Comments on: Age-Appropriate? Not Exactly. Valuable? Absolutely.

By: Nat

Nat — Sun, 11 Jan 2015 19:34:19 +0000

I like the ideas you suggest. In terms of building skills, your descriptions are excellent, and both of your verbal prompts would require critical thinking of your students. I might ask for two different sets of perpendicular lines from the first prompt, so you don’t just get y=4 and x=3 (…although that would demonstrate some understanding as well).

I try to contextualize graphs whenever possible as well. Here is a link to a set of openers I’ve pieced together, which ask students to move between the four representations. I used one or two each day to open class with kids who were just being introduced to linear equations.

https://www.dropbox.com/s/16qqnj01lgd4h81/GAVN%20linear-equations.doc?dl=0

Thanks for the conversation!

By: Michael Fenton

Michael Fenton — Sun, 11 Jan 2015 16:49:02 +0000

Nat, thanks for the suggestion to include verbal. I try to tie in the four representations as often as possible, but I’m not sure (yet) how to launch one of these challenges with a verbal description alone. Maybe something like, “Plot a pair of perpendicular lines that intersect at (3, 4).” Or, for quadratics, “Plot a downward-facing quadratic function whose x-intercepts add up to its y-intercept.”

Is this what you had in mind? Can you suggest some tweaks (or something else entirely) that would have more potential for awesomeness in the classroom?

Also, great stuff over at http://17goldenfish.com.

Thanks for dropping by!

By: Nat

Nat — Sun, 11 Jan 2015 11:46:25 +0000

Many of my students showed up from their winter break pretty rusty with graphing linear equations – even many students who seemed proficient just before winter break. I also wanted to (self)reprimand their teacher from last semester.

I would add “verbal” to your list from resolution #2 (graphical, algebraic, and tabular).

Thanks for sharing these challenges!

By: Michael Fenton

Michael Fenton — Sat, 10 Jan 2015 16:30:58 +0000

I think adding a slider would be entirely appropriate for any of these challenges. I would caution against ONLY using sliders to solve the challenges, as I believe something else goes on in students’ brains when they have to write the equation explicitly, modify, observe, etc.

Maybe students would use sliders for the odd-numbered challenges, or for #1-4?

By: Jane Taylor

Jane Taylor — Sat, 10 Jan 2015 16:27:23 +0000

What about the slider on Desmos? Does that trivialize the task? I want to use Desmos more but I was concerned about students just usu g the slider instead of thinking about the parameters of an equation.

By: Michael Fenton

Michael Fenton — Fri, 09 Jan 2015 05:17:01 +0000

Martin, thanks for sharing. I know I’m not the only one with students who struggle with what should be basic, sometimes it seems that way, so it’s nice to have a reminder that others have similar experiences.

There’s lots of great stuff over at Inquiry Maths! (And obviously on Dan’s blog as well.)

I’m looking forward to developing this idea more completely over the coming months.

Cheers!

By: Martin

Martin — Fri, 09 Jan 2015 05:11:04 +0000

Hello Michael,
I do feel your pain with how students wipe their memories of anything remotely related to linear graphs at times. Recently I had finished working through a unit of work based on graphing quadratic, cubic and reciprocal graphs, yet when I popped a linear graph such as 3x+2y=8 (yes with fractions!), it completely through them!
This is a lovely little task which could open out into something quite deep and worthwhile exploring further and I think it could fit well into the ideas develop from the Inquiry Maths work being developed at the http://www.inquirymaths.co.uk website. I’ve been following this website, along with your blog and Dan Meyer’s blog and getting lots of useful ideas to pursue. Maybe this one could be useful to this type of starting questions too.
Best wishes,
Martin @mart_brown