How do you cut your Pizza?🍕

*This lesson is based on an activity I tried out in my Intermediate Mathematics course at uOttawa.

Slightly adapting it and integrating some technology in the process, I introduced it to my MFM2P students during practicum via Pear Deck, an interactive presentation tool, here. It was my choice of tech for this lesson because it had all the features I needed to set-up the activity with the students and collaboratively showcase our understanding of the actual task before working on it smaller groups. With features such as adding images, text/number responses, drawing/sketching, and the anonymous grid display of answers, I was able to breakdown the activity and gather that diagnostic assessment all through whole-group discussions based on student responses.

First, I displayed this image:mfm2p_pizza_problemThen asked:pizza-problem

We focused our discussion on,”Not equal slices” and “The way it’s cut.”  Both pizzas used only 3-straight cuts, but the one on the left gave us 6 pieces, and the one on the right gave us 7. Why would you cut it differently? My idea here was to provide some meaning as to why we’re about to cut our pizza in such a way …perhaps it depends on whether we’re interested in producing equal size pieces vs. maximum number of pieces.

Next, we introduced 4-straight cuts. Using Pear Deck’s student response and answer display features, we estimated the maximum number of pieces possible, showcased all responses, and consolidated by having a student volunteer to come-up to the board to present his answer —11 pieces.
pizza-cuts-estimatespizza-cuts
In my opinion, I found Pear Deck to be extremely complementary to the introduction of this activity before breaking it down to working in groups via hands-on:

  1. It allowed for students’ initial engagement with the task to be on an individual level, yet in a collaborative environment where they can see each other’s anonymous responses and formulate whole-class discussions around their understanding.
  2. In a sense, it also allowed for differentiation because it created a safe learning space for students to engage with the task—even if unsure of their response—followed by the opportunity to self-assess/reflect by gathering feedback from peer responses and class discussions.
  3. Provided for better time-management through the collective presentation of student responses as opposed to directly introducing it through hands-on experimentation and travelling from group to group to gather diagnostic assessment.

The hands-on portion for this activity was introduced through the main challenge, which was now to find the maximum number of pieces possible using 20-straight cuts. Again, we estimated some numbers together, then they worked on it in random groups of two using the materials provided. Some students took to it and wanted to sketch it out on their boards, even though it wasn’t an easy sketch to draw —kind of left me wondering if this request was a reflection on their preference and level of comfort in working on Vertical Non-Permanent Surfaces (VNPS).

pizza-estimtes

With each answer they came up with for maximum number of pieces, there was still room to find more. Only one group started collecting their data using a table of values, and so we directed our discussion towards this idea and discussed a possible next step —noticing a pattern in the data collected. Once we identified the constant second difference and the quadratic relation, Desmos Graphing Calculator  was the math tool of choice to finally help us solve this question —211 pieces!

solving2_pizzascreen-shot-2017-01-29-at-3-24-16-pm

Overall, the students seemed really interested and engaged in the task, however, I think I could have definitely consolidated it better. I dedicated a bit more time than needed before stepping in to provide some support during productive struggle and thus had less time than originally planned to spend on interpreting the actual graph we produced. My plan was to use Pear Deck’s drawing features to collectively gather and discuss student responses by labelling some points on the graph together.
pizza_responses
Looking back on it now, however, I think a better choice would have been to design the graphing and answering portion of this lesson using Desmos Activity Builder and possibly introducing it as a consolidation activity for the following day. Not rushing consolidation is just as important as providing the necessary time for productive struggle.

My preference in using Pear Deck was mainly for what it’s actually designed for —an interactive presentation for my activity; however, when it comes to solving and graphing, Desmos is the right tool for that task. I need to see precise responses for better assessment and feedback, while allowing students the ease in answering —given the different features offered by Desmos as the interface design is math directed.

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