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?

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Posted in Algebra, Student Work

Tags: algebra, functions, KWL, Math, Ninth grade

I really like the plan of revealing a little information at a time and asking, “what do you notice and wonder now, with that information?” So much easier than trying to take it all in at once, and it gives you the opportunity to focus on the connections — if you first notice that a(x) starts higher, and then learn it’s Aly’s pool, you think, “huh, I wonder what that means? I bet it mean’s Aly’s pool started with more.” vs. trying to think about Aly’s pool is this big and Dayne’s is this big and where can you see that on the graph and which was which again and…

It sounds like for all their math anxiety, your students are chock full of good math ideas, from noticing slope and connecting steeper slope to faster of change to coping bravely with the dreaded function notation!

It was nice to “meet” you at our department meeting on Tuesday!

They are starting to get the hang of function notation 🙂 We’ve been working on it a LOT.

They’re all really smart kids, just get scared off easily. And they know way more than they think they do. If they see something that looks hard they assume they don’t know it, so many just don’t bother to try.

Thank you so much for your ideas! It really did help me get them started. So much better than asking them to tell me what they know from the graph. I’ve tried it that way before and get way less back from them than I did when asking what they notice and then what they wonder.

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Phenomenal post. Some awesome ideas here. Thanks for sharing. I can’t wait for graphs to next appear on my scheme of work!