure data storage, transfer and access. It is applicable to anything from protecting your personal medical information, sending online payments to breaking into the Pentagon computers. In the past century very complex algorithms have been developed to encode and decode such secure data. Many algorithms are using extra-large prime numbers. $150,000 dollar prizes were announced to people that could find such large primes consisting of hundreds of thousands of digits. Even since the Second World War cryptography has been a very hot field and many brilliant scientists are working in it.

A group of them just published a ground-breaking study announcing that you can decode the encrypted message that your computer is sending or receiving by ... looking outside of the computer box. You don't need to break into the computer, instead concentrate outside of the box, just listen to it.  Computer at the end is just a machine that process any keystroke into series of bits that are translated into electrical signals: on and off. And as we all know these on-off switches usually makes tiny noise. In the computer case this noise could be captured by any smartphone microphones. So, if you are a secret agent you can spy on your enemy by accidentally leaving a smartphone near his laptop, taping and transferring the noise to your computer and de-crypting the data at home.
This is one of those things when many other scientists and lay people probably think: It is so simple. Why haven't we thought about it before? We have been concentrating so hard and deep inside the box that we forgot about the outside options.

Next year - let's try to thinking outside of the box.  At work or at home, let's try to step aside and find creative unconventional solutions to any challenge we may face.
Happy New 2014!

Holiday Cookies: the chemistry and math of making them. Plus, a recipe.

How the ball of dough flattens, spreads and bubbles in the oven?
Why tasting raw dough is like playing a Russian roulette?
Why your cookies won't brown at the standard 350F?
How could you figure out that they are ready without using a kitchen timer?

All the answers and much much more interesting details are in this TedEd video:



But wait, there is more:
When you use melted butter instead of the room temperature butter chunks, the dough will spread out faster in the oven creating larger diameter cookies. At the same time meted butter will create more but smaller sized air pockets (holes) making the cookies chewier. Source: molecular biologist Liz Roth-Johnson, UCLA.

And the biggest secret is to make the dough 3 days ahead and refrigerate it for about 36 hours prior to shaping and baking in order to allow all the ingredients slowly penetrate each other and achieve better dough consistency. More details on that are in this NYTimes article.

Finally, as we learned all the science, let's try making the cookies.
My friend and excellent baker Sherene Michlin recommended two of her favorite recipes. One that is adapted from NY baker Jacques Torres and requires two types of flour, two types of sugar and very precise measurements. NYTimes subscribers could find it here.
Another: basic, straight-forward, no-fail - is from the NESTLE website.  I am posting it below.

Ingredients:
2 1/4 cups all-purpose flour
1 teaspoon baking soda
1 teaspoon salt
1 cup (2 sticks) butter, softened
3/4 cup granulated sugar
3/4 cup packed brown sugar
1 teaspoon vanilla extract
2 large eggs
2 cups (12-oz. pkg) NESTLÉ® TOLL HOUSE® Semi-Sweet Chocolate Morsels
1 cup chopped nuts

Directions:

preheat oven to 375° F.

combine flour, baking soda and salt in small bowl. Beat butter, granulated sugar, brown sugar and vanilla extract in large mixer bowl until creamy. Add eggs, one at a time, beating well after each addition. Gradually beat in flour mixture. Stir in morsels and nuts. Drop by rounded tablespoon onto ungreased baking sheets. 

bake for 9 to 11 minutes or until golden brown. Cool on baking sheets for 2 minutes; remove to wire racks to cool completely. 
Enjoy!



Girl Rising

October 11st the UN's International Day of the Girl celebrating the power of education that transfers lives of girls all around the world.  While our cultural stereotypes are preventing our daughters from being strong in math and going for degrees that will ensure their economic independence, cultural traditions or poverty in many other countries preventing girls from receiving any education at all. A new groundbreaking documentary Girls Rising, directed by Academy Award nominee Richard Robbins, tells the stories of 9 extraordinary girls from 9 countries. It is written by 9 celebrated writers and narrated by 9 renowned actresses. You can check for the screenings near you or  organize your own screening:



 Aside from the movie Girl Rising is a campaign and its website help you to create a curriculum that teaches students to think critically about issues related to girls education, ways for each to realize their own potential and and our global responsibilities. Click to bring Girl Rising to your school.

Renovations Math, Smiles and Tears

They told us - be careful; renovations always take twice longer than expected, cost twice more than you planned, stress your work and family life to an unprecedented level and double your chances for divorce.  We thought: Nonsense!  It is just the stairs and a suite on the roof; a few months of work, with contractor and architect from our extended family. I thought I could keep an eye on the whole project while assembling the posts from this blog into a book.  Life showed that they were absolutely right.


