Then, this fall, the kid (age seven) went back to numbers. We hit them hard -- a review of addition and subtraction which, twelve weeks into our school year, has her easily adding three digit numbers together. On her own volition. In her head. Without her fingers.
It was clear I had to do something else with numbers. Obviously multiplication was next but I had no clue how to proceed since I knew the whole rote-memorization thing was not going to fly. She's not that into charts either. Luckily, a great post over at Let's Play Math saved me, and ultimately inspired us down a fantastic new path of inquiry. There's more to this story (having to do with the magic beans) but for now let me just say that, indeed, if one starts to think about what multiplication really is, multiplication turns out to be EVERYWHERE.
Especially in the form of arrays. In the last week or so we've been finding and analyzing the arrays we find out in the world. At the park:
Many leaves, not an array, but very pretty!
One column of long rectangles. 1 times many.
Is it an array or is it a gradient of trapezoids?
Once again, our city's sewer covers provide a fabulous opportunity for math. We saw enough of these on the walk home from the library one day that the 4x4 fact is permanently etched in my daughter's head.
Arrays are everywhere, even in a truck grill. This one is conveniently divided into four parts, so if you really wanted to you could find the number of holes in one section and then figure out the total number of holes in the grate from there, and then, because there are two sides, double that number. Fun times!
These we find at almost every crosswalk. They all seem to have either eleven rows or eleven columns or both.
Is this wall an array? Why or why not?
Simple and sweet. (An upturned recycling bin!)
At the post office!
In front of the library! (How good are your eight times-tables? Or, perhaps you could figure out the number of dots a different way?)
Three weeks or so ago, when I was trying to wrap my head around teaching multiplication without focusing too much on the facts, it was really quite difficult for my seven year old to analyze and compute an array over 3 x 3.
This morning we were working on growing patterns with some square pattern blocks, but while we were cleaning up I played around to see if the number of blocks I had in my pile would make an even array. They did!
I thought to ask my daughter if she could figure out how many there were. It was like magic! Unprompted from there she immediately saw three in each row, counted six rows, noticed a top half and a bottom half in the design, and started skip counting. Even as recently as three weeks ago this kind of structure was not evident to her eyes, but today it took only a couple seconds to thoroughly analyze what she had before her.
"Eighteen, Mama, eighteen! Three times six is eighteen!"
I never knew multiplication was so interesting and so ubiquitous. Thank goodness I get to do elementary math all over again. It is SO much fun!
p.s. It's also fun over at the Math in Your Feet Facebook page! Check it out -- today I put up a link to a video of fun, family friendly percussive body music!