Archives for the month of: July, 2013

Dan Meyer explains the three act approach

A quote from Jo Boaler, inspired by Keith Devlin:

” Mathematics is a performance, a living act, a way of interpreting the world.  Imagine music lessons is which students worked through hundreds of hours of sheet music, adjusting the notes on the page, receiving checks and crosses from the teachers, but never playing the music.  Students would not continue with the subject because the would never experiences what music is.  Yet this is the situation that continues, seemingly unabated, in mathematics classes.

An analogy I have used when trying to explain this to parents, board members etc.:  A certain popular curriculum teaches math as a series of unconnected skills.  Imagine a volleyball team that continually practiced how to bump, to set and  to spike, but never combined the skills and had never played a game.  How do you think they would fare when playing a team who had learned the skills in the context of playing an actual game of volleyball?

Here is a problem I found in Jo Boaler’s book “What’s math got to do with it?” She credits it to Ruth Parker:


A woman is on a diet and goes into a shop to buy some turkey slices.  She buys 3 slices which together weigh 1/3 of a pound, but her diet says that she is only allowed to eat 1/4 of a pound.  How much of the 3 slices she bought can she eat while staying true to her diet?

Instead of having to use long tape measures, students can use their smart phones to measure distances.  Smartmeasure is free for androids.  Theodolite for the iphone is $3.99.  Please comment if you know a free app for the iphone.

A free app that allows you to type in your class roster and award points (positive and negative) to your students throughout the period.  Each student is assigned a colorful avatar, and if you have the right equipment, you can project it on a screen, so students can see when they’ve earned points. You can assign parents and students code numbers so they can check their progress.  Sound affects too.

This is a terrific tool you can download for free.  Not only does it allow you to graph equations, you can type in a generic equation such as y = a(x-h)^2+k, and it allows you to manipulate the equation to see the effects of different values of a, h, and k.

Pure mathematicians may hate this idea, but for Algebra students I explain the notation f(x) as just y in disguise.  My friend, Joy, took this idea a step further and shared this with me:

A note of thanks for the f(x) being “y in disguise.”  I introduced it today wearing two masks (one hidden underneath).  Told them I was planning to go out on Halloween as the “mean green function machine” (masks are green, one of our school colors).  The top mask I wrote on it f(x) and the one underneath was, of course, y.  So when I said you only need to remember f(x) is y in disguise, I whipped off the top mask and they saw the y underneath.   It was great!  And for a Friday, especially my 6th period, it woke them up and they had a blast!  And so did I!

My friend, Ellen and I brainstormed this one at coffee the other day, as an opening day activity.

Hand each member of the group an envelope with 3 to 4 post its, each with a different number on them.  Have the group combine their post its, and place them on a generic number line (not labeled) posted on the wall in the classroom.  Once all groups are finished have them check the work of another group (each group will have their own set of numbers), or do a gallery walk, looking at all the number lines in the class. 

The numbers should include decimals, fractions, integers, square roots, pi,simple cube roots, etc.  NO CALCULATORS allowed.



Here’s a real life problem I gave my students.  It was a lot easier to explain, than to write here as a problem. :).  My students were highly motivated, as I was going to make my decision that morning, based on their findings.   It was great having the students share their solutions with the class, as there were many different methods of solving:


Yesterday I had someone paint the spare room in my house.  When I came home I was dismayed that the color I chose was much darker than I had anticipated.  I went back to the paint store to try again.  Since I liked the color I asked for a lighter version.  The clerk made a “batch” which had a color strength of 25%.  It was too light.  He informed me that he was only able to mix in increments of 25%, so he made a batch of 50%.  It seemed a bit dark.  He suggested I take this 50% strength gallon home along with a quart of white paint, and a large pail for mixing.  I painted a swatch of the 50% on the wall and checked it in the morning.  I was still undecided.  Since my painter was coming back that morning, I needed to make a decision as to whether to mix the gallon of 50% and the quart of white.  The question posed to my students was:  What would the color strength (%) of the mixture be, in relationship to the original paint. 


Note:  most of my students came up with the same wrong answer to begin with, but when I prompted them to try again, they were able to determine the correct percent.

I don’t know what happened to act three, but it’s the sequel that intriques me. After I’ve tried this, I’ll report back.