Growing up I loved playing board games with my family. I continued that love of play when I had kids, and discovered so many awesome board, card, and dice games that bring us closer together. Zombie Dice is a great game that I found and played last summer with my 4 and 6 year olds. It's played with 13 dice in a cup where players take turns randomly selecting 3 dice from the cup and rolling them to get brains (points). After a player’s first roll (if they didn't unfortunately roll 3 blasts) they choose to either...
As I was playing with my kids I noticed that there were 3 different colored dice (green, yellow, and red) and wondered... are there different numbers of brains on each dice that relate to the color? What are my chances of rolling.... AND BOOM! My head exploded with ideas for my probability unit in A.P. Statistics. I developed the following lesson and used it with my students today. It was a hit! They were cheering and talking smack; it was awesome. We spent the first 30 minutes playing (I had to do a demo with a student while everyone gathered around and watched first) and then we did the lesson (took about 45 min).
Topics covered: probability, probability trees, independence.
If you play, let me know! Tell me how you'd tweak it. And even better, tell me how YOU incorporate board, card, and dice games in your classroom:) Happy playing!
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I will be back to update in a full blog post with pictures, but for now for those who want it, here is the PDF of the Independent Math Project I implemented over 8 weeks in my high school math classes.
PDF INDEPENDENT MATH PROJECT [TLDR: Skip to the bottom for the puzzle pages.] I have been putting together these Weekly Math Puzzle Pages for months now and my project is finally wrapping up. I'd like to share them with the math teacher community, or any curious student, who stumbles upon my blog. The idea of doing weekly puzzle pages came about from two thoughts: (1) Homework is inequitable when it is graded, long, and unfocused. In lieu of nightly homework problems I am instead handing out a weekly puzzle page, with a "Problem of the Week," which can substitute as homework. The POW is a challenging problem that directly relates to the material covered in class that week. Nothing on the puzzle page will be graded, but I will hold weekly meetings (both in class and online) for students to discuss the POW. (2) I love puzzles. I love riddles. I love corny jokes. I love fun math facts. I have been trying for YEARS to figure out a way to expose my students to ALL of the amazing videos, fun facts, brain teasers, and jokes I've collected but have had a miserable time finding time to incorporate this collection of THINGS into the classroom. In addition to the POW, the puzzle page also includes logic puzzles, jokes, brain teasers, fun facts, interesting math videos, and notable mathematicians. (3) I want students to see that mathematicians aren't just some old Greek, white, dead guys. So these puzzle pages have a "Google Me" section where I highlight some famous mathematicians and scientists, where 8/16 of them are female, 8/16 are not white, and 5/16 are still alive (RIP Maryam Mirzakhani). The original project was created for my Math 1 students, but you can easily adapt this to any math class by simply changing the POW each week (I plan on doing another set with Math 3 later). I also made these a bit seasonal, as I was working on them in the Fall and got into the holiday spirit with the weeks at the end. So, without further ado, here they are. Please use them as you see fit. I hope they bring you and your students as much joy as I had in putting them together. Thank you to everyone I follow on Twitter through #MTBoS for always sharing excellence, and for making these puzzle pages possible. I've found some amazing blog posts on crafty things teachers and parents are doing with their kids, and some it is holiday-themed. Here are some ideas I've collected (click links for their original posts) that look super fun for Halloween, Christmas, Pi Day, Valentine's Day, and really any day of the week! Soma Puzzle Cube Build your own Soma Puzzle! Soma puzzles originally have 7 pieces, but this project that I found from Project Lead the Way has students combining 5-6 pieces. Use software or don't, students can use isometric dot or graph paper to draw 3-D images of interlocking pieces that form a 3x3x3 cube. Great idea for learning spatial reasoning, and you take take it a step further and incorporate how standard deviation of the smaller cube dimensions plays a major roll in actually putting this puzzle together (this project by Ian Waggoner shows how to do that). This giant Soma cube looks really fun to build too. Here's an article by Amanda Mickus called "Using Soma Puzzles to Master Common Core State Standards." Desmos Picture Ornament This is a link to a really cool Tweet I found from Lauren Deal, an English teacher, who makes simple ornaments of her students' favorite books. I thought it might be super cool if we took a picture that a student created in Desmos (maybe a final project picture that incorporated all the functions we discussed this semester?) and turned it into an ornament or magnet. Pi Day Activity: Radians Sarah Carter has a really cool activity on coloring radian angles in a circle. I'd like to see a variety in my classroom: 1, 2, 3, pi, 1/2pi, radians, etc.! I wonder if pipe cleaners would work better? Nat Banting's "Shape Finders" Uh, wow. Definitely making these for when my kids are in Kindergarten. May make a bunch of these and give them out to the little kids at Halloween (and candy too of course; I'm not a monster!). Directions on how to make them with an at-home printer are in the Tweet. Halloween Spider Web Decoration Plugging my own website here, this would be a cool task for students to do, and then decorate different places around the school for Halloween. Students get practice with Pythagorean Theorem, estimation, and possibly circumference (or half of a circumference). Octahedral Valentine Ben Bolker posted a Tweet showing the octahedral valentine he created thanks to the Museum of Mathematics's template. I imagine having students write mathy love things on them, like, "Baby, our love is like dividing by zero. It cannot be defined" or perhaps a student decides to ask their significant other to prom by writing several equations on the heart boxes that, when graphed, spell out the word "prom?" The dorky possibilities are endless! I would love to add more when I find other crafty things to do with students. Let me know if there's a crafty math project you're passionate about!
