Day 141 – Cubes and Roots


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.

Day 139 – Two Interesting Problems


Math 8Who 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.

Day 137 – Getting it done

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!