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Tuesday, April 9, 2013

Two minuses make a plus

Math, ah! math, the quintessential unpopular school subject if there is one!

For some reason, people love to hate math.

I will not try to dissociate myself from this tendency. From early on math had as much appeal to me as steamed Brussels sprouts (i.e., not much!)

Luckily (or unluckily), my attitude towards both of those calamities slowly changed as I was exposed to A LOT of them. In both cases, this "torture" usually happened at the family table.

You see, I had an enthusiastic Brussels sprouts lover for a mom... and a no-less enthusiastic mathematician for a dad. We were thus served a lot of each for dinner. Literally! My dad always found ways to infuse math concepts in food-related situations!

Eating those bitter green balls (no pun intended!) and solving math problems remained a battle for most of my childhood and teenage years, but as I entered adulthood, and especially as I became a mom, I realized how much progress had been done (or how brainwashed I actually was).

First, I now enjoy (and serve my family) the dreaded green stuff. Second, I now surprise myself giving my kids the same "math is everywhere and let's have fun with it" treatment my dad gave me.

Some examples of what my dad would do:

When he served us food using a spoon (e.g. mashed potatoes, green peas, fruit salad), he would pour a small spoon full on the plate, then say "Okay, this was $5 worth of [whatever food it was]. How much of it do you want? $10? $15? Or maybe you're not that hungry. $7.50? $6.66666? Good thing he did not ask us to calculate volume rebates!

When he served us something that was round (e.g. pizza, pie), he would ask us to tell him how big a portion we wanted by either providing him with a fraction ("I would like an eight of the pie") or degrees ("I would like 30 degrees of that cake") If we made a mistake and ended up with a piece smaller than we expected we had to live with it. 

My dad saw numbers everywhere and I wonder if he did not think and dream in numbers, too. To distinguish between us and the cats he used the terms "biped" and "quadruped". At random moments he would also ask us questions such as "If there are 12 cows in one field and 6 horses in the second, how many legs and ears does that make, total?"

Other common conversation topics were the dreaded faucet problems and the non-less headache inducing train problems.

Example of a faucet problem (from http://www.purplemath.com):

When the tub faucet is on full, it can fill the tub to overflowing in 20 minutes (we'll ignore the existence of the overflow drain). The drain can empty the tub in 15 minutes. Your four-year-old has managed to turn the faucet on full, and the drain was closed. Just as the tub starts to overflow, you run in and discover the mess. You grab the faucet handle, and it comes off in your hand, leaving the water running at full power. You yank the drain open, and run for towels to clean up the overflow. How long will it take for the tub to empty, with the faucet still on but the drain now open?

Examples of train problems (from http://math.about.com):

Question 1: 

A train left Chicago and traveled towards Dallas. Five hours later another train left for Dallas traveling at 40 miles per hour with a goal of catching up with the first train bound for Dallas. The second train finally caught up with the first train after traveling for three hours. How fast was the train that left first going?
Question 2:
One train left the station and traveled toward its destination at a speed of 65 miles per hour. Later, another train left the station traveling in the opposite direction of the first train; it was going at a speed of 75 miles per hour. After the first train had traveled for 14 hours it was 1960 miles apart from the second train. How long did the second train travel?

I honestly thought I would never turn into a math whiz like my dad, and for the most part I haven't. But...
When I buy something oftentimes I calculate the price minus the rebate plus the tax and tell the cashier the exact amount it's going to cost before they tell me.
When my kids were preschoolers I would make patterns out of Legos and ask them to put the piece that should come next.
When we played hopscotch, instead of the traditional one I would draw it out of various shapes, and the kids had to name them as they went across: "octogon, oval, rhombus..."
The other day I was having breakfast with R, my 9 year old, when I noticed that the 4 tea lights on the table were arranged in a 2X2 square shape. I quickly went to get some more so I could arrange it in a 3X3 square, then a 4X4, and we spent the next half hour discussing square numbers and square roots.
It reminded me that the first time I showed my daughters how to play checkers, I also explained to them how you can count the squares on a chessboard by multiplying the number of squares (rows X columns) instead of counting them all one by one (my kids were probably 3 and 5 at the time).
A few weeks ago, our school had its annual "Math Night". We don't attend all of the school's special activities, but this is one I am adamant we do not miss. We got to play all kinds of fun games including one where you separate Smarties by colors, then count them, then make a graph out of it. The older kids were encouraged to calculate the mean, median and mode through this exercise. (My youngest mostly wanted to eat the Smarties, but I still managed to get a little bit of math out of the experience.)
At one point during the aforementioned Math Night I somehow ended up at the Grade 5 table with my Grade 1 daughter, A. Not ones to be easily defeated, we enthusiastically started working with the contractor, drawing different angles and comparing them. I explained the concept of right angle and asked A to find some in her surroundings (she pointed to the corners of the sheet of paper, of the table, of the door). I showed her that when she stands up she makes a right angle with the floor. To illustrate smaller angles I used a Pacman analogy. A loved that Pacman can open his mouth so big that it closes back on itself, making poor Pacman disappear completely! (360 degree angle).

