Then. Oh my goodness, you guys. THIS. Visual Patterns. 3 figures. Different kinds of patterns. Some of the diagrams aren't even sequential! Some are 3.D.
And then I did.
And then... I CHECKED IT. ON. THE. WEBSITE. See how they asked me how many squares were in step 43? Bam. No waiting until the next class to see if they got the right answer. It's right there.
So then I had to open my computer back up and change Friday's homework. B period Math 1 (9th graders, Algebra-level), you are about to figure out Pattern #109. Granted, I'm going to also make them document their thinking on paper. Because I'm more interested in their process than the answer for the 43rd figure. Does that take away from the coolness of doing mathematical thinking on an outside website? Not sure that it does, or that I care too much.
I'm excited because this is right in line with what we've been doing - finding rules and patterns. But it's presented in a different way than they're used to, and as I always tell my students, "you know I love when there's more than one way." They've pretty much mastered linear patterns at the point (we're halfway through our first term), but they need practice and periodic reminders, which this is perfect for.
Plus there's a nice variety of kinds of number patterns, from my initial investigation. So I'm going to lead them in slowly (Friday's Pattern #109 is linear and it gives them the first 3 figures). Freshmen can respond in interesting ways to change. "Wait, I was supposed to click on the link to open it?" So let's make the math super familiar at first.
Then maybe Pattern 82. Still linear and give them the first figures in order, but with legos. So that's fun. Then Pattern 111. Still linear, but the change in x, if you will, is no longer 1. Then maybe Pattern 103, a smooth quadratic. Pattern 102, a more tricky quadratic (in the category of "well, it's not linear, so try quadratic. Close, can we make it work?"). Then hit them with Pattern 108 - quadratic, but way above their level to figure out algebraically, so they have to use the shape. Back to a more reasonable quadratic with Pattern 101. Go to Pattern 95 - a straightforward cubic, but in THREE DIMENSIONS? Throw in a Pattern 107, which looks nonlinear perhaps (it's made of squares after all) but isn't. Pattern 29 which is in context so therefore trickier to apply strategies that may have become rote. Have them pick one - who can find the most interesting pattern that we haven't done yet?
Okay, now they're probably tired of the site. But spread out over several weeks, some in class and some at home, and the discussions we're having are about how you found the pattern. What was your strategy? Did you draw the next one? Make a table? How did you decide what kind of pattern it was? I'm betting we develop an even stronger toolbox of pattern-seeking and rule-finding strategies. And that is what I'm all about.
A non-Math 1 pattern
Just for fun, look at this one.
I found the table pattern (adding cubes). And that leaves us with a constant fourth difference. So this must be a 4th degree function. I could find it in a huge system of equations. Is there a better way?