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February 07
 Inside the Classroom - The Big Drip in Room 5

We want you to have a glimpse into some of the learning inside our classrooms at Belfast.  Part of our School Development Plan focuses on the creation of Low Floor / High Ceiling tasks that engage students in solving complext problems. The following documentation of an interview with  Mr.  Sangster one of our Grade 3/4 teachers. He describes
a Low Floor High Ceiling task that students in room 5 have been investigating as a math inquiry.

Inspiration:
Students observed the dripping faucet in the class.
Dripping taps are very common.

The Question:
I posed the question to my students: If the faucet drips once per second, is this a lot of water? The wait time before any response came was much longer than I anticipated. Some inferred yes, it is a lot of water. Some no. There was a lot of doubt within their inference statements.

The Conjecture:
I asked students to form collaborative groups where each group shared the same inference.
The group was tasked with creating a conjecture: a statement that clearly told their inference or prediction.

The Proof:
After conjectures were written and shared, strategizing began to build a proof that either proved or disproved the group’s conjecture.
The students lacked the experience and math skills to immediately see a path toward proof, however they struggled and truly collaborated in testing various strategies.
It was exciting to watch as they secretly looked for progress clues from other groups. In fact this informal sharing between groups was essential step to group advancement towards proofs of their conjectures.

Aha moment:
The first was when I introduced to them the 5ml medical syringe.  One group of kids realized that the syringe could be used to measure exactly how much was dripping. The next aha was when they realized that they needed a chunk of time to work with to accompany the measurements (eg, how much drips in 5 minutes?).  5 minutes was chosen because the students intuitively knew that it was an easy number to work with.  This led to…how many 5 minute chunks are in an hour? Kids who applied these understanding to a repeated addition strategy found this frustrating; one student said” this would be a good problem for multiplication!”  and then he proceeded to try to figure what this looked like.

Next Steps:
According to the Jo Boaler course I took, learning happens when the student have a need for new learning (a situation to anchor their leaning to).  We are now doing pre-multiplication activities, especially working with arrays (visual model) and games to meet this need of moving beyond repeated addition. The students are right on the cusp of using a decomposing 2 digit  x 2 digit multiplication into the place value parts.

Kids are already shocked that 720 ml drips in one hour; let alone the calculation over a day which we haven’t done yet! This will be our next step!
In addition I would like to extend this to a much bigger concept of the waste of water on a global scale.  What is the rippling impact of the waste of water?

Is there anything you would do differently?
I might have provided the tools /practice to measure capacity of water first before I introduced the problem.