Beading Wrap-up
Today we finished our week of beading. We have gone through the steps of learning a new skills, struggling and figuring it out, making progress, helping each other, celebrating accomplishments, and reflecting on how far we’ve come in a week. These are all skills that apply to math class as well, along with all the emotional regulation skills we used to keep our mindset good while we were working as to not put any negative energy into our work. We learned how to notice our emotions, find a strategy to use to regulate, and then to return once we were calm and ready. We will be putting all of those skills to use as we move into the challenges of lap 3 of our course.
The final steps of the beading involve weaving threads to create a tab of fabric to glue the finishing leather to.
Next we applied glue to the strings so they would stay bonded together
Then we cut the work from the loom and used leather glue to glue the hide to the ends to finish the keychain.
We’ve got many finished pieces resting on the windowsill, while we work on our writeup that explains all the math in our work.
We can talk about the number of beads we used, and how we can calculate that with our strategies. We can determine the fraction of beads of a certain colour, or we could report that as a percentage. We can discuss symmetry, reflection, translation, rotation, various shapes or angles, areas and perimeters. We could talk about repeating patterns, or growing patterns and use proportional reasoning. If 1 motif takes 5 red beads, then 3 motifs would take 15 red beads. Some students thought of the math first and planned their beading accordingly, and others are starting with the art, and developing the math later.
We are also reflecting on the learning skills and emotional regulation skills we learned, as well as the teachings and connections to Indigenous ways of knowing and understanding pattern and math.
Beading update
Some students are almost done their masterpieces! We had several in working at lunch and making very good progress.
After the beading is done, we weave the thread across the loom threads to make a fabric tab to glue together and attach leather to. Once the threads are firmly fixed they can be cut from the loom, then leather added and then they are left to dry on the windowsill.
Tomorrow we will finish beading, and start out mathematical writeup and reflection on learning skills that we used.
How many times can you fold a piece of paper in half?
Today grade 11s were working on modelling exponential growth and decay. We folded paper in half repeatedly and modelled the number of sections that we get after more and more folds.
We decided this was exponential growth and the equation is y=2^x
We also looked at the page area, and how that changes as we folded more and more. Some called the initial page area 1 (measuring with a “page” as a non standard unit of measure), and then we saw that the area of each folded section decreased each time (the base is 1/2). The exponential decrease function is y=(1/2)^x. Others who measured the page and had the area in cm^2 then would have that as their “a” value for their equation.
Tomorrow we will be working on modelling word problems, so this is a good introduction to those skills.
PS. We had papers folded 7 or 8 times before it got to be too challenging to fold any further. We tried with larger pages too without any luck. Here’s a group that managed to use toilet paper and fold it 13 times.
Beading Begins
Today my grade 9s started their beading projects that we planned yesterday. They are all looking so good!
Each row has 11 beads, which all need to be strung in order then threaded again to lock them in place on the warp threads on the loom.
Some are designed with geometric patterns, or representing various things like flowers, ducks, music notes, or books on a shelf. I look forward to seeing what other images will be revealed.
Students store their work in giant ziploc bags with their name on it so it will all be organized and ready to go tomorrow when we pick up where we left off.
It is impressive to see what students are able to come up with, and how quickly the beadwork comes together once the initial lesson is complete.
Many thanks to our guest from the school board who is sharing their expertise with us and helping when there are challenges. We are remembering the teachings and working on keeping a good mind while we work. We are being sure to take a break and ask for help when we are needing to.
More updates to come tomorrow.
Split 25 with grade 8s
Today I had the opportunity to lead a grade 8 class through the split 25 question “thinking classroom style”.
we got into random groups of 3 using my team shake app, and then working at the boards I gave this prompt. Split 25 up into pieces. Example: 20+5 or 1+1+1+1+1+…+1 and then multiply all the pieces together, so we’d have 20×5=100 in the first case and 1x1x1x1x1x…x1=1 in the second case. We want to split up 25 in a way that maximizes the product of the pieces.
Groups knew the rules of 1 marker per group, and the person with the marker writes the thoughts of the other members.
We had some interesting approaches. Some groups used big pieces, some used small pieces, some used equal sized decimal pieces, and one group wanted to start off thinking about negative pieces (something I didn’t expect at all).
