Pee In the Pool and Other Summer Problems – Problem Solving Resources

As part of my daily brush-up-on education news, I read over my Twitter feed to see what interesting articles or problems the many great educators and educational resource companies I follow might have shared. I laughed so hard when I saw the Tweet from @YummyMath asking how much pee was in the water, with a picture of a large pool and many people in it. Come on – let’s admit it, we have all asked that question at one time or another (especially if you are a parent!!)  It’s a great question. And now I am curious. Where to start? My thoughts are I’d probably need to do some research on the average amount of pee found in a pool and then go from there. The great thing here – Brian Marks from @YummyMath has done that work for me, and even has an engaging ‘lesson starter’ video to go along with the lesson (link to the lesson). So – this would be a really fun problem to start out with that first day of school – funny, lots to notice and wonder about, getting ideas from students on where to begin, what information they might need, etc.

In an early post this summer, Summer Vacation – Use Your Experiences to Create Engaging Lesson Ideas, I talked about how your own summer experiences could raise questions and interesting problem-solving experiences to bring back to the classroom. But – as the tweet from Brian Marks @yummyMath reminded me, there are other amazing educators and resources out there who are already thinking of these questions and even creating the lessons for you. No need to reinvent the wheel, as they say – if there are some interesting questions and resources already being posed and shared, then use them. Saves time, maybe provides some ideas you hadn’t thought of before, or maybe it takes something you did think of and provides some questions or links that you hadn’t found yourself. As educators, we need to really learn to collaborate and share our expertise so that we are not individuals trying to support just our students, but we are educators trying to work together to improve instructional practices and student achievement. Isn’t that what we try to stress within our own classrooms – i.e. working together, communicating, and sharing ideas because this leads to better understandings and new approaches? Same goes for our teaching practices and strategies.

Here are some fun problem-solving resources, with lots of different types of problems, but definitely some ‘summer-related’ things already started for you!

  1. YummyMath – (check out the ‘costco-size’ beach towel activity….that’s funny!)
  2. Mathalicious – (Check out the ‘License to Ill’ lesson – relevant to todays’ debate on Health Care & Insurance)
  3. Tuva|Data Literacy (Check out their lessons and their technology for graphing and analyzing data, and their data sets – so much here!)
  4. RealWorldMath
  5. TheMathForum
  6. Illuminations 
  7. Center of Math
  8. MakeMathMore.com
  9. MashUpMath

 

Learning from Webinars

Online learning takes many forms, of which webinars are one. For teachers, webinars are nice because they are usually content or instructional strategy focused and they are relatively short in length, so you can fit them into your busy schedule. Webinars are often live – meaning happening in real time, and you register and sign on at the designated date & time and can interact with the presenter (usually via a chat forum).  This is nice because if you have questions, you can ask them right away. But – the disadvantage here is you have to have the time to sit in on the webinar, which is often not the case, considering our crowded school and personal schedules. If you can participate ‘live’, I highly recommend it. When I worked at Key Curriculum and hosted our weekly webinars, I know the live interaction was a very positive aspect of the learning.

Let’s face it – the reality is it is not always easy to get to a scheduled ‘webinar’, even if it is the most interesting topic in the world. Which is where the beauty of technology helps out – because most webinars are recorded and archived for on-demand viewing (much like our on-demand television binge watching craze!). Most education companies or organizations that host webinars will have them archived somewhere because they WANT you to log on and watch – it’s good for business. There are a couple of good sites listed below that have some educational archived webinars that might spark your interest:

There are more out there, but this should be a great start. And – not to let Casio be outdone, we have many archived webinars as well that focus on integrating Casio technology and math content. These are free and accessible on our Casio YouTube site  We have short how-to videos on this site as well, so the way to determine a longer, content focused (and/or technology focused) video is to look at the time stamps – those that are 20 minutes or longer tend to be the webinars. I’ve included one below on Proportional Reasoning, since this is such a huge issue with students of all ages, and the presenter, Jennifer N. Morris is one of my favorite people and math teachers. Enjoy!!

