Math 8 – The main goal for today was deliberate practice on calculating cubes and cube roots of perfect cubes. That part of the lesson was started with a comparison between the concept of a square and cube, then quickly going over a couple of worked examples, and then practice.
Before the cubes though, we did some voting on a Pythagorean problem. It was a direct copy of a homework problem. Lots of students didn’t do the three homework problems which sort of surprised me. I’m well aware of student attitudes towards homework and I personally think that most of the learning needs to happen in the classroom. But some practice is beneficial, particularly if the majority of students have a decent understanding of the topic.
Parts of today’s lesson were not that dissimilar to my physics classes yesterday, were cognitive science concepts such as distributed practice and deliberate practice come into play.
Math 8 – Who Gets There Faster, Jim or Stan?
Today I worked on giving most of the instructions/prompts verbally. I thought it would be prudent to write down the numbers required though. Maybe I should have tried it without the writing.
And a nice solution below…
While several groups clued in that distance/speed is time, lots of groups used equivalent ratios for their solution, which I was fine with. The reasoning would be something like “Jim goes 9km in 2hrs, 13.5 km in 3hrs, and over 11km in 2.5 hours…”
The next problem was simply stated: I have a rectangular prism with side lengths 8, 9 and 12. What is the furthest distance from one point to another? One solution is shown below. Once students were able to picture the vector they needed, many were able to find the correct answer. I liked this problem because it had a low floor – all groups were able to find some diagonals using the Pythagorean Theorem.
I was very proud of this lesson, both for what I had planned and on what students were doing. Virtually all the students were engaged and accountable. Even border kids who typically sit back a bit were interested in working on possible solutions.
Math 8 – The picture above shows some students finishing their ladder project. Check out the curricular and core competencies on the back wall. This project was primarily about reflecting on process competencies.
Today the students also did a quiz on tilted squares. I wrapped up the tilted squares by asking the classes if anyone wondered why we studied it, if we already new the Pythagorean Theorem. A few students said they did, and I showed how a right triangle with side lengths a and b can be used in a tilted square to offer a proof for the Pythagorean Theorem. It turns out we can trust 2500 year old Greek mathematicians after all!
Math 8 – I had a substitute teacher (TOC) for the afternoon, here is the note that she left me. I love the last line! 👍
Math 8 – Having worked on a similar problem in groups, today students started working on this assignment the goal is to explain their thinking individually and focus on a reflection at the end.
Copy of the assignment.
Math 8 – Today was my first day back with the grade 8’s, with my awesome student teacher, Jenny Yim, finishing last week. She did a great job.
Today I wanted students to work with titled squares as an alternative to the Pythagorean theorem. I framed it like this: “I don’t trust 2500 year old Greek mathematicians. Especially ones that throw their friends into a lake because they think that there is something called an irrational number.”
Once students are comfortable with using the titled squares I’ll show how it can be used as a proof for the Pythagorean theorem.
Professional Development – I was fortunate to be able to attend a two-day workshop with Jay McTighe, via the Coast Metro Consortium. Jay’s working partner for many years was Grant Wiggins, who unexpectedly passed away in 2015. McTighe and Wiggins’ books have been very formative for me, particularly Wiggins because of his blog.
I have a couple of McTighe and Wiggins’ books, Understanding by Design and Essential Questions: Opening doors to student understanding, so the content of the workshop wasn’t all that new to me. However, it was a fantastic opportunity to hear about the more subtle aspects of UbD, the kind of thing you can only learn in person. It was also a great chance to collaborate with like-minded people, I feel lucky to have attended. Thanks go out to my Principal, Ranjit Bains, for getting me into the workshop! With respect to my previous post on this blog, Jay really emphasized that “covering content” is not in the best interest of students and that he and Grant explicitly decided to focus on quality rather than quantity. Sacrifices may need to be made in order to achieve the most important things in education. I think that in terms of UbD this means that
To top things off, I was lucky enough to have Jay sit at our table for lunch the second day! Four of us got the chance just to chat about education and share our interesting experiences.
The pictures above come from some collaborative work we did at our table, working on a financial literacy unit for Math 9.