Let’s Explore with Geometry and Start the School Year Off Right! (New Features with ClassPad.net)

I admit it. I am a geometry nut.  It is my favorite subject to teach, which I have been doing for the past 30 years (wow….said that out loud!!). Geometry to me is all about logic and connections and relationships of shapes. It should be hands-on, it should be visual, and with technology, is should be dynamic – meaning you can see and discover relationships through movement and manipulation. There are many good resources out there (for those of you looking for a ‘textbook’, Discovering Geometry has always been my go to – it’s all about learning geometry through hands-on discovery and connections. It’s on it’s 5th edition, and the ebook has dynamic investigation using ClassPad.net (formerly used Geogebra), and ClassPad.net has made huge strides in advancing it’s geometry functionality, which is what this post is focused on. My goal over the next few posts is to focus on specific geometry explorations using some of ClassPad.net’s geometry functionality, but today’s post is an overview of what’s new.

ClassPad.net has all the tools you would expect a geometry software to have – i.e. points, straight-edge tools, polygon tools, display tools, expressions, equations, etc. It has some others don’t have – i.e. tools for conics for example. Below is a list of some of the added features as we continue to improve the functionality of the software (which is FREE, btw!!)

Quick List of New Functionality:

  1. Compass Tool
  2. Ability to add in images and use them as part of your geometry explorations
  3. Ability to create sliders for transformations (dilations, rotations, translations, reflections)
  4. Trace feature
  5. Multiple Grids, including isometric
  6. Ability to lock constructs
  7. Ability to create a rigid polygon (meaning it won’t change shape once constructed)
  8. Ability to add tick marks to sides and angles
  9. Ability to change the style of points – i.e. dot, square, x
  10. Ability to measure exterior angles explicitly and create angles 0-360
  11. Ability to construct a specific regular polygon (n-gon) by constructing one side and choosing n (number of sides)
  12. Ability to duplicate constructs without have to ‘reconstruct’ them.

I will be creating videos on each of these features and how to use them for future postings, but today, I wanted to show you where you can find the different new features. Be sure to visit ClassPad.net and sign up for an account (so you can save any work you do). Both the Free and Basic accounts are completely free and have everything you could need for a classroom (don’t forget there is calculations, graphing, statistics, financial tools, and text as well as geometry!). Below is a quick how-to on finding where all the new features for geometry are – stay tuned for future how-to’s on using the specific features. Meanwhile, why not try and explore things on your own? Have fun!!

 

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Math In Motion – Creating Simulations with ClassPad.net

The beauty of dynamic software is the ability for objects to move in real-time and measures and other objects connected and/or controlled by those also move. Basically seeing change over time happen. This allows for the ability to create some interesting simulations – such as simulating cars moving at different speeds and directions to explore rate of change, or objects turning to explore rotational symmetry and angles of rotation. Many possibilities.

Obviously thinking of ways to incorporate simulations into the teaching of more abstract concepts can be time consuming. This post, I am sharing a How-to created by Ismael Zamora, where he shows how to create moving images (using cars) and also provides a couple related ClassPad.net papers if you are interested in the activity he created.

The idea of the activity, Math In Motion, is to have students first Notice & Wonder about the movement of the cars and how they are related, what the sliders control, and is it possible to answer the question of when they will meet?

Here are the links to the publicly shared papers:

Below is a How-to video that explains how Ish created the motion of the cars, involving images, and sliders.

 

Teachers Rock! Show Your Appreciation in a More Personal Way – Tell Them

It’s National Teacher Appreciation Week, for those of you not in the know. In schools everywhere, teachers are probably getting nice little ‘treats’ from parents and students, or having special lunches or breakfasts brought in, or being treated to free ice cream or nice messages or pep rally’s – lots of things to show how much everyone appreciates the work they do. Obviously these celebrations and expressions of gratitude vary around the country, but there is usually, based on my own personal experiences in middle and high school, some recognition for teachers at some point during this week.  Which is great. Teachers deserve to be told how wonderful they are and what a difference they make in students lives, because they do. They do every day, whether they or you realize it.

It’s the little things that teachers do every day, which often go unrecognized, that really make a difference in students lives and learning. That extra time put in to make a lesson really engaging, that eating in the classroom during lunch to spend time with students who just want to talk or get some help, the personal money spent on supplies and classroom decoration so all students have what they need and to make the classroom a welcoming place, the smile at the door as students enter, the late hours grading, the phone calls to parents to share good news about students (yes, teachers do that!)….there are too many to list here, but every day teachers are providing not only learning experiences, but emotional and physical experiences that help to mold and build students confidence and understanding. This is what I don’t think people who have never been teachers understand – teaching is unlike any other job. You can’t just come in, do the same thing every day, and go home at the end of the work day and forget about it. Teaching is more than teaching content. There is a lot of emotion and dealing with students on so many levels, and navigating that, along with teaching content, makes teaching one of the most difficult jobs out there.