It all went like in the kids' classic: "If you give a mouse a cookie." Stair redesign led to flooring changes and required a new kitchen layout; while we were at it we extended the kitchen into the garage that demanded new garage doors; since the floors were open we were advised to renew the pipes; then came the bathrooms and the doors. It all got so expensive that we gave up on the roof suite dreams and re-planned for it in the basement. At the end we thought that perhaps the original stairs were OK but with 5 workers and a cement mixer inside the house it was too late:).

Double the time and double the budget but still married, we are now only in the middle of the process. My book dreams were put aside, as well as summer travel.  Museum and park visits got replaced with tile, parquet and furniture shopping. The whole adventure did give us a lot of valuable construction knowledge that unfortunately will not come to use as we swore to never ever renovate again.

As I was immersing in, more and more renovation math shoved on me daily by general contractor and designer. I was trying to keep our kids involved and stimulated by occasionally translating to them these real life math puzzles:


  • If it took 3 days to destroy all the walls, how long may it take to build new ones?  1) 3 days. 2) one week 3) three months.  #3 is the correct answer.
  • Which room is bigger? Calculate the area and compare.
  • Can you help me figure out how much tile will we need for your room?  What about the whole basement (split into rectangles and calculate)?
  • What is the length of the railings that we will need to order for the roof?
  • How many stairs are we going to have? Our old stairs were surprisingly cumbersome: uneven, too high, slightly tilted. To lower the stair height we had to increase the overall staircase area extending it into the kitchen. The new stairs were supposed to be 7" each so my daughter and I calculated the number of these new stairs:  (ceiling height + ceiling-to-second-floor thickness) /7
  • How many 6" tiles could you fit into a 60" x 60" area? 100? We were wrong! There is a 3mm-wide grout in-between every tile connection.
  • How many parts a bathtub shower and faucet may possibly have?  More than you could see and imagine!
  • How many white colors do you think exist in this world? One? Wrong again! But they all would look the same to you if it were not for your designer biasing your perception.
I am sure you all have your own share of renovations math puzzles or experiences that I invite you to share with us to make me feel a little bit better.



Summer Learning Activities from PBS Kids

Summer is officially here and for most of us it is an opportunity to do things we couldn't do throughout the school year - take it easy, spend more time outdoors, do something adventurous, learn new skills, and spend more time with the friends and family. It is a time to see who really your kids are, what they like and where they need a bit more confidence, tell them about things you like and teach them to manage their leisure time with some structure. Below is a list of resource links from the PBS Kids of fun summer science and math activities.

PBS KIDS Lab Home Activities:

Keeping Kids’ Math Skills Sharp All Summer Long

Fun Summer Science Projects:
http://www.pbs.org/parents/education/science/tips/summer-science-projects/

Transitioning family from summer to school:
http://www.pbs.org/parents/education/going-to-school/back-to-school/transition/

13 Ways to sneak learning into summer fun

Simple Tips for Summer Math Learning
http://www.pbs.org/parents/education/math/math-tips-for-parents/summer-math/

Creative Car Game for Summer Road Journeys

Summer crafts
http://www.pbs.org/parents/crafts-for-kids/category/seasonal/summer-crafts/page/2/

The Power of Ten, by Eames.

The Eames Chair: one of the design gems of the 20th century, a unique combination of beauty and comfort. Designed in 1956 and continuously produced by Herman miller ever since; available at the Design Within (Without?) Reach for $3,500+.


Turns out that the designer couple behind this legendary chair, Charles Eames and Bernice Alexanda ("Ray") Eames, were interested not only in furniture but also textiles, photography and film. Fascinated by the relative size of things around us and our perception of the universe they created an interesting short movie called Powers of Ten. It starts with a couple on a lakeside picnic near Chicago and every 10 second shows the same scene from 10 times further out until the galaxy is visible only as a speck of light. It then quickly goes back down to the picnicking couple and zooms deep into the men's skin. Short and powerful! Click on the image below to open the film in a new window. Watch with the kids.




All About Tracy



This week we are cheering to Tracy Z. who slowly and consistently climbed toward 50 puzzle points, and honoring Tracy with an exclusive interview.

Congratulations, Tracy! As you were answering these questions, you were preparing to go camping on the Cape Cod. In this picture you sent you are also hiking with a baby in tow and what seems like a giant backpack. What an amazing energy!

This picture is of me and one of my kids on a trip that we take every winter.  We and friends hike into a very rustic cabin (no electricity, no plumbing) in VT for a long weekend, and carry all our gear in via backpacks and sleds.  We’ve been doing it since pre-kid days.  I spend a lot of time for work and at home in front of computers.  Many of my fondest memories though come from the times when I unplug the computer and get outside for a weekend, a week, or longer.  I love hiking, biking, kayaking, and cross-country skiing and snowshoeing.  


