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Wednesday, July 15, 2009

Math around the House

There are any number of reasons parents are motivated to supplement the math their children are getting at school. They want to slow the loss of understanding and skills over a long summer. They are concerned about the school's wholesale adoption of Everyday Math. They are concerned about the school's wholesale adoption of Saxon. They suspect the fourth grade teacher is not a great math teacher. Their child is either ready for more than, or not ready for, the grade-level expectations at school. All of these motivations are entirely reasonable.

Ideally I think parents should make understanding organic to daily occurrences. If they treat math like spinach (we have to get through your multiplication flash cards before you can have fun, because it's good for you) their child will grow to resent it. Gaining real understanding of logic, structure, measurement, relationships, and numbers, done well, should be a creative, joyful process.

These are some things I've noticed while puttering around the house. I hope they are helpful. For all of these ideas, I would:
  1. Know at least a little about the concept/solution before posing it (I put very broad categories after each one to possibly make research a little easier.)
  2. Respond to the child's curiosity - don't force her to do anything.
  3. Don't try to turn everything into a textbook math problem. It's ok to start with undefined terms and not enough information. Learning how to ask clarifying questions is part of learning how to solve problems.
  4. It's ok to start with too-complicated a problem. Learning how to pose a simpler problem is a part of learning how to solve problems.
  5. Don't be afraid to leave questions unanswered for another day - give the ideas time to marinate. Cultivate patience with irresolution.

Notice two cylinders side by side and wonder aloud which uses more material, and which holds more. (Canisters for oatmeal, tennis balls, and Pringles come to mind.) Follow up: roll up a 8.5 x 11 piece of copier paper both the tall way and the short way. Wonder which way holds more. (Volume/surface area)

Do you frequent a particular ice cream place? I bet they offer well-defined options for ice cream flavors and toppings. Wonder how many possible different sundaes you could order. (Or the related questions, such as how long would it take you to eat every possible sundae, if you had one a week?) If the initial problem is too complicated, solve a simpler one. (Combinatorics)

Does your family ever clink glasses at the dinner table? Next time you do that, wonder how many clinks. (They don't have to be clinks. Do they smooch all their relatives at family gatherings? High five them?) If you only have 4 people, this is easy and boring, but if you can get them to wondering at the pattern for 5 people, 6 people... (Combinatorics)

When you are cutting a cake, or pancakes, wonder how you can get the most pieces out of the fewest cuts. (Quadratic relationships)

While traveling, set them to figuring out "How much longer?", using the data from highway mileage signs and the speedometer. (Distance/Rate/Time)

If you are playing a game with two dice, wonder what outcome is most likely. What implications does that have in the game? (Probability/sample space)

"I need 1 and 3/4 cups of butter. Can you get them for me?" When she does this successfully, talk about how she divided by a fraction to arrive at 3 and 1/2 sticks. Draw a picture, write it out with symbols. Notice how weird it is that a division can yield a result larger than the thing you were dividing. Be on the lookout, together, of other examples around the house where one might divide by a fraction. (Division/fractions) (Thanks for this one, Jackie.)

Find number-y fun in your child's favorite sport. These examples are from baseball because I know more than nothing about it: How many outs in a perfect game? Minimum/maximum at-bats in a scoreless game? (Multiplication/division)

Take advantage of anything a child asks about. Sometimes they will hear an older friend or sibling refer to something exotic: prime numbers, or square roots, and wonder about it. I have seen parents give a definition and not exploit the opportunity! Don't stop at "A prime number is only divisible by 1 and itself." Say something tantalizing like, "I wonder if we could find all the prime numbers between 1 and 100? That seems impossible!"

And finally, I can't recommend highly enough a collaborative math circle (as opposed to the type geared toward training for competitions.) If I had kids, I'd be googling "my city math circle" to see what's out there, and starting one up if it didn't already exist.

I'd love to hear about other things you and your kids have come up with! Happy math-ing!


  1. Playing with my nieces and nephews the other day, we were talking about people's ages.

    "So, I'm 4 and he's 6. So when he's 16 I'll be 14". All while we were just splashing by the pool. This evolved into a whole discussion... when grandpa was 44 you were 20...

    I thought it was an amazing discussion.

    Then the five year old wondered how many seconds in five minutes. That was fun too. :-)

  2. Have you read "In Code" by Sarah Flannery? In the first chapter or two she talks about how her father (a math professor) was constantly presenting puzzles and challenges to her and her siblings, and the tremendous impact that had on her. Would that more parents would do the same (or similar).

  3. Cool story, Jackie! Sounds like a fun afternoon. I can't wait until my newborn niece can talk and start to think about these things. Part of the inspiration for this post was thinking about ways I could help her have fun with math without intimidating her.

    No I haven't read that Matt, sounds cool, I'll add it to the list.

    I was trying to think of ways non-math-professor parents could engage their kids in some math incidental to their daily lives. You know? It seems lots of people are intimidated, but it should be natural, if you know where to look.

  4. It's so natural (well, at least for me it is). We have great discussions about numbers and math all the time. They just don't know it. :-)

    Then again, we play rhyming games and make up stories too. It's just how we play.

    I love being an Aunt. Enjoy!

  5. Percentages and probabilities abound in day to day life.

    When the weather forecast gives rain percentages for the next week figure out the probability of no rain, two days of rain etc.

    When the Gap has 20% off with an additional 15% off when you open a Gap card account figure out the total savings being offered.

    I always like catching people on tv making math errors. On Top Chef Masters recently four chefs were competing when one chef got eliminated. One of the three remaining chefs commented that his chance of winning just increased by about 30%. It's understandable how he could make this error but 30% is horribly wrong.

  6. Going from 1/4 to 1/3 increases probability by a factor of 4/3 which is an increase of 33.333% It seems to me that 30% is a pretty good approximation to that.

    What is so horribly wrong?


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