Unlike many other jobs, teachers often never know the impact they had on their students. Sure, we can see grades and scores on tests, but that is a moment in time in a students life, and we don’t often ever know if what we did as teachers has long-term impact (which we hope) as students grow and move on. We think it did. We hope it did. But often, we never know. Unless a student comes back and visits, (or, we are now friends on FB, years later!) – we never really know if the things we thought would make a difference did in fact make a difference. Which makes teaching different from many other professions, who can usually see immediate results or impact of their job. Teaching is a profession of faith – where we believe our efforts are the best we can provide and are something powerful that contributes to our students potential future selves. And though we often never know, we do believe.

What I think would be a really powerful way to show appreciation during this week is for students, current and past, to let a teacher know what it is they are doing or have done that has an impact on them or helped them. Reach out to that Spanish teacher who made class funny, and embraced your obnoxious sarcasm, and influenced your decision to become a teacher yourself, or write that math teacher who helped you survive Calculus and helped you become an engineer, or that teacher who smiled at you every day and gave you a hug so that you loved coming to school. Get your kids to write a note to a teacher (now or in the past) that made school exciting or turned them on to reading or helped them perfect their dunking. It’s those little recognitions’, those personal recollections that really make a teacher feel appreciated and know that what they do is making a difference to someone. Those of you who have been out of school for a while, it’s pretty easy to locate a former teacher via FB or LinkedIn. Those of you still in school, write a note, even if anonymously – it will brighten that teachers day and reaffirm their commitment to teaching.

The U.S. Department of Education has shared some really great videos of teachers sharing what makes them feel appreciated, so I am providing links to those here:

  1. https://youtu.be/dLZXKu8fxnc
  2. https://youtu.be/eqi_kE31tZU

My favorite is what students say about their teachers though, so I am sharing that video here:

 

Weather and Integers – The Importance of Real World Connections

A lot of my math teacher friends have been posted images from weather reports on FaceBook and Twitter, like this one to the left from @seemathrun, showing the real-world application of integers due to the extreme weather conditions that are happening across the country right now. It really is a perfect opportunity to show a true application of mathematics that students can definitely relate to, especially if they are in those freezing climates. Add in the wind chill, and you have some interesting data and comparisons and a chance to talk about the relevance of math and understanding numbers.  Here’s an image to the left showing wind chill, temperature, and frost bite times someone else shared that could help explain why so many schools are closed, even though there may not be any snow on the ground, (which is usually the reason behind winter closures). I know one of my colleagues and friends, @ClassPadnut, was sharing with me yesterday that with the wind chill, it was -60 where he lives.  Yikes!!!

There is obviously a lot of different math concepts you could explore with students, dependent on grade level and questions asked. I find the wind chill graph the most interesting. Looking at the wind chill chart, the drop in temperature is almost, but not quite, constant, like you would think – i.e. You will note that there is an equation for the calculation of wind chill at the bottom of the image. I was  curious about whether students could find that connection from the data alone -something to challenge students with. How would they graph this data? Could they? Thinking of statistical tables, what would they enter and what statistical plots would be appropriate? If students are in areas where schools actually closed, you could talk about how the data supports the decisions, and what is the ‘cut-off’ temperature/wind speed that might influence the decision? Lots of things to explore.

I found another image that showed the lowest temperatures reported in each state, so you could do a comparison across states. Even Hawaii is cold!!!  Crazy.  Below is the image, which I then used to enter the data in a table in ClassPad.net, and then make two different plots to represent the data – a histogram and a box-plot. You can see from the box plot five-number summary that the median temperature in the U.S. for this day in January is -40.  Wow!!! (And boy, don’t want to be in Alaska at -80!) Again – think of the interesting class discussions about integers, about how these temperatures will impact things such as the orange crops in Florida or the tourism in Hawaii or California. (Here’s a link to the Classpad.net paper that has the image, table, and graphs shown below: https://classpad.net/classpad/papers/share/b61b70a0-0eed-47da-947a-580e1d835f8d.

As you can see, using what is actually happening right now in our country, i.e. REAL world connections of weather (temperature, wind speed, wind chill), is an amazing opportunity to help students see the relevance of integers and statistics and how this data is being used to make important decisions, such as do we close schools? Who should not venture outside? How long before you get frostbite? The visuals help students ‘see’ mathematics in action, and particularly if we focus on the integer aspect, provide a clear connection to integer addition (and subtraction, depending on the questions asked), something many students struggle with.

