Halloween – Fun Statistical Exploration Ideas

As I walk down my street and see the spider webs on the bushes, the witches and ghosts flying from the porches, and the glowing pumpkins, it’s hard not to think about Halloween. If you live on a street with lots of younger kids, it’s even harder! On my street, in a small town, Halloween is a big deal – all the neighbors come out, we build a bonfire, adults without kids hang out while those adults with kids walk around trick-or-treating with their children. There are hand-made costumes, adorable family costumes, lots of candy and a few ‘adult’ treats as well. I admit – I tend to dress up just for the fun of it, even though my own children are long grown. All of this has me thinking about the amount of money that people spend on this day of fun – i.e. the decorations, the costumes, the candy. Naturally, this had me out exploring…..

I found several articles, and let’s just say the numbers are pretty astounding:

From one article, it’s estimated that $2.6 billion is spent on candy and $2.7 billion spent on decorations. Wow!  That’s a lot. Though, after looking at the price for one bag of candy, I shouldn’t be too surprised.

Of course, I LOVE when data is displayed visually, since this really helps students in particular see data and make sense of it. Found this chart from Statista about last year’s Halloween and how the spending is divided across categories. The costumes for pets sort of cracked me up!

Infographic: The Shocking Scale Of U.S. Halloween Spending | Statista

As always, I like to think about how this type of information could be used with students. Especially as math teachers, where we are always looking for real-world problems that are in fact real world (not textbook ‘real’….i.e. contrived) and that engage students. Halloween is definitely something that engages students, so there are many ways teachers could incorporate some Halloween real-world data and questions into the math classroom.

There are several articles and places that have data about Halloween, so one way would be to collect data and create graphs of these for comparison. So perhaps comparing the trend of spending over several years and then maybe exploring what might have been happening in the years where spending seemed lower or higher and making some connections there.

Or, having students look at Halloween adds for costumes and/or candy and compare pricing and make some decisions on where they should buy their Halloween supplies, factoring in things such as sale prices, buying in bulk, type of candy, etc.

You could have some fun with candy as well – maybe estimating the number of candy corns in those small bags, and then collecting data (i.e. open several small bags, count the number, record the data, then find statistical measures and graph. Really, same thing could be done with any of those Halloween-size bags of candies, such as M&M’s, Skittles, etc.  A fun exercise in weight vs. quantity.

Students could collect data on costumes (i.e. survey other students in their school on what costume they plan to wear, and see what the trends are for costume type (see chart to the right, where for kids, Princess is #1 and then Superhero).

You could include some health statistics too – i.e. does the number of cavities found in people increase after Halloween?

And let’s not forget about pumpkins!! According to this article, $377.3 million was spent on pumpkins last year (for carving). So – how do farmers plan for the run on pumpkins? How many pumpkins are planted that are not used? Is there a state that grows the most pumpkins? Where are pumpkins grown in this country??There are lots of questions we could ask about pumpkins, so get your students thinking! And, there are lots of statistical plots reflecting the data on pumpkins (and more) that could lead to some really interesting exploration and questions and analysis.

Let your students generate some questions themselves and then help them explore finding information and then presenting the data and their conclusions. There will be a lot of different kinds of math going on, based on the avenue they choose to explore.

Have some fun!!!

Here is a quick video of some data taken from this article that I put into ClassPad.net (first as an image, and then I made my own table). Here’s a link to the CP.net paper if you want to use it.

 

 

 

 

 

 

 

 

 

 

 

 

 

You will find more infographics at Statista

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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!!

 

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.

 

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!

 

Quadratic Functions – Sample Lessons and Resources

I am starting a monthly feature where I will be focusing on some specific math content areas and providing some resources, in the form of how-to videos (both calculator and Classpad.net) and some ready-to-use math lessons (either PDF or links, depending on the tool used). I know math teachers are always searching for resources that will help them provide more open-ended math activities, where students are collecting and using data, using multiple representations to analyze and solve problems, and where students have to make decisions and support their decisions with mathematics. And integrate technology as well! So, at least once a month I am going to be picking a math content to focus on and provide some technology options as well, sometimes both calculator and online, and sometimes one or the other, depending on content.

This week I would like to focus on quadratic functions and helping students use a real-world context to work with quadratics. I am going to utilize Classpad.net, which is FREE web-based dynamic math software where I can do statistics, graphing, and calculations in one place (geometry as well, but for this activity, our focus does not include geometry). I am using this technology for a few reasons:

  1. It’s free, so all of you should be able to access the created activity, including your students, as long as you have a mobile device with internet access.
  2. I am able to create a complete activity (i.e. directions, tables, graphs, and place for students to show work) in one place and then share it easily via URL.
  3. Everyone who opens the activity can create their own copy of it (as long as you have a FREE account on Classpad.net) by duplicating into their account. Then you can modify, answer the questions, etc. and create it’s new URL to share with others (or for students to share with you). To learn more about duplicating activities, click here.

The Problem

You are fencing in a rectangular area of your yard to create a garden. You have 36 ft. of fencing, of which you plan to use all. You can cut the fencing into whatever lengths are needed, as long as you use all 36 feet. 

What dimensions should you use for your garden?

The Lesson

I have created a shared paper on Classpad.net called Quadratic Functions – Area of a Garden which you can access by clicking on the title. The idea behind this problem is that there are actually multiple solutions since the question is rather vague. I did NOT ask what is the largest garden, so students can work on collecting and analyzing the data and come to different conclusions depending on what they think is important. Some might choose largest area for the garden, some might choose largest perimeter, some might only want a rectangle some only a square, etc. By leaving the question a little more open, you are giving students a chance to explain their reasoning and come to multiple solutions based on this reasoning.

In looking at the activity (click the link above), you will note as part of the lesson, students use multiple representations. They first use their prior knowledge about dimensions of a rectangle, perimeter, area, and an understanding of feet and inches to record different dimensions for the garden. In the directions, students are asked to create at least 10 different rectangular gardens that use all 36 feet of fencing, where some of the width and length dimensions are fractional/decimal numbers and where width is sometimes larger than length. They record their dimensions in a table to start with, and then use those table values to calculate area (and perimeter if they choose to do the Extra Challenge), and use those table values to create statistical plots (scatter plots), and from the scatter plots and tables, create functions and graph those functions to fit their data. At different points along the way (after the table and scatter plots, and then after plotting their functions), students are asked to answer the question about what the dimensions they would choose for their garden and back up their reasoning using the information at that time. The idea here is to help them see that each representation provides insight into the dimensions, and some representations help you be a bit more precise or see the relationships between the quantities a little better. And also, depending on your goal for the garden, your reason for choosing certain dimensions may differ from others. There is also an extra challenge at the end (this is a way to support students who finish early, don’t need as much teacher guidance, and/or want to explore more), where students explore how the problem might differ if there was a fixed perimeter.

ClassPad.net – Lesson In Action

This is a video that shows using the activity and parts of doing the activity to get a feel for how this looks with students. I would recommend students working in pairs or small groups (3-4). All students can be recording on their mobile devices, or if you have one per group, choose a recorder.

Other Quadratic Activities and or video links. 

Here are a few more links that are focused on quadratic functions and also utilize ClassPad.net