I Love Math is a season in the school year when students, teachers, parents, and the whole community celebrate an everlasting love for math. It is also a time when we work on some of our most profound hopes for Mustard Seed School students for their growth as mathematicians. This is a season for:
• helping students learn more of the breadth and beauty of mathematics
• enjoying playful problem solving
• expanding children's understanding of what math is
• building persistence
• developing mathematical creativity
There will be more information on this blog in the coming days about I Love Math season. But sometimes there is nothing better than jumping in, and getting down to work on a good problem.
In that spirit, here is the problem that students in Grades 6, 7 and 8 were given on Monday, January 9. We encourage parents to join their children in struggling with this problem and discussing it at home. No need to solve it, unless you especially like the challenge. It is enough to just ponder it together, wonder about how it might work, and try out a few ideas:
Checkerboard
and Dominoes
Here is a
checkerboard.
---How
many small squares does it contain?
---If I
gave you 32 dominoes, each one a rectangle exactly the size of two small
squares, could you cover all the squares?
---See if
you can come up with 2 or 3 different patterns that would completely cover the
board with dominoes.
Now,
remove the small square in the upper left.
Then remove the small square in the lower right.
Since we
have taken away two squares, now you may only work with 31 dominoes.
Show one
or two patterns by which to cover all 62 small squares.
If you
cannot find such a pattern, you should turn in an argument (a “proof”) that
would convince a skeptic that it can’t be done.
