Desmos + Two Truths and a Lie
I’m absolute junk in the kitchen (Dan Meyer speaking) but I’m
trying to improve. I marvel at the folks who go off recipe, creating delicious
dishes by sight and feel. That’s not me right now. But I’m also
not content simply to chop vegetables for somebody else.
I love the processes in the middle – like seasoning and sautéing. I can use
that process in lots of different recipes, extending it in lots of different
ways. It’s the right level of technical challenge for me right now.
In the same way, I’m enamored lately of instructional routines.
These routines are sized somewhere between the routine administrative work of
taking attendance and the non-routine instructional work of facilitating an
investigation or novel problem. Just like seasoning and sautéing,
they’re broadly useful techniques, so every minute I spend learning them
is a minute very well spent.
For example, Estimation 180 is an
instructional routine that helps students develop their number sense in the
world.
Contemplate then Calculate
helps students understand the structure of a pattern before calculating its
quantities. Which One Doesn’t Belong helps
students understand how to name and argue about the names of mathematical
objects.
I first encountered the routine “Two Truths and a Lie” in college
when new, nervous freshmen would share two truths about themselves and one
lie, and other freshmen would try to guess the lie.
Marian Small and Amy Lin adapted that icebreaker into an instructional routine
in their book
More Good Questions. I heard about it from
Jon Orr
and yesterday we adapted that routine into
our Challenge Creator technology
at Desmos.
We invite each student to create their own object –
a circle graph design in primary;
a parabola in secondary. 
We ask the student to write three statements about their object – two that are
true, and one that is a lie. They describe why it’s a lie.
Here are three interesting statements from David Petro’s circle graph
design. Which is the lie? 
- The shaded part is the same area as the non shaded part.
- If these were pizzas, there is a way for three people to get the same amount when divided.
- If you double the image you could make a total of 5 shaded circles.
- The axis of symmetry is y=-2.
- The y-intercept is negative.
- The roots are real.
The teacher encourages the students to use the rest of their time to check out
their classmates’ parabolas and circle graphs, separate lies from truth,
and see if everybody agrees. Our experience with Challenge Creator is that the class gets noisy, that students react to one another’s challenges verbally, starting and settling mathematical arguments at will. It’s beautiful.
So feel free to create a class and use these with your own students:
