This past Tuesday at the Global Math Department Max presented a conference on noticing and wondering. I’m glad I was there for it! I learned a lot about tying in what students already know to what we are trying to learn next. I’ve heard of and used KWL’s before (know, want to know, learned), but noticing and wondering worked so much better!!

My 9th grade class really struggles with math. Many of them get very frustrated and shut down when anything seems even slightly challenging. Unless it’s interesting too. Or is presented in an excessively non-threatening way. Asking what they notice instead of what they know did that for them this week. We actually got through what I wanted to for the day plus some extra things.

We are learning about features of functions (maximum, minimum, increasing, decreasing, intercepts, etc.) and how that all looks with graphs, tables, equations, and in interval notation.

I started with asking students what they noticed about this graph:

They noticed that:

– the lines intersect

– one starts higher than the other one

– the lines are straight

– the lines have different slopes

– the lines have different labels

Next I gave them a context:

Aly and Dayne work at a water park and have to drain the water at the end of each month for the ride they supervise. Each uses a pump to remove the water from the small pool at the bottom of their ride. The graph represents the amount of water in Aly’s pool, a(x), and Dayne’s pool, d(x),over time.

I asked them again what they noticed now:

– Aly’s pool drains faster

– Aly’s pool is bigger

– the pools drain at a consistent rate, even as the water gets low (we had a problem a while ago where that wasn’t the case)

Then I gave them some more information. Dayne’s pool started at 24,000 gallons and finished draining after 24 minutes. We also talked about what it means when they cross and how that can be expresses as a(x)=d(x)

They wondered:

– When do they cross

– How much water did Aly start with

– When was Aly’s pool done draining

When talking about those we also talked about:

– what a(x) means, and what a(5), a(6), etc mean.

– when is a(x) > d(x)

– what does d(x) = 2000 mean and what would that x value be?