Day 75

Day 75

They finished choosing (creating) their best three questions for each station today. It was a bit of a gong show. Some did not seem to understand that writing "How high is the bridge?" when there are 4 pictures of bridges, was insufficient for me to provide them the information needed to answer the question. Also, many had questions that did not actually relate to the MFM2P curriculum (sigh). And some had questions like "How high is the bridge?" and where they listed was information they needed to know to answer the question, they wrote "Height of the bridge." Not a brilliant day. I went through all their best 3 questions this afternoon and modified as needed. I gave new questions where needed (which really defeats the purpose of what we have done so far). Now I have to get all the information they need prepared for them to answer the questions. 

Unrelated, I finally got around to taking pictures of some of the Sum-of-Squares/Similar Triangles/Trigonometry poster projects my class did a while back.

Day 74

Day 74

We picked up where we left off yesterday - sorting questions by curriculum expectation. They had 3 stations left to work on today. Once those were complete they started the process of choosing the best 3 questions for each station along with determining what information they would need from me in order to answer each of them. This took significantly longer than I expected. Some groups realized that they didn't have enough good questions (or any!) and had to come up with more. They were receptive to guidance in this process - they realized that they were stuck and needed help. I am certain that this process will pay off next week when they write the actual summative.  As we didn't finish this round, they will do more tomorrow. And I will add information to the pictures so that they can answer all 18 of their questions.

And here is a pic from my board. Bet you didn't know I go by "B-Dawg"! (neither did I!) I less than three this class.

Day 73 - Summative Prep Begins

Day 73

This week is all about summative preparation. In our board (district) all grade 10 academic and applied students write a board-wide summative task and a board-wide exam. Next week my students will be doing their summative, which focuses on the mathematical process expectations (similar to SMP in the US). Alex Overwijk created this summative prep and blogged about it here. We tweaked it a bit at our last meeting, but the credit definitely goes to him.

Students walked in to find their names in groups (chosen randomly) on the board and papers awaiting them at the tables. Each group had a set of pictures, an envelope along with the names of the members of the group and their "home station". Here are the pictures with which they worked:

I explained to them that everything was colour coded. Each group would be working on a particular colour of paper and with one marker. Their first job today was to come up with as many questions as they could for each station. They started at their home station, placed their questions in the envelope when they finished then moved on to the next station. They weren't all completely on-board with this process. This was also the first time that many students complained about the groups. I can't even say how many times I said "Please put your phone away" today. I even confiscated two phones, which rarely happens. With a little encouragement from me, most wrote down some decent questions. I need to think about how I can get better questions out of them if (when) I do this again. I am sure that if more than 5 of them had been in class on the day we did the tree activity, it would have helped.

This process continued until they had all been to every station. Here are the questions they came up with:

Next, they had to classify the questions at their home station by curriculum expectation (each group again got the same colour of paper). Some questions were not mathematical in nature, so could be ignored. Some questions were repeated by all groups. Some of the curriculum was not represented by any questions so they could look at the pictures again to see if they could find any questions that would fit. When they finished at their home station they put all the questions back in the envelope and moved on to the next station. They got through 3 stations today. To be continued tomorrow...

Days 71 & 72

Day 71

We started with more Estimation 180 today. We did about 5 of them. This one (day 160) was the most difficult for them:

The guesses ranged from 5500 to 2.5 million. All of which are far from the correct answer. Clearly my students need to build a few more Millennium Falcons!

We started today's cup stacking with the Styrofoam cups. This was basically a repeat of what we did yesterday, but everyone was working on the same method of stacking.

They got right to work. I gave each group 6 cups and suggested they would need a ruler. They measured and collected data and wrote an equation and made a scatter plot. I circulated and looked at their data. 

One group had 1 cup with a height of 8.5 cm, 2 cups with a height of 17 cm, etc. I stacked cups and asked if the height was actually 17 cm.

I could tell which groups hadn't measured very well - they said the lip of the cup was 1 cm.  When I showed them 6 cups with a ruler next to them and asked what the height was, it was apparent that they needed to be more precise with their measurements.

