Causality vs Causation and an Intro to Graphing

The second spiral was a short introduction to relations.  I started off with the concept of a rate, and created my own version of the "pumping gas" problem from Mr. Orr's "tap into teen minds". 

One of the best things that Mr. Dan Meyer stated about this was how the video can be used as a 'hook'.  Boy, did I underestimate the power of this hook.  Combine this hook with open ended questions, and Dan Meyer was absolutely correct - all sorts of learners participated, even the weaker math students.

The video even out the playing field and it was magical to have such engagement in an applied classroom.  In all of my eight years of teaching (I know, I'm young), I have never, ever seen this.

Another thing that has me pleasantly surprised - were the questions being asked.

"What car is it?"
"How many litres can your car hold?"
"How many litres did you put in?"
"How big is your car?"


"How much did you pay?"


It is so intriguing as some of these questions did not come to my mind, yet each of them are indeed connected to math.  In many ways, my converging mindset could only think of the one question I really wanted (ie:  what is the price of gas per litre?)  I must work on my divergent thinking.

After a day of rates, we went on to the topic of scatterplots.  Now understanding the importance of a hook, I started the students off with a 30 second paragraph of Tyler Vigen's graphs of spurious correlations

The causality vs correlation issue is often a huge source of consternation for those who frequent the forums online, and I just wanted to introduce this common pitfall. 

Hence, my Friday assessment of scatterplots and rates was chicken and crude oil related, much to the delight of some of my students.  Or chagrin.  I'm still learning to read some of them one month through.

On a side note, a few of my students were trying to force a connection in this above relationship depicted by the line graph to make sense and ventured a hypothesis thinking that the chicken was being cooked in the crude oil. 

My mind is still blown that I have such a high engagement level. 

I'm proud of the students.  Let's see how long we can keep this up.

Look ahead:  I'm spiraling back to the Pythagorean theorem by starting off week 4 with  perimeter of composite shapes.  Now that we've completed an initial assessment and a reassessment of week 1, I know exactly who to target tomorrow for individual help.  This is an incredible advantage of the spiral curriculum. 

Assessment of the First Spiral

Even though I've been teaching for eight years now, I turned everything absolutely upside down.  I'm now working with a spiral curriculum, performing Dan Meyer's 3-act math on a regular basis and implementing some serious classroom management techniques that was recommended to me from my last year's mentee.

My first spiral which consisted of Pythagorean theorem, perimeter, collecting like terms, polynomials, area and distributive property was a success by my books thus far.  They did well on certain portions of their assessment, but other not so well.  I crunched a lot of material in 1.5 weeks, and they struggled with the last portion - distributive property.  Or rather, I didn't give enough time to allow for the students to work with it.

Nonetheless - I borrowed some growing success initiatives from my science department, my wife, and another math colleague.

1)  An adaptation of my science department's concurrent credit recovery policy,:  if the students failed the assessment overall, they could get a second hack at the assessment.  They must perform at a level 3 (~70%) for me to bring their marks (all of K, A, T, C) up to 50%.

2)  Wife:  Since I was devoting class time for students to have a second hack at the assessment, I allowed the other students to try to upgrade one question.  My one page double sided assessment had a couple of thinking questions - one from homework which I took up and another one that was a little extension.  As a result, all of my students had 'something' to work on.

3)  After going through the whole assessment, students can choose to look in their binder to help them with any question that they may have trouble with.  I've been trying to give students incentive to keep an organized binder, and especially with this spiral curriculum, we have topics everywhere.  Well, armed with their organized binders, students can now use their binder (at the cost of 50% of the mark for the particular question), students can now and try to get the remaining 50% of the question.

Intro to Pythagorean Theorem

Today, I have officially decided to follow and jump on the Dan Meyer bandwagon by introducing a problem using his 3-acts.  However, I have more specifically jumped on Mr. Orr's bandwagon, as he seems to be the Canadian version of Dan Meyer from what I've read on his blog.

To start myself off on this 3-act business, I have copied Mr. Orr's video on "Corner 2 corner" with this video below:

I requested that the students write down any questions that come to mind - even non-mathematical ones.  I had some trouble amalgamating their questions as well as leading them to the question that did matter - but I have tremendous students that eventually got to the question I wanted:  what's the length of the room from the top corner to bottom corner? 

My favourite part of the whole exercise is the estimation portion.  As per Dan Meyer, it's best to ask students to answer the following:

•  What's a number that's too low? 
•  What's a number that's too high?  
•  What's the exact measurement?

Take a look:

We then discussed a plan of how to find the length of the string.  With some guidance, a couple got the concept.  Reinforcement is definitely necessary tomorrow.  

Instead of giving all the measurements, I felt that my 9s needed some movement - so I split them up into groups and they went about counting the tiles on the ground to calculate the width and length of the class.

We finished it off with some calculations and got the answer.  We have two people who guessed very close to the answer!

I'd say my first 3-act execution was somewhat of a success.  Let's hope I improve on the next one!

Activating Prior Knowledge

Well - here I go, trying to spiral my way through 9 applied math.  First day started with some serious structure laid down in hopes of preventing those inevitable fires that come about in the oncoming months.

As one of my favourite colleagues from MDHS often described teaching - it's "trench warfare out here." I certainly laid a dug a deep trench and it started well.  My students and I battled the math together on the first day.

We started with some prior knowledge activation as was suggested by my fellow colleague Ms. Phan out in Ottawa-Carleton District School Board suggested that I do.

Here are some of the results of today's prior knowledge activation in which they tried to brainstorm as many topics as possible and categorize them under different levels of confidence.