4 Good Things

I’ve been making time on Sunday evenings to go through my Google Reader and peruse the blogosphere of all things math.  The problem is my dedicated one hour becomes two hours, two becomes three, and then it’s already past midnight.  We all know that Mondays come too soon.

Here are 4 really good things I gained yesterday:

1. Of course I learned something new from reading Dan Meyer’s blog.  More importantly, this post — itself a good lesson for my 6th graders today — reminded me to pull out other great lessons from Professor Malcolm Swan.  I bought these two books (from England) that Swan and the Shell Centre Team had written.  Each book now costs £24 or $40 — worth every penny!  My only minor America-is-the-center-of-the-universe complaint is the books are approximately 8.5 in x 12 in, so I have to re-size all the worksheets to fit our letter-size papers.

languageoffuncsandgraphs5860 prbmswithpatterns8486

I’m going to do “Hypnotic Drugs” (from the red book) tomorrow because I’m introducing the algebra kids to exponential functions.  My anal self retyped (and revised just a bit) what was in the book to make everything fit nicely onto 8-1/2 by 11.  Please click here for the sleeping_pills lesson in docx.  But we can’t start this activity until we are done discussing a lesson I did in #2 below.  Ahh, so many good lessons, not enough time!!



2. It is a small enough blogosphere when Malcolm Swan’s name came up again 30 minutes later as I read Sam Shah’s post in my Google Reader.  Sam shared a post from Justin Lanier, titled “Modeling – Part 1.”  I love these types of problems or “measures tasks,” and Justin credits Swan and Ridgway for the lesson.  I did this “square-ness” lesson today with my 6th graders but obtained results I hadn’t anticipated, so I tried it with my algebra 8th graders and again discovered that despite having had two more years of math these 8th graders still had many different rankings of the seven shapes from most square to least square.

I stole the same shapes and questions from Justin’s post.  Or you could use the lesson from Swan and Ridgway.


Algebra class was almost ending when we’d already noted 14 different rankings of the seven shapes.  I gave the students a second chance at their original ranking — are there any changes you’d like to make or keep it as is?  I can’t wait until tomorrow for us to discuss this problem further!

3. I registered my 6th grade class to use the new Math Reasoning Inventory (MRI).  The “interview” format looks good.  I’m thinking of having one of our teaching assistants do this with the students because I’m not sure how I could carve out the time to do it myself — and maybe we could select a smaller group of students. From Math Forum Internet News:

Marilyn Burns recently announced the launch of a new online formative assessment tool.

The Math Reasoning Inventory (MRI) reveals how students think and reason through questions that focus on number and operations based on content from the Common Core State Standards (CCSS) for Mathematics prior to sixth grade. Check out, in particular, the more than 80 face-to-face interview video clips of students demonstrating appropriate reasoning strategies, exhibiting lack of understanding, self-correcting, using a procedure inappropriately, and more.

4. I downloaded MathJax but haven’t had time to check it out; this would be really helpful.  Also from Math Forum Internet News:

A major new version of MathJax came out earlier this week. Rendering “beautiful math in all browsers,” this open source JavaScript display engine for LaTeX, MathML, and AsciiMath notation delivers high-quality typography across all web apps.

MathJax lets you copy equations from web pages into Word and LaTeX documents, science blogs, research wikis, calculation software like Maple, Mathematica and more — all without browser plugins or font installations. Because it uses modern CSS and web fonts instead of images or Flash, MathJax also features the ability to scale all math in a page or zoom in on a particular equation. Together with the Internet Explorer add-on MathPlayer, MathJax makes math accessible to screen readers, to screen magnifiers, and to learning disability software.

Maybe it wasn’t all work this weekend.  It was unusually warm this weekend, even for southern California, so we took Mandy to the beach on Saturday.  Apparently Mandy is an English lab — must be, other people keep say so.


On Sunday we rode 70 miles to Santa Ynez (somewhere in this Valley is Michael Jackson’s Neverland Ranch).  Kind of a fun little town — looks like the Wild Wild West all of a sudden.


I love going through the twisties, but sadly there was a head-on collision between two motorcyclists on our way back.  We turned around and used an alternative route.



[Updated 03/07/12]

It was the first time the students work with x as an exponent.  Although the first part of the assignment was plug-and-chug, it was useful for them to learn how to use the exponent button on the calculator and become aware that A changes after each hour.

I was surprised that half of the students picked the middle graph in question #2 to model the numbers they got in question #1.

But most them changed their mind and picked the third [correct] graph in #2 after they did their calculations for the second drug Nitrazepam and had to roughly sketch its graph.

I did a simulation: filled a container with 4 cups of water (the blood) and added 16 drops of food coloring (the medicine). Poured out 1 cup of this solution and replaced it with 1 cup of pure water (dissipation of 1/4 of the drug in a 4-hour period).  Repeated the process until the water turned clear (medicine had worn off).

To save time, we graphed the equations together using Excel (the kids have done quite a bit of work with Excel when we did systems of equations).  We agreed that after 8 hours the drug Triazolam had dissipated.

We skipped #6 but I talked with the kids about half-life and C14-dating.  (I have a Biology degree, not math :)


[Updated 03/08/12]

I really love this activity.  The kids tried to convince each other that their ranking of the “squareness” of the shapes were the correct ones — their arguments were sometimes plausible and sometimes flawed, but they were all talking up a storm.  While everyone eventually agreed that C is the most square, and B and E were the least square.  They had a much tougher time agreeing on the rest, and I hadn’t anticipated this.

kids working

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