Whenever possible, we should be trying to connect the math concepts students are learning and using to a real-world application. Here’s a perfect opportunity, no matter the grade level, to have some great class discussions about the impact of weather on our world, about the relevance of integers, and about how statistical information is important to decision making.

 

Math Hardware versus software – Similarities & Differences with Casio

Students using technology as part of learning math is important because of the extension of learning that is possible, the visual connections, and explorations that become possible as a result of technology. The most common technology students use these days are their phones, tablets, computers, and of course, hand-held devices such as calculators. It all depends where you live, what schools you attend, what’s allowed or not allowed, and also what resources are actually available and understood by both teachers and students. From my own research, some schools/teachers have a multitude of resources, but most schools have limited options. And – even if there are many technology tools available, teachers tend to utilize the tool (s) they are most comfortable with, and that the majority of students have access to. Basically, it comes down to choosing a technology that is going to support the learning and that students and teachers can use relatively efficiently, so that time is not lost to ‘tool logistics’. Often times, again, based on my own research (dissertation), teachers choose tools that may NOT be the best choice for learning because they know how to use it over a much better, more appropriate tool, that they are unfamiliar with or uncomfortable with, so many times better technology tools go unused because of the ‘learning curve’.

What I wanted to use this post for today was to show how Casio has really recognized the ‘learning curve’ issue and tried to keep functionality consistent across handheld models and even in their software, providing intuitive steps and menu options right within the graphing menu itself that alleviate some of that ‘learning new tool functionality’ concerns that teachers and students often face when using technology. Our graphing calculators basically use the same steps, buttons, layout, even from the very basic ones (fx9750) (fx9860), to the more advanced ones (CG50), so if you know one, you know them all. And, even the new software, ClassPad.net, is built along the same lines, though obviously with more features and capabilities.  But there is no ‘searching for menus’ – relatively intuitive no matter the tool. Obviously, as you get into the newer models and then into the software, the functionality and options increase – we go from black-and-white displays to color, we go from intersection points on the graphing calculators to union/intersections on the software. But knowing how to use one tool makes transitioning easy, and if you had students with several different models of the handhelds, you could still be talking about the same steps and keystrokes.

The best way to compare and demo is to show you how to do the same thing on the different models. I’ve chosen to show graphing two inequalities, so that you can see, even on the older models, that shading and intersections occur. But also to show that as you progress into the newer and more powerful tools (i.e. memory capacity, color, larger screens, resolution, etc), allowing for more options and learning extensions.

Here are the two inequalities that are being graphed in each of these short GIF’s:

Each GIF below graphs the two inequalities and finds intersection points of the two graphs. The software extends that to allow for finding the Union and the Intersection of all points.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Be sure to check out the free software that does calculating, graphing, statistics and geometry: ClassPad.net.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

New Year’s Resolutions – A Chance to Explore Some Statistics

As I was at the gym this morning, noticing the increase in people that were there, I got to thinking about New Year’s Resolutions. I personally dread the month of January at the gym because inevitably, it is a lot more crowded with all the ‘new memberships’ given as gifts over the holidays, and full of new people who have decided losing weight and getting in shape are on their to-do list for this new year. As someone who hits the gym regularly, this month at the beginning of the year is a bit frustrating because machines are taken, the parking lot is crowded, and my regular routine is often interrupted due to the increase in the number of people. I admire everyone’s new-found commitment and applaud the goal of getting in shape and being healthier – however, my anecdotal evidence over the past several years is that this commitment is short-lived for many.  By February, things tend to get back to normal because, sadly, many of our ‘new years resolution’ folks lose the commitment and stop showing up, allowing the rest of us to get back to our routines.

Which brings me back to my thoughts about New Year’s Resolutions (NYR).

From my own very unscientific observations at the gym, those that made NYR to get in shape, lose weight, etc. usually last about a month – and this is based solely on the increase in people during January, and then the slow decrease in people as the month progresses, to the return to the regular crowd by February (with, granted, a few new ‘regulars’ who stick it out). I wondered, as I was cycling, are there any statistics out there that actually show the follow-through on New Year’s Resolutions – i.e. what were the resolutions made at the beginning of the year, and what was the actual end result at the end of the year?

I was able to find statistics on the most popular NYR made last year (2018)  However, I couldn’t find any follow-up statistics to see how many people in the survey actually stuck to their resolutions, which is what I think would be interesting to explore.

 

 

 

 

 

 

 

 

 

 

 

 

 

I then found another source that listed the 10 most popular NYR’s made for this year (2019).  A lot of the same resolutions, though maybe different priority. Some different ones as well, which could be a factor of many things – i.e. the economy, the political climate, the source of the survey, who was surveyed, etc.