Tracy, have you ever had a big or little life dilemma that you solved with math?
Little:  I’ve used math to estimate a number I can’t actually fully compute.  For example, in a contest to guess the number of peanuts in a very large bag, I came closer than anyone else and won the whole bag.  It was too much to eat. 

Bigger:  At my house, we once wanted to estimate where a property line was located without having to hire a surveyor.  We wanted to know which trees were on our property and which were on an adjacent property.  We found survey markers for two corners (A & B) on one side of the property and used very long pieces of string and triangle geometry to estimate the border on an adjacent side of the property.  Here are the details: We took the straight line distance between A and B (let’s call the distance x) and assumed the adjacent border from corner A to the unknown point C would be a right angle to side AB (the assessors’ property maps suggested the angle was 90% or very close to it).   We created a string of length x and a second string of length (sqrt(2))*x.  We tied the x- length string at corner A, and tied the (sqrt(2))*x-length string at corner B.  At corners A and B, we then rotated the two strings until they intersected when each string was fully extended.  This intersection point was point C.  Once we knew C, we knew side AC was on the property border.  AC was long enough to go past the trees in question, but if it had not been, we could have run another longer string along AC as far as needed. 



Have you ever did any miscalculation using logic and numbers in real life?
One type of miscalculation I make far too frequently is underestimating how long it will take me to get somewhere, such as for an appointment.  I think about what time the appointment starts, and then make the assumption that that time it will take me to get there will be the minimum time that such a trip would take under ideal conditions with no delays of any kind.  I allow for little margin of error and as a result I am often a wee bit late. Fortunately, I had just a few times where I have been very late.  Too bad personal teleportation is not yet an option. 

Do or did you ever use math professionally?
I use math personally and professionally almost every day. I was a math major in college. In my professional life, I have had positions gathering and analyzing data regarding: the energy and cost savings of energy-efficient household appliances; the population, economic, and land use trends for regions and communities; and the contributing factors behind motor vehicle crashes and fatalities.  I currently work in a research laboratory that conducts studies of driver behavior (such as driver distraction) in driving simulators and on-road environments.  We collect a variety of data on our participants during their sessions, including their demographic and driving histories, and their eye movements, head movements, their travel speed, acceleration, and lane deviation while driving, and use this data to develop training programs to improve drivers’ skills. 


Some people say that best ideas come to them in the shower, for some it is while they are asleep, for some - while they are jogging. For you, what conditions, mood or environment are the most optimal to tackle a hard puzzle?
I get many of my best ideas for how to proceed on a hard problem when I outside walking or biking.   I also get great ideas, especially for Math Mom puzzlers and other brain teasers, by talking them over with my spouse or kids.  They love math and logic puzzles as much as I do.  


To whom or what you are attributing your interest in math – a teacher, parent, TV program?
There are two people to whom I attribute my interest in math and logic.  The first is John Powers, a wonderful teacher who mentored me in middle school. He encouraged me to create a book of logic puzzles and to develop a curriculum to teach logic skills to kindergarteners and first graders. The second is Dr. Arthur Eisenkraft, my high school physics teacher. He frequently had us put down our textbooks and engage in real-life exercises to better understand the concepts he was teaching us.  We’d have labs where we threw and hit baseballs (studying speed and distance); dropped objects out of 3-story windows (gravity), and honked car horns while driving at different speeds (Doppler effect). He made science and equations live.  Dr. Eisenkraft now runs a center at UMass-Boston that focuses on improving the teaching and learning of science and math for all students, from kindergarten through graduate school.

Thanks, Tracy!
Curious to know more about our other puzzle-solvers? See our previous interviews: All About Ilya, All About Jerome, All About Anne-Marie, All About Tom, and All About Kim.

Bat Mitzvah Favors, Messy And Full of Math.


This is a guest post by my very good friend Ellina who is celebrating her daughter's Bat Mitzvah in a few weeks.

In a strange and unexpected moment of creative inspiration (channeling my inner Martha Stewart, which I didn't know I could!), I decided to make chocolate-covered Oreos as favors for my daughter's Bat Mitzvah party, where we will have 70 kids in attendance. Some strong math should really have been involved in my decision, but I usually shy away from having to calculate anything, so I thought I'd "be creative" and "enjoy the process." What is there to do - buy a few packs of Oreos, dip them in chocolate, use food coloring spray and stencil to "Mazel Tov" on each, pack them in bags of 3, and here we go - 70 delicious and festive favors.

I was told that there is a person who charges $2 per cookie when she does this, and I thought it was an exorbitant price. I needed 70 x 3 = 210 of those and wasn't ready to pay $420 for that. 