Failure is Key to Learning & Perseverance – ISTE Keynotes

I was unable to attend one of my favorite conferences this year, the International Society for Technology in Education Annual Conference (ISTE), which was held in San Antonio, TX June 25-27 a couple weeks ago. I was doing some training in Austin, TX so could not make it. But – because it is a technology conference, they video many of the presentations, especially the keynotes, and make them available on their ISTE Youtube Channel

This years completed videos are not up yet, but there are some ‘teasers’ of the three keynote presentations. I particularly like the closing Keynote speaker, Reshma Saujani, the CEO and founder of Girls Who Code, on coding and how coding is all about the iterative process and failure – i.e. learning from failure and doing things over and over until you get things to work. This is how we develop that creative thinking, that problem-solving, and that critical thinking in students – letting them fail, learn from that failure, and try again. It speaks to the mathematical practice of making sense of problems and perseverance. Here is the excerpt that is currently posted on the ISTE website – short but worth a listen:

This is the excerpt from the opening keynote, Jad Abumrad, the founder of RadioLab, also about learning from failure.

Both of these speak to something I have been focused on this summer in a course I am teaching – how to get students to persevere in problem-solving and be okay with ‘failure’. Instead of giving up, to have that drive to find another path or look for another solution. I am sorry I missed the conference, but it’s nice to get a peek into some of what was focused on, and I think it’s something educators really need to think about as we use the summer to plan for next year – how can you support productive struggle and learning from failure and perseverance in students?

The Numbers Behind Fireworks – Math Could Save A Finger or Two

I certainly hope everyone enjoyed their 4th of July celebrations. I know I had a lovely time at the beach with my husband and friends. And, as we were at the shore, naturally we, along with hundreds of our ‘closest’ beach-going celebrants, headed down to the oceanfront with our chairs to enjoy a multitude of firework displays put on by five different beach cities. It was actually really nice because you can see all these shows, with some closer than others depending on where you are, and they are timed so you can see the end of one as another is beginning – about an hours worth of city-sponsored fireworks. At one point in time, I saw our cities show and in the background, with 3 other shows at varying distances away (due to the curve of the shore). I did try to capture it on film, but it was night – with a phone – so not the best of pictures!

While we were waiting, again with hundreds of others on the beach for a good many miles, there were those folks who brought along their own fireworks – sparklers for the children, high-grade fireworks firing off – all in all, very impressive and very scary. Especially as the bangs went off, and the ones on the ground smoked away with children running all around – and then there was the falling ‘sparks’ and debris from those larger ones set off by the water landing on folks all around (setting off some screams). The city firework displays are all set off on barges out on the water, done by professionals. Not so much the ones being set off on the shore – right around hundreds of people. While it was all good and fun, and everyone was celebrating the birth of our nation, it was actually a little frightening as well – considering how many of the ‘fireworks’ almost exploded right by us or went towards the houses instead of out to the water….

Naturally, as is my way, I felt the need to look up some numbers. The National Fire Protection Agency has research numbers specific to fireworks. And it’s kind of frightening really. Perhaps the most frightening one is the sparklers, which all the children were running around with and what I believe most people feel are fairly harmless. This little temperature graph might make you feel a bit differently. We are afraid to let children near pots of boiling water or get too close to a fire, yet we let them run around with sparklers in their hands that are burning at 1200 degrees, almost 6 times hotter than boiling water.  WOW!  That’s an eye opener.  And, as a result, according to the NFPA, sparklers account for more than 1/4 of emergency room fireworks injuries – and who is it that is usually walking around with those sparklers – young children. Just to frighten you a little more with the numbers, the circle graph to the right shows the types of injuries that occur – notice, hand & fingers have the highest chance of injuries, with head and eyes tied for second. Again – think of those kids running around with the sparklers……

If we explore the data a little more, we find some interesting statistics:

So – makes sense, if we look at the graph on the right and the graph in the middle, that because sparkler related injuries are the most prevalent, that kids 5-9 have the highest risk for injury since they tend to be the ones running around with those sparklers. But notice in the circle graph to the left that ages 25-44 actually had more reported injuries, which, based on my own experiences and observations, also makes sense when you look at the type of fireworks that are causing the injuries (graph to the right) after sparklers – illegal firecrackers, small firecrackers, those with re-loadable shells. In other words, this is what ‘the dads’ are doing or the ‘adults’ or, as evidenced last night, the large group of college-age kids. They are the ones setting off the big, scary fireworks on the beach – and getting injured more.