Other examples of math in everyday life include the question I asked the kids yesterday as we were getting ready for the puppy training class: "It's 4:42 now and we have to leave in about 30 minutes. What time will it be then?"
Of course, the main reason why the kitchen is the perfect place to do math is because of the recipes, as my mom (who seems to think math is sexy - or at least that mathematicians are; that's why she married one!) loves to say: the best way to teach children math is cooking and baking! Whenever we bake homemade muffins, the girls help me measure the ingredients; for extra challenge (and extra muffins obviously), I usually have them double the quantities.

Finally, one of my favorite Sesame Street character is Count Von Count, and I certainly exposed the kids to a lot of him before they went to school!

Isn't he awesome?

But I truly realized how permeated I was with my dad's legacy when I recently said to my trainer "It's kind of boring to just count my burpees. Let's say prime numbers in ascending order instead, one for each burpee". She looked at me like I had just landed from a distant galaxy.

The most important math lesson I have learned from my dad, however, would be that "two minuses make a plus". Once, coming back from his weekly hockey game, that's the concept he used to explain how the two weakest players on his team had managed to score an incredible goal together.

I have kept this in mind and adopted it as part of my life philosophy. Therefore I try to look for the positive even when what's most obvious is an accumulation of negatives.

To finish beautifully, there is the ultimate meeting of math and words: a Fibonacci sonnet. Try it!

For more on the Fibonacci Sequence:


For more on parental legacy, be sure to read my previous post:



  1. I always thought, about the train problems, if the two trains are not going at the same speed towards one another or following each other, then let them crash! That's why we have speed limits, brakes, and railway interchange areas so let's use them!

    Might explain why I'm not too good at maths though! Oh well, it's not like I'm a rocket scientist... or am I? ;-)

  2. Lesson number one: never let rocket scientists solve train problems! ;-)

  3. Hi Julie! I raised my children in much the same way. My oldest daughter is an industrial engineer. My second daughter is getting her master's degree in computer information systems. My third daughter is competing in nationals for Urban Debate League. My son is starting to make a documentary.

    Whatever world you make for your children is the world they know and understand.

    :-) Marion

  4. Marion: that's what I call a complete success! :-) With all that math I still became a translator, but my brother is a computer scientist (and my mom worked in finance). I'm curious to see the path my daughters will choose (their dad is on the Faculty of Medicine so that could have an impact as well - when I asked the youngest what she was most interested in she said "how the body works"; the oldest calls herself a "bookworm"). Open all the doors, then let them pick the one they'll go through! :-)

  5. Math IS sexy. I always found the process of solving those problems very pleasurable, and math jokes are the best.

  6. If you have some math jokes please share them! :-)

  7. That aliens with hats comic is how I feel about math word problems! Laughed out loud at that. But I think if I grew up with more math 'awareness' like you did, maybe I wouldn't dislike it so much.

    1. It's the math "awareness" and it's the notion that math can be fun. :-) I know some teachers are able to instill that in their students. :-)

  8. Great!!

    I was running through math like $hit through a Canadian Goose until I hit the brick wall of Calculus!

    I still don't think any person in almost any field needs it. I suppose banging my head against the Calculus wall for a semester did make me stronger, or so the theory goes.

    1. What an analogy! LOL Or should I say an ANAL ogy?!? ;-)

      Someone recently told me "I would have gone to Med School if it's wasn't for Calculus... and what do doctors need Calculus for anyways?"

  9. My daughter is a math minor in college and would love this! My dad was a math whiz and would quiz us with all kinds of complex problems when eating dinner. Maybe that's why dinner was so stressful!

    1. I guess the line between stressful math and fun math is pretty thin Diane! :-)