Preparing the project, I created a list of supplies:

  • I have three molding trays that make 6 Oreos each, so I can make 18 at a time
  • I have three different decorative stencils -- one says "Bat Mitzvah", one says "Mazel Tov!", and one is a Star of David -- every favor will get three cookies, one of each design
  • There are 36 Double-Stuf Oreos in one package
  • A package of chocolate melt wafers is 14 oz.
  • A can of pearl white food coloring spray (that is used to spray the stencil design onto each cookie) is 15 oz.
  • Each set of 3 cookies will go into a little cellophane baggie, tied with a piece of decorative ribbon (about 8" of ribbon per baggie)
  • Ribbon comes in rolls of 9 feet
  • Baggies come in packs of 100 (so I will need only one pack -- this one is easy!!)
  • Each baggie will have a piece of cardstock stuffed into it, as "decorative backing" for the cookies.
  • Cardstock comes in sheets of 12" x 12"
  • Each baggie will need a 4" x 4" piece of colored cardstock
  • I want to alternate lavender and light blue cardstock (trying to stick to the party's color scheme of lavender, white, and light blue)
Just in time, the AC Moore store was having a sale on chocolate melt wafers (normally 2.49/bag, sale price of 1.99/bag), so I stocked up, got 12 bags. The first time. Little did I know that I will have to go back two more times, for wafers and other ingredients... 16 bags of wafers total.
Got 6 spray bottles of white food coloring -- with the way my spraying was going, I knew I'd need a few!  Got 4 more during a later trip. 
Double-Stuf Oreos were also on sale (normally 3.69/box, sale price of 2.99/box), I got 7 boxes and then went back for another 4 (36 cookies in each, I needed to make a total of 210, but underestimated the amount of broken cookies, eat-while-I-work cookies, cat-stole-and-dropped-down-off-table-to-share-with-dog cookies, and family-sneaking-finished-product-late-at-night cookies). 
Found cute ribbon for only $1 per roll (9 feet each), but all I could find was 3 rolls (will not be enough, as I need 8" per baggie, and need to make 70 baggies, which would mean almost 6 full rolls). Tried to find 3 additional rolls later that would be the same, scared away fellow shoppers as I frantically clawed my way through the $1 ribbon bin -- alas, to no avail. Will end up with two types of ribbons closing up the baggies. Keep reminding myself that kids don't care.

Then, I planned the actual steps and slowly perfected them through trial-and-error:


  • Melt chocolate wafers (three 30-second intervals in the microwave)
  •  Pour a bit of the chocolate melt into one cookie mold slot



  • Put Oreo into cookie mold, and push down to get the chocolate to come up around the sides
  •  Pour a bit more chocolate over the top, and spread to cover up the cookie
  •  Tap the bottom of the mold a few times to get air bubbles out, and to ensure the chocolate has spread evenly around/over the cookie
  •  Repeat for remaining 5 cookies in the mold
  •  Put into freezer for 15 minutes



  • Repeat with remaining two mold trays, ending up with 18 cookies 
  • Pop out cookies, take a stencil (one of the three choices), place over cookie, spray with food coloring





  • Put 18 cookies into large ziplock bag, make bag airtight by sucking all air out with a straw
  • Store bag in kitchen cabinet
  • Repeat while tolerating rolling-eye expression from daughter and husband
  • Curse Martha Stewart. 






Now, you are probably starting to wonder what got me thinking that this could be fun. Well, so did I, but this was already too late into the adventure. The kitchen was an ugly mess. Every few hours I was going into sugar-induced shock from breathing cheap candy wafer fumes, and food coloring spray fumes. I then run to the fridge, took pickles out of a jar and ate them to decrease the sugar overload. Ate them quickly, to balance out the sugar.  At that point it is important to recognize that the assembly of the favors was still to come....



Favor Assembly Steps:

  • Take pre-cut piece of cardstock, put into cellophane baggie
  • Put three cookies (one with each design) into baggie, with cardstock as background
  • Take pre-cut pieces of ribbon
  • Tie ribbon into knot
  • Repeat
   
The final result:


Overall time investment: 35 hours so far.  

Total money spent: about $110 .
Chocolate consumed: 1 pound+



59 done, 11 to go... I've somehow miscalculated my sets of 18, so I now have too many Magen Davids, 7 Bat Mitzvahs (need 11), and no Mazel Tovs at all... Bought one more box of Double-Stuf Oreos...
Honestly, when this is done, I don't think I'll be able to be anywhere near another Oreo for what is likely to be years... :-)


Plan on bringing the not-yet-assembled pieces to a Memorial Weekend retreat to get the extended family help me put it together. Need to feed them ice cream before to prevent any pieces being eaten.

Exhaustion and excitement are up.
Time to the party: 2 weeks
Next on my list: video montage and table centerpieces.



From TheMathMom:  Ellina -  I am sure these elaborate multi-week home preparations make the anticipation even more special and the whole event much more personal and memorable.