Obviously, not many people think about statistics when planning for some fun on the 4th of July (or New Years or other firework-worthy celebrations). It’s about the fun. But – my guess, especially with parents of younger kids who don’t see the harm of those little sparklers – if you showed them some statistics, especially that temperature graph with sparklers at the top, there might be some reconsidering of the ‘playing with fireworks’ mentality. Math could save a couple of fingers…..

Education Growth Mindset – So Important for Teachers and Students

I just came back from Kaiserslautern, Germany, where I was working with Department of Defense Education Activities (DoDEA) math teachers as part of the DoDEA/UT Dana Center College and Career Ready Standards Initiative. Our focus this summer, which kicks off the next year of continued support and training, was on helping teachers create a classroom culture of student discourse and a growth mindset that allows students to develop deeper mathematical understanding and become problem-solvers and confident mathematicians. It was a fabulous two days, and the teachers, some who had never explored this idea of ‘growth mindset’, really had some powerful conversations around this idea of providing students productive struggle opportunities and helping them develop this sense that they can solve problems, and they can improve mathematically, and they can learn. It was rather eye opening for many.  How many of us educators have come across those students who give up without even trying because they think they can’t do it? Or they have been so ingrained in the idea that they are ‘bad at math’, so they don’t even try? That’s what this idea is about.

Carol Dweck is a leader is this field of Growth Mindset, and how to motivate and help support this idea of a growth mindset. In fact, the teachers I worked with as part of our workshop, read an article by Dweck that provided some insight into what we as both teachers and parents, inadvertently sometimes do that prevents students/children from having a growth mindset. Something as simple as the way we praise can actually interfere with this growth mindset. More here.

Many of you may be unfamiliar with what a growth mindset is, so I found a great TedTalk from Carol Dweck that explains the idea behind it. As educators, this is something to really think about because we want to develop in our students the willingness to persevere and solve problems that may seem difficult.

 

Free Online Casio How-to’s & Content Focused lessons – Great Personal Learning Resources

I am clearly on a ‘what should you do with your summer’ kick, if you look at my previous two posts. But – my belief is that summer, while a time for fun and relaxation, is also a time to brush up on some skills you may be lacking or things you want to learn, find new ideas for the classroom….basically, use the time to foster your own personal learning.

This learning doesn’t need to be expensive, it doesn’t need to be long – it’s all about improving skills or learning new ones. With that said, I thought I would remind all of you, whether you are a teacher, a student, or a parent of a student – if you want to brush up on your Casio calculator skills, we have a lot of free online tutorials and how-to’s that might fit the bill. In my interactions with teachers, I am often asked if we have ‘tutorials’ so that the teachers can support all those students coming to class with Casio calculators (because they are more affordable and much more intuitive to use).  The answer is yes!

In this post I am just going to share some links to our free online resources, and highlight a couple of the videos here as well.

Casio Education has a Youtube Channel where we post previous webinars (so these are longer and actual ‘lessons’), shorter how-to’s, and some quick reference videos and overviews as well. Here’s the link to the Casio YouTube Channel.

A couple highlights here:

Here is an example of a short look at the fx-9860 Stat menu:

Here is a much longer lesson with the Casio Prizm on families of functions:

There are also Prizm specific guided tours at this link.

And I have my personal YouTube channel where I do comparisons and how-to’s on the different calculators, so there might be something of interest there as well.

Here’s a quick how-to using the fx-991 Scientific Calculator to solve systems of equations (and use the QR code):

So – if you have a spare 10 minutes or a spare hour, there’s something for you and we will continually add to these so come back often!