With a bit of experimenting and some calculators, we got right into the task.
Some groups got really big values for the product, but still are searching for the biggest.
I consolidated the task by talking about thinking creatively and responding well to challenges, and also we talked about how to write their repeated multiplications with exponents, so it could be a more streamlined process of they continue calculating at home.
I’m proud of them for diving in and giving it a good try. I’ll have to bring another good challenge to them next week.
Beading in Grade 9
Grade 9s learned about loom beading today from a member of the Indigenous program team at the school board. We have a project we are working on this week: to learn about patterning, symmetry, ratio, percent and area while designing a beaded bracelet or key chain.
We learned about the importance and significance of beading as part of Indigenous culture, and saw many examples of beadwork. We learned about how beads were made, and saw several examples of wampum and learned about the agreements they represented.
We learned about how it is very special to be learning this artform, as there were efforts over the years to prohibit Indigenous people from doing traditional cultural practices. We are thankful to be learning this new skill, and exploring math through a different lens.
We started to plan out our designs. We have 11 beads across in our pattern, so we draw designs on a template, and will start the loom beading tomorrow.
Modelling growth in grade 12
Today I was in with my colleague’s grade 12 college math class. We were working on modelling various patterns yesterday, and continued today.
We made pictures, then tables, and noticed that they double and double and double. We made graphs, and explored what would happen if we went to figure -1 and figure -2 and figure -3, we’d be dividing by 2 as we move up the table.
Next we explored making patterns of our own to correspond to pattern rules (equations). Some groups had linear patterns, others had quadratic, and one had exponential.
Once they represented their pattern, they got a graph paper, and transferred their tiles to make the graph.
Groups got another set of rules, built the patterns, then the graphs. Some had time to do a few patterns. In the end we consolidated their work with a gallery walk and introduction of new vocabulary.
We could see how same slopes, and same y intercepts impact graphs. We could see the difference between x^2 and 2^x as well. I’ve done this task with lines often, but I am enjoying how many functions we could explore with this method.
M&Ms Task
Grade 11s are learning about exponential growth and decay, and to get us started we did a task with M&Ms.
With each pour, they removed the m&ms with the m side up. The number of m&ms that remained got smaller and smaller until all that were left was the ones with no “m” at all.
Groups made graphs, and we looked at features of the graph, then tried to make an equation. We used our reasoning skills about how we were losing half each time, so we’d be multiplying repeatedly by (1/2), which led to the creation of an exponential equation. We noticed that in our situation there was a horizontal asymptote that was not 0, there were a few m-less m&ms. We played around with transformations to see if we could fit the data better.
Finally we did a desmos regression to see how the program would do it. Using the the exponential regression that’s built in forces the asymptote to be at y=0.
It was a fun task. Looking forward to doing more exploration tasks as we move forward.
Taco Cart
Grade 9s are working on pythagorean theorem, and we worked on the 3 act task: taco cart.
We watched act 1 (available here)
and we noticed and wondered about who would get to the taco cart first. The students immediately knew that they needed more information and to my surprise asked for both the speeds and the lengths of the paths.
Here is the information to start act 2:
Dimensions and Speed information
We had a good time working with unit rates, and pythagorean theorem, and then converting time to minutes and seconds to see how much time separated the two people at the end. I had a hard time locating the final video in the moment (websites were down), but here it is!
Patterning in Grade 12
I’ve been invited to come work in a grade 12 class for a few days to work on patterning, reviewing linear and quadratic, and introducing exponential.
We did a few warm up patterns, and then tried these questions: are the patterns growing linearly or not.
Students got into it, drawing the missing figure, determining pattern rules, making tables and deciding if it’s linear or not. There was some debate about the growth in the 2nd pattern. There were some excellent conversations happening around the room.
Groups got into exploring the tables to see what happened when the x values are negative. They used their 2nd differences to help fill it in, or used their equations to calculate the y values for negative x.
Next we looked at this pattern that grows as a rectangle. We looked at patterns in the dimensions, and also how we can see 2 squares of the figure number, and 1 group of the figure number, so the equation is 2x^2+x.
Tomorrow we’ll introduce some exponential patterns then do an activity with blocks to show some graphical connections.
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