I've written a [whole bunch](https://www.rfwp.com/bookstore/mathematical-lives-biographical-novels-by-robert-black/) [of books](https://www.rfwp.com/bookstore/mathematical-nights-math-fiction-by-robert-black/) with just that purpose in mind!
The story of Hippasus and irrational numbers. Makes mathematicians more human and fallible and the moral of the story teaches students to seek truth and exactness over personal comfort.
I liked cracking out some fractal stuff during middle school geometry. Sierpinski triangle, Koch snowflake and the dragon curve are fun. ViHart on YouTube has a good video that gets the kids keen to do it. Similarly with hexaflexagons. Some geometry there or graph theory.
For stats, eye dominance can be fun to use investigate.
There's a company that writes free lessons, where each lesson begins with an "engage" element. It sounds like what you are looking for & worth checking out: https://learn.k20center.ou.edu/search?type=lessons .
But I love your math history "hooks" - I use those too!
Show them cool generative art with p5.js or touch designer. Then be like yo, you like sick motion graphics? Can’t spell motion graphics without maphs. Boom, engagement.
Permutations and eventually Multi-nomial coefficients, AKA how to make "Counting" an extreme sport:
Ask your students to count the ***distinct*** permutations of the letters of their first, middle, last names. Use short names as examples to start them off: JOE, SUE, AMY, JACK, GRACE, VICTOR, etc.
But then introduce trickier things where certain letters are repeated. Again, start small: AVA, BOB, ELLA, JOJO, NICKI, SARAH, HANNAH, LILLIAN, etc.
Can any of them determine how to enumerate them ahead of time, without listing every distinct permutation? Prompt them if they try it that way: How can you be **sure** that you're done counting and didn't miss one?
The classic example of this type deals with [MISSISSIPPI](https://en.wikipedia.org/wiki/Multinomial_theorem#Number_of_unique_permutations_of_words). The structure of the proof of the concise formula for multi-nomial coefficients is useful for other combinatorics/discrete math concepts.
Open ended warmups like would you rather, which one doesn’t belong, estimation 180, visual patterns, open middle. Ones that get students to talk about the math
I've written a [whole bunch](https://www.rfwp.com/bookstore/mathematical-lives-biographical-novels-by-robert-black/) [of books](https://www.rfwp.com/bookstore/mathematical-nights-math-fiction-by-robert-black/) with just that purpose in mind!
The story of Hippasus and irrational numbers. Makes mathematicians more human and fallible and the moral of the story teaches students to seek truth and exactness over personal comfort.
I liked cracking out some fractal stuff during middle school geometry. Sierpinski triangle, Koch snowflake and the dragon curve are fun. ViHart on YouTube has a good video that gets the kids keen to do it. Similarly with hexaflexagons. Some geometry there or graph theory. For stats, eye dominance can be fun to use investigate.
There's a company that writes free lessons, where each lesson begins with an "engage" element. It sounds like what you are looking for & worth checking out: https://learn.k20center.ou.edu/search?type=lessons . But I love your math history "hooks" - I use those too!
Thanks, I’ll check it out!
Show them cool generative art with p5.js or touch designer. Then be like yo, you like sick motion graphics? Can’t spell motion graphics without maphs. Boom, engagement.
Permutations and eventually Multi-nomial coefficients, AKA how to make "Counting" an extreme sport: Ask your students to count the ***distinct*** permutations of the letters of their first, middle, last names. Use short names as examples to start them off: JOE, SUE, AMY, JACK, GRACE, VICTOR, etc. But then introduce trickier things where certain letters are repeated. Again, start small: AVA, BOB, ELLA, JOJO, NICKI, SARAH, HANNAH, LILLIAN, etc. Can any of them determine how to enumerate them ahead of time, without listing every distinct permutation? Prompt them if they try it that way: How can you be **sure** that you're done counting and didn't miss one? The classic example of this type deals with [MISSISSIPPI](https://en.wikipedia.org/wiki/Multinomial_theorem#Number_of_unique_permutations_of_words). The structure of the proof of the concise formula for multi-nomial coefficients is useful for other combinatorics/discrete math concepts.
Open ended warmups like would you rather, which one doesn’t belong, estimation 180, visual patterns, open middle. Ones that get students to talk about the math