Summer Vacation – Use Your Experiences to Create Engaging Lesson Ideas

Sea Turtle at the Big Island, HI. How long do they live? How far do they travel??

I know most students and teachers this time of year are very familiar with Alice Cooper’s song “School’s Out for Summer”  (Seniors are probably focused on the line “school’s out forever….”  Maybe even some teachers!)  No doubt, summer is a time of rejuvenation for students and teachers – a much needed break, both mentally and physically. Note: Those of you who do not teach, and see teachers as having it ‘easy’ with the summers off, might try to spend some time in a teachers shoes before making those ridiculous assumptions, or read up a bit on what teachers actually do (they work more than 40 hours per week) and why summer breaks are so important.

Summer break is fast approaching for many, and some may have even started theirs. I remember those first couple of weeks literally not wanting to even look at anything related to school, students, or teaching. But – as most teachers will attest to, there comes a point where summer vacation weaves into professional learning or preparing for the next school year to begin. We never really turn off completely – we take classes to learn something new, or research some new technology or applications we want to try in class next year, or we revamp some lessons from the previous year. Summer vacation always ends up, at some time or other, connected back to teaching and learning – either personally for our own professional growth, or related to how we can be even better the next school year for our new group of students.

For me personally, everything I do always has me thinking of ways to create an interesting lesson for my students. It’s that pervasive idea that whenever possible, connecting the real world back to what students are learning will make the learning engaging and relevant. Just last week, sitting on the beach in Sea Isle City, NJ, watching this big machine out in the water that was dredging sand to replenish Avalon Beach, all I could think about were questions I would want my students to investigate.  Just a few of my questions, as I sat there:

  • How much sand is being pulled up? Is it from the same spot (my observation, since the dredge is in a different location each day, is that no it is not)
  • What happens to the sea animals and plant life that are ‘dredged’ up with the sand? Or, is there a filter that only allows sand in?
  • What are the impacts on the sea life?
  • How many hours a day do the dredges run? (seems like 24 hours to me!)
  • How long does beach replenishment last? (if you don’t have any storms to wash it all back to sea) How long does it take to replenish a beach?
  • How many pounds of sand is needed and where do they place the sand?

Lots of questions just from sitting and watching. What a great #STEM lesson this would be for students – there’s math, there’s science, there’s engineering and there’s definitely technology – it’s quite the endeavor. There is probably a ton of data out there and information about sand restoration projects, so you could have students researching, doing the math, checking out the science, investigating the machines used and the manpower needed. I did an initial search and found a couple articles already where I learned things like the grain size of the sand determines where the dredge pulls sand from (has to match the beach they are replenishing).  Pipelines are created to carry the sand from the dredge to the beach (so, how big are those pipelines? What happens after they ‘finish’ – do the pipes get removed?) Sometimes this is done to protect sea life, often times to protect commercial and residential properties, so this then begs the questions such as what’s the cost (money wise and to the environment), who benefits, what are the potential dangers and damage (to environment/sea life, etc). Here’s just a few articles I found.

My point here is not to give you a lesson on beach restoration. Instead, my point is that I was just sitting on the beach, enjoying my vacation, and saw the

Two clear streams in Costa Rica that when they meet, the chemicals in them react and turn the water blue. Why

machinery and started thinking. Posing questions. Realizing that there could be an amazing #STEM lesson here, which got me excited and doing research and yes – vacation or not – planning for teaching.  I think it is a natural tendency as a teacher to see a ‘lesson’ pretty much anywhere we go, which is what I want to emphasize here. Even on vacation, if you have a great idea based on something you are doing or seeing, some idea you think would be an engaging lesson, go with it. Take some pictures. Write down some ideas. Do some research. Use your own experiences and ‘time off’ to discover teaching ideas and spark your own enthusiasm for the next school year. Bring your vacation into your classroom and build relevant, real-world, multi-content lesson ideas that will spark student engagement, questioning, critical thinking and problem-solving.

Enjoy yourself and your summer, but never stop learning and looking for great ideas to bring back to your classroom.