Introducing systems today. Had the students make 2 lists; one where pairs of numbers summed to 6, and the other with pairs of numbers whose difference is 11. Then asked them to find a pair of numbers that are on both lists.

Absolute crickets.

I had to ask leading questions, give hints, ask them if they had tried such and such. I really had to drag them along before they realized they could do something other than stare at their paper.

So the next period I had them start standing at the whiteboards before I gave them this task. And I did not have to seed them at all. Some were graphing the pairs and realized they made lines. Others were finding the equations of the lines and realizing they needed to find the intersection point. All in all, in 15 minutes I watched the whole class figure out systems of equations. I taught them nothing.

I really feel like when the students are sitting in their desks, they are waiting for me to give out answers and pour knowledge into their brain. But when they are standing at the whiteboards, they take control of their learning. They are willing to try different things, take risks. And they don't wait for me to tell them what to do.

#ThinkingClassroom for the win.

#Algebra2 #MTBoS #ITeachMath #ClassroomMath

It's been a long week. We lost a student from our school over the labor day weekend and the atmosphere has been low. Time for a light hearted activity to end the week.

Inspired by Fawn Nguyen's "Vroom Vroom" post on her blog.
https://www.fawnnguyen.com/teach/vroom-vroom

Students measured the pullback distance of a car and then measured the distance it rolled. Graphed the data. Found the line of best fit by eye, then found the linear regression. Made some predictions, calculated some residuals. Summed up all the stuff we've been learning the past week.

I then picked a random distance and groups calculated their pullback distance. Everyone lined up their cars that distance from the finish line, pulled back their calculated distance, and let 'em rip. The group whose car got the closest to the "finish line" (marked by tape on the floor) got bragging rights.

#ThinkingClassroom #ClassroomMath #MTBoS #iTeachMath #Algebra2

Task today: Write linear equations (in point slope form) which meet the conditions listed. Try to write as few equations as possible.

Overheard student discussion: I found an equation that meets 6 conditions at once.
Wait a minute, is that even possible?
I wonder if I can do this in only one equation?
How would you write an equation with both a positive and a negative slope? It cant be done!
Hmmm...which is the 3rd quadrant again?
Look! If we just shift the line this way, we can make the x-intercept negative.
I think you need at least 3 equations because...

This was a very productive 20 minutes of class reviewing lines. Thanks to Menu Math for the great idea. http://natbanting.com/menu-math/

#ThinkingClassroom #ClassroomMath #MTBoS

Needed an extra lesson on lines in #Algebra2 since one class met an extra period this week for some unknown reason. Bouncing ping pong balls to the rescue! Students dropped ping pong balls from different heights and measured the rebound height, plotted the data and found a linear model. We haven't learned about regressions yet (soon though!) so they used a ruler to eyeball the best line.

Challenge time. I took all the balls away and told them to use their model to calculate the proper drop height for the ball to rebound to 78 cm. I rigged up a small hoop I had lying around at just that height so everyone in the class could tell whether the rebound was to the right height. Hilarity ensued when several groups realized their drop height predictions were below the rebound height. Turns out they plugged in for x when they should have plugged in for y. A good learning moment.

It was a pretty basic, last minute lesson, but I think it went ok. It was nice having everyone's data, graph, and model on the whiteboards around the room for all to see. I have whiteboards on all 4 walls (no windows though!).

#ThinkingClassroom #ClassroomMath #MTBoS

Day two in #Algebra2 went well. Did the checkerboard problem (Counting the number of squares in an 8x8 checkerboard, look for patterns, extend to an nxn board). Yesterday we experienced how using tables to organize our thinking could be useful and illuminate unforseen patterns, so I was happy to see many groups using tables today. I was especially giddy when two groups saw they had different numbers in their tables, but they added up to the same total, and then proceeded to spend some time trying to understand eachother's approach. All in all, a good day.

