If you aren't familliar with Spiralling,

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Craig Barton takes a look at how student brains learn and think and uses that to inform his teaching. This book has changed the way I see teaching math. Here is my 1 page summary:

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I have been working on incorporating mostly 1-4 in my classes so far but are working towards the rest.

Especially interesting is how the framework incorporates 21st Century competencies, especially...

- Collaboration
- Knowledge construction
- Real world problem solving and innovation

- Used to build an intuitive understanding of projections in MCV 4U
- Link to Desmos

The requirements were:

- Functions had to be piecewise with at least 3 pieces
- Functions had to be continuous from x = 0 to 10
- At least 3 different types of functions had to be used.

Here is an example of one of the really interesting submissions:

Samantha and Katherine (Reciprocal): https://www.desmos.com/calculator/k6ta1hpjr1

Melvin (Polynomial): https://www.desmos.com/calculator/pcytghpgp2

Malcom and Jonathan (Absolute value): https://www.desmos.com/calculator/s18vpu6eyt

Ahillan (Sine): https://www.desmos.com/calculator/moj40jbkeg

Gerardo and Patrick (Sine): https://www.desmos.com/calculator/02bxuszbjn

Jose (Cosine): https://www.desmos.com/calculator/i9jqcvknsw

Nana S (Sine): https://www.desmos.com/calculator/7aam6jjs0p

Lucas (Polynomial): https://www.desmos.com/calculator/84qr54wycg

Almendra (Sine): https://www.desmos.com/calculator/gkoosz85js

Noyangbe (Radical): https://www.desmos.com/calculator/ycku94ltoe

Monica (Radical): https://www.desmos.com/calculator/xm17lhvipf

Lawrenda (Polynomial): https://www.desmos.com/calculator/x4wxfuoerk

Nardos and Priscilla (Cosine): https://www.desmos.com/calculator/70rrejqt3y

Mirabel (Polynomial): https://www.desmos.com/calculator/ttg4pb1uf9

Brian and Joshua (Reciprocal): https://www.desmos.com/calculator/c0ucoms3w5

Jad and Nathan (Sine): https://www.desmos.com/calculator/h6u1bbz00f

Faith (Sine): https://www.desmos.com/calculator/t9ujrlfflz

Donovan and Ranvir (Reciprocal): https://www.desmos.com/calculator/hz19ixgc0k

Anitha (Sine): https://www.desmos.com/calculator/0kxlczcguw

Jayestha (20th degree polynomial, sine, absolute value): https://www.desmos.com/calculator/xghnljuqcu

Ethan (Reciprocal): https://www.desmos.com/calculator/llggi5zedd

Nana O and Michael (Root): https://www.desmos.com/calculator/dlfqhn8cuu

Kurtis (Reciprocal): https://www.desmos.com/calculator/bnrqwevbne

After seeing Andrew Stadel's File Cabinet 3-Act Lesson, we thought it would be an easy one to do with our 10 applied classes near the beginning of the semester. We didn't just want to watch the Andrew Stadel video though, we wanted our students to

After going through the Andrew Stadel 3-Act lesson as a class, I put a few post-its on the cart. After recording some initial estimates, they immediately got to work measuring and calculating...

Not every student needed to be involved. After a quick lesson on calculating surface area, I asked the 2 or 3 students who finished the surface area practice problems quickly or the students who were finding it too easy to do it. As the rest of the class practiced calculating surface area, they stuck 'em on. It did end up taking the better part of a period but those students were happy to do it!

The anticipation in the class grew as more an more post-its were added. It was super satisfying for everyone to get a final, definite answer (see video below). It was also great to see the Grade 9's and 12's who came into the classroom afterwards spontaneously start asking questions about the post-it covered cart.

I brace myself for the classic question from students, "But when are we ever going to use this???" But the question never comes, since they already know the answer: to find the cost of Jujubes and Smarties from a receipt, obviously.

Shamelessly appropriated from Alex Overwijk at Slam Dunk Math by my teaching partner and I, this activity is one of our favourites from the semester. The kids love it too. They get to problem solve and eat some candy while doing it.

Aside from the obvious, "Who buys 4 Smarties?" they come to "How much does one Smartie and one Jujube cost?" fairly quickly.

*So can we figure it out?*** **After coming up with a few different possibilities for the costs by manipulating the Smarties, Jujubes and "pennies", the conclusion is nope. There is more than one possible answer.

*What about if I had another receipt from the same store?*** **Now we're getting somewhere. The cost of a Smartie and Jujube has to work for BOTH receipts!

After they solve their required 4 pairs of receipts, they ask for more. That's when I throw one at them that doesn't have a integer solution, or one that has multiple solutions and let them debate it out amongst themselves.

After the activity:*You folks realize you solved some pretty complicated math problems today? Awesome work. What about if I gave you a problem like this?*

After the activity:

They realize it's not practical to use physical Smarties and Jujubes to solve the problem. *If only there was an easier way...*

Cue Elimination, with a distinct lack of "Why are we learning this."

]]>Cue Elimination, with a distinct lack of "Why are we learning this."

Play with the Desmos file by opening it in the Desmos web app.

]]>Link to Slope Puzzle 1 Desmos

I believe there is way too much emphasis on algebra in the high school math curriculum. Not enough time is spent building a deep understanding of the concepts.

Even though it's saved for the end of Grade 12, as a rite of passage to mathematical prowess, differential calculus isn't a difficult concept! Even my Grade 9's could solve this puzzle after some practice.

Even though it's saved for the end of Grade 12, as a rite of passage to mathematical prowess, differential calculus isn't a difficult concept! Even my Grade 9's could solve this puzzle after some practice.

Link to Slope Puzzle 2 Desmos

Solving these puzzles builds an intuitive understanding of differentiation without having to perform any algebra at all. I plan on using these puzzles in my Calculus class from the first day of the semester to help build that intuition.

I also plan on having Calculus students create their own Slope Puzzles in Desmos as a way to test their understanding of piecewise functions and function continuity.

]]>I also plan on having Calculus students create their own Slope Puzzles in Desmos as a way to test their understanding of piecewise functions and function continuity.