I drive past this building every day on my way to work. It is Young Tower at 6080 Young Street in Halifax. I think it is pretty interesting... I used this picture as a problem solving warm up activity for a group of grade 10 math teachers recently. I gave each group of teachers a large piece of chart paper and asked them to divide the paper in half with a line. I asked teachers to brainstorm what they notice about this picture and record it on one half of their chart paper. I asked them to look at the picture using a number of lenses. What would an architect notice about this image? What would a person who worked at this building notice about this picture? What would a mathematician notice about this picture? After about 5 minutes of brainstorming, I asked each group to tell me one thing they noticed and I recorded it at the front of the room. Groups noticed things like the number and size of windows on the building ("about half the lateral surface is glass"), the shape of the building ("almost a cube"), the picture must have been taken on a weekend because there are very few cars in the parking lot, and the weather was really nice that day. Next I asked them to brainstorm what they wonder about this picture and record in on the other half of their chart paper. If this picture was the start of a math problem, what could that math problem be? What things that they noticed sparked their curiosity? After another 5 minutes, I asked each group once again to tell me one thing that they wondered. After looking at all the questions that the groups posed, we selected one and asked everyone to estimate an answer to that question. I also asked them what information would they need to make a more accurate estimate. Once they had an initial estimate, I gave them some additional information about the building and let them revise their estimate. We had several really interesting questions posed by groups. Some questions concerned the shape of the building, like "How close to a perfect cube is this building?" Other questions focused on finance such as, "How much revenue is generated by leasing all of the office space in this building?" One of my favourite 'wonderings' was, "How much wrapping paper would it take to wrap this building up like a Christmas present?"
This "I Notice/I Wonder" problem solving strategy is one that I saw shared by Max Ray-Riek from the Math Forum. He has a blog where he talks about Noticing and Wondering in High School. This strategy starts off with brainstorming to let students get familiar and engaged with a problem situation before jumping into a specific question to solve. By having students come up with questions, you'll often get more engagement and interest. It also allows you to respond to interesting suggestions from students that you might not have considered. It allows everyone in the class meaningful participation in the conversation because everyone has something that they can notice. This strategy might also create additional opportunities for differentiation by using several different questions that students suggested.
One of my favourite activities recently has been Fawn Nguyen's Snap Hotel. This activity can also be found on the NCTM Illuminations website. You might see this activity online under a few different names... my favourite is Hotel^3. It is an engaging problem solving task. Students are given 50 multi-link cubes and instructed to build a model hotel. Each cube represents one hotel room. Some rooms are more desirable than others and can be rented for higher prices. The number of windows and whether or not the room has a roof determine the rental price. Students also have to consider costs associated with property and height. The hotels that students create in this activity remind me of Montreal's Habitat 67. Students might talk about the costs and benefits of this type of architecture. This activity can be used to assess a number of Nova Scotia mathematics curriculum outcomes.
The Rules - As a team, build a hotel that yields the highest profit.
Below are some hotel's created by teachers during a session at the NS MTA conference in Oct. 2015.
Suggestions for Improvement
Below are my Powerpoint introduction and a student handout. Also included is an analysis of several different hotels to see how their profits compare.
Why I Like This Task
Nova Scotia Curriculum Outcomes