It was really interesting to see their equations. The lip of the cup was about 1.3 cm and the rest of the cup was about 7 cm, so the equation should have been 
height = 7 + 1.3(# of cups), but they had equations with y-intercepts (height-intercepts) of around 8. They had taken the first value in the height column as the "fixed value" without realizing that it also had the height of the lip. So we came up with this table which caused issues because 0 cups have a height of 0 cm.

They saw how to fix their equations and came up with 127.5 cups to reach my height. We tested this out and they were exactly right!

Next I asked them to work on the relationship when they stacked the red cups this way:

Only one group had finished this yesterday (they got to stack the cups a different way). This is the data they came up with, along with the pattern in the # of cups and the pattern within the pattern.

They had to continue the pattern up to 10 rows then plot their data. They saw that it was quadratic so the next step was to input the data in the graphing calculator to get its equation.

Now the equation related # of rows and # of cups, not height. To figure out the # of cups needed to reach my height they needed to figure out how many rows first. They knew the height of one cup from yesterday's work.

Sadly, we didn't get a chance to test this one out today. And I am doing in-school PD all day tomorrow so we likely won't get there.

Day 72

Tomorrow is tying cup stacking to systems of equations. They will start with this, stolen from Dan Meyer:

Hopefully that will help them with the next question:

I will leave the cups out for my substitute teacher to get them to test out their answers!

That will be followed by some solving systems questions (in context) using both substitution (for equations in y = mx + b form) and elimination (for equations in Ax + By = C form).

Day 70 - Cup Stacking

Day 70

Today we started cup stacking! But first we did some Estimation 180. It was good to get back to it. 

I have done a version of Dan Meyer's cup stacking activity for several years, but this time I started with "cup stacking wide open" - they could stack the cups any way they liked! I started by putting one red Solo cup on the floor next to me and asked them what questions came to mind. Fairly quickly someone said "How many cups would it take to reach your height?" - bingo! I put them into random groups and handed each group a sheet for them to draw a diagram of how they wanted to stack the cups, along with a guess that was too low, one that was too high and an actual guess. Once they had that done each group got a handout and 10 cups. I also wrote my height on the board.

They had fun initially stacking the cups and having them fall which made a lot of noise. Good noise, though. You know, the trying something and having to adjust because it didn't work kind of noise. Only one group chose to stack the cups one inside the other; all of the other groups stacked the cups like this:

They collected data which they graphed then came up with an equation to represent the relationship between the height and the number of cups. They were good at this because they understood that the height was dependent on the number of cups and that each cup measured the same. They came up with their calculation for the number of cups to reach my height then moved on to a different way of stacking the cups.

They tried a lot of things. Here is a sample:

Many of these options were deemed unbuildable (I just made that word up) so the one in the last picture was what most groups started tackling. It is complicated because they are looking at the relationship between the number of rows and the number of cups, not the height. The height is related to the number of rows, but it is definitely not as straightforward as the first stacking method. They will continue working on that tomorrow.

We spent the end of the period trying to see how close their predictions were to the actual number of cups needed to reach my height. But the towers kept falling down! The vents were blowing cold air and the draft seemed to be everywhere so we spent a lot of time getting nowhere. Eventually, with the help of someone holding the tower part way up, they got the 16 cups stacked and saw that the top of my head was somewhere between cup 15 and cup 16 exactly as they had predicted. Yay!

Day 69

Day 69

Today's plan was to finish up the Shell Center matching activity then start Cup Stacking. But we never got beyond the matching activity. Some groups did finish, but for others it was like pulling teeth. They even asked me how I had so much energy first thing in the morning. If I didn't then we would be doomed! It took a lot of work to get them to associate the different representations, but they made progress. Here are some of the finished products:

And tomorrow we will do cup stacking!

Day 68

Day 68

I organized desks in rows for the students who needed to continue working on their tests, while the others worked in groups on a matching activity from Shell Center. I really like this activity and have done it for a few years now. It involves connecting linear and quadratic expressions, words, tables and area models. Here is some sample student work:

And zooming in a little:

I also asked them to add a graph to each set. Only one group started on this, so I think they will all need a little more time to work on this activity tomorrow.