Algebra Middle School Statistics

Ring in the New Year with Fun Classroom Lessons!

Now is a good time to reflect upon the past year, and think about all of the professional growth I have made through the people whose ideas I have shared and experienced through the twitter-sphere and blog-o-sphere (are these actual words?), and to send thanks from all of the new math friends I have made.  I took a look back at all of my posts from the previous year, and here are 5 great activities you can use tomorrow is your classroom.  Share them, adapt them, expand upon them…it’s all good.  Just pay it forward and share your best works, or leave a comment /contact me and let me know if you use them!  Enjoy.

Conic Sections Drawing Project – this was the most popular post of the year.  For algebra 2 or pre-calc, this project just got better with the Desmos online calculator, which is my favorite new tool of the past year.

Tapping Into the Addition of Bubble Wrap – bubble wrap, iPads, and slope meet for a fun exploration.   Look at rate of change through student-produced data.

Tall Tales for Probability – Featuring the poker chip drawing game, and examples from the Amazing Race and craps.  Probability should be fun.  Make it so!

Let’s Play Plinko! – I have used Plinko as an introduction for binomial distributions for years, but in this presentation from last summer’s Siemens STEM Academy, tech tools like PollEverywhere and Google Drive are used to increase interaction.

Composite Functions and ESP – Use this activity with middle-schools and see if they can develop the pattern.  For high school, have students write and justify their own ESP puzzles.  Also features Doceri, another favorite new tool of mine, for iPad.

Algebra Middle School Technology

Siemens STEM Academy – Sunday with Lodge

This week, I have the incredible opportunity to participate in the Siemens STEM Academy, held at Discovery HQ in Silver Spring, MD.  This year, I am serving as a team leader, after having been an attendee (fellow) last year.  What a tremendous week of sharing with colleagues who are are all into advancing the cause of STEM education.  As a team leader, I am excited to share my skills and ideas with the group, and will post parts of my presentation to the blog later this week.

Right now, the group is hearing from Dr. Lodge McCammon, a pioneer in using music and video to stimulate and educate students.  This year’s group of 50 fellows, after some initial networking, are hearing about Lodge’s process for putting together his songs, which often require the recruitment of his mom and dad to perform musical parts.


But moving beyond the songs, Lodge seeks to have students symbolize the lyrics through movement, the “Kinesthetic Lecture”.  Today, the fellows learned new “moves” to share for Lodge’s “Mitosis” song.  Check out there lyrics here (you can also experience more of Lodge’s great songs there), and the kinesthetic moves below:

Lodge is also an expert in the “flipped” classroom model, where teachers produce videos of lessons and concepts, for students to watch and review at home.  In the presentation, Lodge shared anecdotes and ideas for implementing the flipped model.  Many of his ideas and resources can be found at his FIZZ site on the Friday Institute for Educational Innovation.  Here’s a quick introduction by Lodge explaining the flipped concept:

I have worked with a number of teachers who are interested in the flipped model, and the flipped ideas have received much press through sites like Khan Academy.  Lodge has collected data on the success of the flipped model through middle school math teachers he works with,  including a comparison of a teacher-created video lesson versus Khan Academy.  I appreciate that Lodge stresses the need for teachers to produce their own videos, and continue to be identified as their students’ educational expert:

It’s critical that the teacher be the deliverer.

Teachers teaching cannot be outsourced and replaced.

Teachers matter now more than ever!  You can follow Lodge on Facebook at  What a fantastic kick-off to the week. Looking forward to hearing about and sharing more classroom ideas.


Why Do Kids Need to Factor?

One of the joys of my job as a math coach is having conversations with colleagues about the hows and whys of math class.  Often, the best conversations come from unplanned meetings, just chewing the fat about what is happening in classrooms.  Earlier this month, I visited a second-year high school teacher with a quick question that turned into a deeper conversation after I noticed her posted objective: “factor polynomials where a > 1”.  The objective was for our academic-level algebra class.  I asked how things were going with the class, and the teacher expressed the usual frustration of teaching kids the process of factoring, which led to her asking what I would do differently…what did I have in my “bag of tricks” to teach factoring?

I had to think hard about my answer.  Like most math teachers, I had taught Algebra I many times, and had gone through the process struggles students have with traditional factoring.  I’ve never really subscribed to a “trick” for factoring:  I have some colleagues who use a chart method, while others attempt grouping.  But it occurred to me that the entire premise here was flawed…just how important is factoring to teach and learn?  My second-year teacher friend thought for a minute, then gave the answer many teachers would give:

They’ll need factoring in Algebra II and other classes they take down the road.


Is that really the best answer we, as math teachers, can give for learning factoring?  It’s just a cog in the polynomial machine: add – subtract – FOIL – factor – simplify rationals – graph.  How exciting!

In a previous chat with a different teacher, I suggested that we upset the entire process.  Why do we save fun, neat stuff like projectile motion for “later”?  Dive right in, look at some non-linear graphs, and develop new ideas about quadratic functions, symmetry, intercepts, and vertices right away.  If you have never been to the PhET (interactive science simulations from the University of Colorado), go there now.  Check out the projectile motion applet:


Have fun tossing Buicks across the sky.

Think about the number of kids who never get to experience these great math models, because we beat them with a stick with pages of FOIL and factoring worksheets, before they ever get to see a parabola.

So, what of factoring?  Let’s say I wanted to re-write the following function in factored form:

Is it wrong to have students graph the function and look for intercepts?


If we have an intercept at x = 2, then we know that (x-2) must be a factor.  From there, we can piece our way to the second factor of (3x-7).  Is it “wrong” to teach students to look at polynomials this way?  I suspect many would call it blasphemous, but somehow I know that my kids know more about the inter-connectedness of functions, intercepts, and polynomials than theirs.

I want my students to utilize and switch between multiple representations of all families of functions: equation, table, graph, context.    Unfortunately, most textbook ensure that these topics will continue to be taught in a linear fashion.

Let’s take that old objective of “factor polynomials” and change it to “develop and understand quadratic models for natural phenomena”

And if the reason we teach anything in math is because “they’ll need it for their next class”, then we are doing math wrong.