I am curious why there is no follow-up from those that conducted the surveys at the end of the year. It would be fascinating to see what the graphs look like at the end of the year compared to the beginning and why or why not some people dropped off their NYR and some stayed true.  I couldn’t find any ‘proof’ for claims such as “80% of all NYR’s fail by February“, though again, going back to my personal observations, I would agree with this claim. There are definitely a lot of articles about how to ‘keep’ your resolutions, and plenty on why people don’t stick to their resolutions, but no statistics that actually support this claim that I could find. But it would be nice to have some data or evidence that supports observations – which leads me to my final thought on a fun ‘real world’ statistical study that teachers might explore with their students for the remainder of this school year.

During this short week, where school has started up again but students tend to still be in vacation-mode, why not start a long-term study to see if we can get some statistical data about NYR’s? Have students in your class make a list of 3 NYR’s – so some goals they really plan/want to accomplish by the end of the school year. Better yet, pick a specific month and/or date (so May 30 for example). Then, compile the class data to create categories and percentages, similar to the charts above. (My guess is students will have some different things on their top 10 list, which would be interesting in itself). Have students keep a record of their progress towards their goals, and maybe on a monthly basis, do a quick survey on students progress/commitment to their NYR’s.  Then at the proposed deadline, do another survey on the success/failure to see who is still working on their goals and who is not. Obviously it is going to be self-reporting, but it would be interesting, as time goes on, to see who is staying committed, who is not, and more importantly, WHY they are not staying committed if that is the case. Do the class results verify that 80% drop off by February? Is there a common theme for those that do not follow-through on their NYR’s?

I wanted to share this as an idea for teachers who might have made their own NYR to be more creative in their math class. The only NYR I ever made each year was to try at least one new thing in my math classes every month – for me a pretty easy resolution to stick to. I would imagine many teachers do something similar. For those of you who have made NYR, good luck and Happy New Year!

 

Systems of Equations – Sample Lessons and Resources

For this months lesson feature, I am going to focus on Systems of Equations. I chose this topic because I just did a workshop with Algebra 1 teachers in NJ, and this is where they were in their pacing guide, so I am making an assumption that many algebra teachers might also be focusing on this content as well this time of year. I am using a problem from Fostering Algebraic Thinking with Casio Technology in order to provide a real-world problem-solving experience (and I have the resource), but I have altered the problem so that I can utilize the all-in-one capabilities of Classpad.net (tables, graphs, equations, geometry, text).

The Problem

In 2010, there were approximately 950,000 doctors in the United States, and approximately 350,000 of them were primary care doctors. It was estimated that more than 45,000 new primary care doctors will be needed by 2020, but the number of medical school students entering family practice decreased by more than 25 percent from 2002 to 2007. With laws reforming health care, many more people will be insured in the United States. 

For many reasons, including a growing and aging population, the demand for doctors will likely increase in future years. The number of doctors available is also expected to increase. But, due to the high cost of insurance and the fear of malpractice lawsuits, many have predicted that the increase in the number of practicing doctors will not keep up with the increase in demand for doctors.

The table to the right provides data from a study conducted in the state of Michigan. These data approximate the number of doctors that were or will actually be licensed and practicing in Michigan, called the supply, and the number of doctors that were or will be needed by the people of Michigan, called demand.

The question is, will there be enough doctors to provide all the services? The shortage of doctors is a problem that challenges the entire country, not just Michigan.

The Lesson

A shared paper has been created in ClassPad.net called Systems of Equations Help! Not Enough Doctors, which you can access by clicking on the title. The idea behind this problem is to provide a real-world context where students can use tables, graphs, and equations (along with calculations) to create a system of equations. They can solve these using methods such as substitution, elimination, and graphing. Students will also be practicing how to model with mathematics, applying what they know about relationships and being able to create a system of equations that fits the context of the situation in order to find a reasonable solution.

In the activity, there is obviously some focus first on getting students to really understand the problem and what the numbers represent, and then the idea is to have them look for patterns and relationships as they look for a solution. First in the table, then by looking at a scatter plot of the data, where they again try to determine a solution based on a visual. Continuing to look for trends, they use prior knowledge to recognize linear relationships, create equations that model the data, and then graph those equations to find a more precise solution. Then, as a check, they solve their system of equations algebraically. It’s all about multiple representations and helping students see the connections between all the representations, and depending on whether you want a specific, precise answer or just a generalized answer, you might choose a different representation.

ClassPad.net – Lesson In Action

The video below shows the activity and does a brief walk through of some of the components and what it would be like doing the activity from a student perspective. I am a big believer in the think-pair-share approach, so I would suggest having students do the Notice and Wonder individually first, then pair up, then share so that you can make sure that any misunderstandings about the context, and clarification about the numbers is figured out before students start solving. Then I would suggest small groups for working on the problem itself.

Other System of Equation Activities and/or video links