Spent all 80 minutes (with a 5 min My Favorite break halfway through) working on integration problems. I find these work days (if you can fit them in) do wonders for the confidence of these students. They have time to work together, make mistakes, and fill in a bunch of cracks in their knowledge. They all have different cracks too. They had a choice for where to work, and as shown, all used whiteboards and most prefer the vertical whiteboards.
While they are working, I’m sometimes completing the key on the tablet, but mostly walking around and helping/questioning.
Nothing amazing here. Give pairs of students a random factored form quadratic, cubic, quartic, or quintic function. Ask them to find standard form, find roots, find sum of roots, and find product of roots.
Next write down two random standard form polynomials and see if they can find the sum and product of roots after looking for patterns.
I should have anticipated more errors, man did they make a fair amount of algebra errors. Grade? C. Trying again tomorrow.
We were working through finding the volume of rotational shapes in IB math HL. First example was looking at the area under y=5-sqrt(x) from x=0 to x=5 rotated around the x axis. Pretty straightforward disk method example. After that I set them loose to see where they could get by rotating the same area around the y-axis; significantly more tricky. They knew it was a difficult task, I wanted to see their reasoning and work and see where they could get. Here’s some quick scratch work:
Here are some 3D prints of these shapes that I made with code in some beta software (madeup from Kickstarter).
The Introduction to Programming kids are working through quick python walkthrough designed by google.
Some neat things that they’re figuring out, python handles integers and floats(decimals) very differently. (** in python means raise to, “^”).
As a preview to studying graphs of polynomials after a quiz, the students were going through a quick introductory Desmos activity that I built, Polynomials and Roots, to explore the connection between the degree of a polynomial and how many roots the polynomial could have. Can a cubic have 2 roots? Can it have 0 roots? etc.
A nice mix of misconceptions and answers to talk about while we did our quick notes. Here’s a sketch of the possibilities of a cubic function that one group came up with after talking it through together.
The student mentioned after solving that it was the longest problem he’s solved in math. So many places to trip up; it’s such an accomplishment to get the correct answer. Well done IR.
Started up My Favorite with a brain scrambler: Banach Tarski paradox. Watched a video clip and then the student explained why he found it interesting.
Really nice discussion on Rational Functions, and how to get information about them, in Pre Calc H. Here’s a student graphing a rational function by hand by finding asymptotes, x and y intercepts, and using some test points to find out where the graph is going. BTW, their asymptote knowledge is all from desmos investigations, we haven’t gone over a single rule as a class. Fun.
Code Check 2.
For the beginning of today’s lesson in Introduction to Computer Programming, they had the task of writing out pseudocode to make this shape, and then translate it to the Scratch environment. Some students were able to fully implement it in pseudocode so when they went to Scratch, it drew the shape right away. Some students had to fix some bugs.
20 seconds after I took this picture, he screamed out in joy, and called me over. Only had to change one number to solve the puzzle. Good stuff.