How teaching helped me prepare to be a mother, and how being a mother helped me be a better teacher.7/10/2019 Teaching is the hardest job. It's thankless. We are expected to get up the next morning with a smile and put on a "show" of the happy, sage educator when the day before one of our students yells at us, "f*** you!"
How teaching helped me prepare to be a mother... NO HARD FEELINGS For a long time I took it personally, but I got over it and learned that those insults had little to do with me, but mostly with the struggle that students were facing on the inside, and occasionally I made it worse. I learned to be more empathetic and patient, and realized over time that students don't care how much you know until they know how much you care. And when we both show up the next day and I say to them, "hey, I'm glad you're here today," I'm showing that student that there's no hard feelings, that I still care about them. Same for tiny people! When my toddler needs to take a time-out I DO get very frustrated at the moment because why the heck did you just hit your sister in the head with your train AGAIN after I told you NOT to TWICE, but when those 10 minutes are up we talk, we hug, we go right back to playing with trains (on the tracks, NOT on sissy's head). ONE THING AT A TIME Teaching also taught me how to handle keeping 10 tabs open at once in my head, and how to juggle 10 jobs to be completed in varying order by the end of the week. All while remembering to breathe and pee. Cue kids. Babies and toddlers require A LOT of patience. I really want to take a break sometimes and leave the room (and I've done that on occasion to REALLY calm myself down), but I need to remember back to when I was teaching and get a handle of doing one. thing. at. a. time. It's the only way I got anything completed when I was teaching and it's the only way I've been able to keep my kids fed, changed, and happy, while getting the laundry done, groceries bought, and dinner made. I NEED A BREAK...BUT I CAN'T CALL IN SICK It's SO HARD to go right back to playing with trains when just the moment before my toddler pitched a fit about not wanting to go to the potty and then pooped his pants a minute later (we're potty training). And as I'm cleaning him up his baby sister is wailing in her crib to be fed. One person against 2 little ones is TOUGH. I just want a BREAK sometimes. i want to flop on the couch and watch "Stranger Things." But teaching taught me how to handle the go-go-go and how to APPRECIATE the times when I actually CAN take a break (like when both kids are napping!). Listening to podcasts while folding the laundry is also a game-changer. How becoming a mother taught me how to be a better teacher... WAIT TIME Watching my toddler develop listening and speaking skills is truly amazing. I remember being shocked and awed when I could tell Eli to do something like, "go pick up that ball" and he would execute the entire command. What was EVEN MORE amazing was when I strung commands together ("go put the ball in the basket") and he did it. Now he's my big helper-tiger and puts baby sister's diapers in the trash can! If he's got a job to do, he's set. He is 2 now and is at that stage where his vocabulary is EXPLODING. He's repeating everything he hears (uh-oh...) and is really growing his range of sounds. I've learned that when I speak, whether it's giving a command, asking a question, or telling him to repeat a word I'm saying, I need to give him several seconds of wait time. His brain needs time to process the information I'm sending. I can't stand it when other people ask him a question and when he doesn't respond immediately they ask again OR tell him the answer. Like, give the kid 5 seconds to think about what words he want to choose to use and I promise you, he will amaze you. I feel like I WAS THE IMPATIENT PERSON when I taught! I need to give my students more wait time to process what I'm saying, and to think of a response, and I'm sure they will amaze me too. THE WAY WE LEARN MATH SHOULD BE THE WAY MY SON LEARNED TO USE A FORK The first time Eli used a fork it was messy. The second time was messy too. It took him a long time to figure out how to get most of his food in his mouth. He's pretty good at using a fork now, but when he first started and did a poor job at feeding himself I didn't take the fork away, sigh, and say, "well, better luck with the spoon!" NO WAY! We kept giving it to him because we knew he would get it right, out of necessity of feeding himself. And we didn't make him feel BAD for sucking at using a fork, in the same way we shouldn't make students feel bad with a grade for not mastering a concept within a week or two after we introduce it. That's why in the classroom I use Standards-Based Grading and multiple demonstrations of mastery. Actually I started doing both of these in the classroom before I had kids, so allowing my students to fail and dust themselves off and try again with no finger-wagging from me helped me be a better mom when my kids