#ThinkingClassroom #MTBoS #ClassroomMath

#ClassroomMath #Prompt4 #MTBoS #ThinkingClassroom

Here is an oldie, but a goodie: Having students calculate the perimeter and area of the Koch Snowflake over several iterations, derive a formula for the nth iteration, then determine if the perimeter and area are finite or infinite. In Algebra 2 this year I used it as a way to spiral back to sequences and exponentials while introducing infinite series and a look ahead to the idea of limits.

I always enjoy this lesson because it bends the students minds and gets them excited. It also comes during a point in the school year when everyone is tired/stressed, and this is a nice problem to get the class energized again. And of course, fractals are always fun!

#classroommath #prompt1 #introductions

Adrienne here in Arizona. Teaching Algebra 2 and Multivariable and Vector Calculus this year. Working to incorporate as many rich tasks as I can into my #ThinkingClassroom .

Bread > Cake > Pie > Donut

Favorite things: reading, baking, Star trekking, origami, crochet, and of course mathing. 🖖

Hello #mtbos . Been offline the past year. Excited to get back to learning from everyone and sharing my journey as #iteachmath . I have taught it all over the past 20+ years and will be teaching #Algebra2 and Multivariable and Vector Calculus this up and coming year. I’ve been trying to build a #thinkingclassroom the past 2 years and am always on the lookout for good, rich, spiraling tasks.

Hab die erste Klausur mit #ThinkingClassroom approach geschrieben und das tiefere Verständnis der SuS ist wirklich enorm. Insbesondere bei den problemlösenden A ohne direktes „Kochrezept“ gab es eine Vielzahl toller und sinnvoller Lös. Insbesondere haben die schwachen SuS profitiert. Ich habe keine 5 in der Klausur gehabt, obwohl KuK das Niveau als angemessen bezeichnet haben. Ich bin der UReihe zur Vektorrechnung von der Pike an in 6 Doppelstunden bis zu der Lagebez von Ger gekommen. #FediLZ

Recently watched a session with Peter Liljedahl about an introduction lesson about #linear functions.

He talked about starting the lesson off by putting bunch of books on the table one by one and looking toward the ceiling, wondering when he'd reach it.

Scattered around the room there where photos with different stacks of books with there height in cm (but unbeknownst to the students plus the height of the table itself).

Anyone have a link/info about this talk?

#ThinkingClassroom #iteachmath

#highered #math #calculus for business students: no "rules for computing derivatives"... none... no rote memorization... so students are allowed to refer to this sheet when solving *any* problem in my class... quiz/exam questions are about interpretation and making decisions around the results they see and what is needed to make those decisions #thinkingclassroom

I teach a "Business Calculus" course -- we used real data to plot a "best fit" curve (quadratic) and used secant lines to approximate the slope of the curve at a point (using the idea that the secant line needs to be parallel to the tangent line); I call the approach "Calculus Without Limits" (I will be introducing the word 'derivative' tomorrow) #ThinkingClassroom #highered

First post on Mastodon! I’m excited for this new change in social media. #MTBoS let’s follow each other again! High school math teacher here:) #thinkingclassroom #sbg

@dhabecker what a fantastic resource! Thanks for sharing.
For anyone who's interested: https://docs.google.com/document/d/1EMq1w2gdI--oSN5cRUrItqSzvjQq7VMXwkOu2O1Wz3Q

#ThinkingClassroom

#introduction post. Following a few people I follow on other sites here to mastodon. #iteachmath including AP Calc BC, Honors Precalculus, Honors Trig and Geometry. I use #ThinkingClassroom in my class.

@NerdQED hi! I don’t know if we were friends on the old platform (which won’t be named😂). I feel like we should have been! I am also in #ThinkingClassroom #MTBoS and teaching the 11/12th precalculus and calculus. Trying to create a PLN using this platform now.
I don’t post too often, maybe I’ll try to get better at that. I’ve learned so much from the years on the other platform.