struggle with things (like potty training- OY). Now in the classroom I'm moving towards a written-feedback-only strategy (without grade) to drive the learning further. Becoming a mother has been a wild ride, and I believe teaching has helped me through some tough bits. I also now have a few more nuggets of wisdom after raising two children for a few years to use when I return to the classroom next year. Is there anything you've learned from your kids (whether school kids or home kids) to help you be a better parent or teacher? I'd love to read them in the comments:) Take care! Emerging after a whirlwind of blogs and tweets on low-floor, high-ceiling tasks and notice/wonder visuals I'm left with considering another main component of teaching: assessment. How do I know they learned the learning goal for the day? How do I know they can apply that learning goal to more than just the problem(s) from class? How do I know they can retain the information a week, a month, a semester later? I've been reading some cool books and listening to podcasts on the topic.
Hacking Assessment describes how we need to create time in class for what we value as teachers, and assess on what we value as well. If we value reflection, then we need to make time for reflection. I also highly value collaboration. It made me REALLY think of ways to adapt my quizzes and tests to do this. I think when I go back to the classroom my assessments will look like this:
At one point one of them mentions FreshGrade, and how it acts as a digital portfolio for student learning. Students upload examples of mastery, whether it be problems from assessments or problems they made up and answered at home, and their "grades," (from what I hear) are color-coded to show students what they're proficient on, and what they haven't yet mastered. Colors aren't averaged together give a student an ultimate color or overall grade. Students choose whether or not they want to gain proficiency in the standards they see needing improvement.
I LOVE this idea of color-coding grades. I've been using Standards-Based grading for about 4 years in the classroom, as well as unlimited reassessment, and it's been a HUGE improvement from my former system of traditional grading ("oh you failed this test? Sorry, better luck on the next one, even though it'll cover the same material!" UGH). However! I ALWAYS have students come in to reassess and ask me their overall grades before reassessing, and STOP reassessing as soon as their grade reaches a D. It doesn't happen to every student, but enough to make me have a handful of conversations every year like, "hey, you know you have the ability to push yourself harder than a D, right?" I think color-coding sends the message of "you know this well" or "you need to improve your understanding" without a judgmental grade attached. And I LOVE LOVE LOVE the idea of grade interviews (I can't remember which blog I read where the teacher does this, sorry!) every few weeks, where I sit down with students and basically say, "the gradebook says --%, but do YOU think this is an accurate reflection of your knowledge?" The idea that grades can change based on reflection and interview is exciting, and will be exciting for students too, and I think it's exactly how we should be doing things if we want students to LEARN and not just get a nonsensical grade. Imagine a fan blowing full force in your face, comically forcing your lips to flap against your gums as your hair whips around and slaps your cheeks, eyes watering trying to stay open. That's me about a month ago when I discovered #MTBoS (Math Twitter Blog-o-Sphere), Sara VanDerWerf's blog, and Peter Liljedahl's research on "Building Thinking Classrooms." At the same time. If you haven't already read "Building Thinking Classrooms" go do it now. I'll wait. Laura Wheeler also made these nifty posters you can reference (I printed mine out and put them in my "Ideas Based on Research to Use in the Classroom" binder) here, and here's 1 of the 3 posters she made: Reading and seeing what everyone's been posting on the math ed twitterverse has drastically altered how I plan on teaching when I return to the classroom (quite some time after I have baby #2, but I look at the 2 years I'll be away from teaching as an extended planning period during nap time).
I'm already making my own set of "mindful notes" with the guidance of The Amazing Laura Wheeler (via this blog post). And I'm collecting rich, open-ended tasks on the standards I want students to learn by checking out places like:
This is the breath of fresh air I've been waiting for. Or an almost-too-much-to-handle gust of air I've been waiting for. Either way, I'M SUPER PUMPED! [I hope my neighbor doesn't mind that I took these pictures]. As a math student, what do you notice? What do you wonder? Hopefully you notice that's a wicked awesome gigantic spider web. And how could anyone who's feelin' the spirit of Halloween not think, "how can I make one?!" What information do you need to figure this out?
We need to know how much string to use! So how can we figure that out? Well, it looks like the web is attached to the base of the flag pole, so how high is the flag pole off the ground? Student can estimate how far off the ground the flag pole is (6 feet?) How far out do we want our spider web to reach? Maybe longer than the height? 7 or 8 feet? Now, how can we find the length of the string given all that other information...? As I'm coming up with the "possible student approaches" sheet a la 5 Practices for Orchestrating Productive Mathematical Discussion, this problem is becoming juicier. [Try the problem yourself before seeing my approaches! It's fun!] I think this is a great low-floor/high-ceiling problem where I originally intended the students to use Pythagorean Theorem to get good guesses, but there's so much more students can do with this problem. I imagine many students will estimate the lengths of the "vertical" pieces, very easily over estimating how much string to use. With estimating, these students should finish faster than those who planned a more precise approach, so I can ask, "do you see any problems with estimating the length of each rope to be X feet?" and steer them towards a more precise approach. Here's how I see student approaches: Beginner Level: Estimating (everything) On-Target Level: Pythagorean Theorem (estimating height of flag pole, how far out do we want the web to reach, and lengths of horizontal pieces) Advanced Level: Pythagorean Theorem & Circumference of Circles (with estimations from "Appropriate Level"). I have a powerpoint with these pictures, along with images from the Lowe's Home Improvement website of what lengths of spools we could buy. One spool available to purchase is 325 feet. The best part: I did 2 different student approaches so far (beginner and on-target), and one is slightly over 325 feet, and the other is under 325 feet! How many spools should we buy? Let me know if you use this task in your classrooms and tell me how it goes! Who says "pwned" anymore? How old am I? Anyway! Thanks, Jo Boaler for once again blowing my mind and drastically altering the way I thought I'd start off the year teaching Math 1. Ugh, it's a lot of work to change what we're so used to, especially if we feel we've gotten a system down that works, but I feel it's my job to be always adaptable. Seriously, if we as teachers didn't adapt our instruction based on the exhilarating new research on how people learn math (specifically algebra and the concept of a variable), then we wouldn't be good educators. And it's not a BIG change, like change-ALL-my-units change. Just the 1st one. A big ol' review of simplifying expressions, solving equations, and solving inequalities. You know, the only one I always feel the most confident about each year, but nevermindwhocares. Let me just put this drool-worthy quote up for you from Boaler's website, referring to the 4 weeks of free algebra curriculum she and her team provide: "It draws upon algebraic research showing that it is more helpful for students to learn algebra through studying pattern growth where a variable represents a case number, and can vary, before learning about 'solving for x.' When students start learning algebra by solving for x they come to believe that a variable stands for a single number and does not vary. Later when they need to understand that variables can vary, they meet a conceptual barrier, and many do not ever get past that barrier. We recommend that students learn first about pattern growth and see that algebra can be useful for describing growth. Later, when they encounter situations when the variable stands for one missing number, they see this as a subset of their broader learning about variables and there is no confusion." From the website: Check out the lessons. They're all patterns. Generalizing. Growing, decaying. Linear, quadratic, cubic, exponential. Students just jump right in to functions and how different types of patterns grow or decay. It's wonderful.
So now instead of teaching the "boring bits" as Dan Meyer says at the beginning of the year with equations, we can start with empowering students with patterns, and create the need for solving equations later, then with a better understanding of what a variable is. BIG IDEA! Can't attend Meet the Teacher Night but want to meet me, check out what we're doing in class, and ask any question in real time? Are you a student who needs help with homework problems/review sheets but can never make those after-school tutoring sessions with the teacher? Well, check out: I'd have to create my own Facebook teacher account (gotta get approval) to do it. But what a great idea- to use Facebook Live as a way to communicate with parents and students from the comfort of their own home? Ask questions and get answers instantly, and watch the play-back any time you want. And all the videos are stored online to watch for a refresher for the final exam!
I can see it now: Tune in with me every Tuesday and Test-Eve at 7:30 p.m! Has anyone tried this before? I'm sure I'm not the only one who's thought of this-I'd love to see what other teachers have done with it. :) |
AuthorTracy Conte is a high school math teacher in Raleigh, NC. Archives
November 2019
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