Thinking Ahead – Planning for Next Year’s Classroom Culture

I was in Austin all last week training for UT Dana Center (@UTdanacenter) International Fellows
(#UTDCIFF) and Department of Education Activities (@DoDEA) College and Career Ready Initiative teacher workshops happening this summer. A major focus for the week was on classroom culture and how important this is to mathematical learning and student discourse. Everyone at this training was either a current math teacher, a supervisor, mentor, coach, professional development provider, etc., so naturally, as part of the conversation, the following questions/concerns arose:

  1. What is classroom culture and why does it matter?
  2. How do you get students to talk to each other and engage in productive learning?
  3. How do you respond to teachers who say things like, “well, this would never work with my students” or “I can’t get my students to talk about math when we are in groups”…

You get the picture, and I am sure you have either thought these things or heard these from teachers you work with.

The short answer – it takes planning, training, and consistency. If a teacher thinks that they can just put students into groups, give them a problem, and they are going to immediately start talking and working together, they are very quickly in for a big surprise. Especially that first time, and especially if you have never done these types of collaborative learning with your students. Which brings us back to classroom culture.  What is it and why does it matter?

There are many definitions out there of classroom culture. I will give you my perspective. Classroom culture is a classroom environment where students feel safe making mistakes, they are comfortable sharing their thinking process with other students and with the teacher, and all ideas are entertained and acknowledged. Everyone’s voice is heard, everyone gets a chance to participate, and there is respectful conversations and debate about the work being done.  This matters because then students are given permission to persevere in problem solving situations where they may not know the answer, or may have a different approach then someone else or may have a question about something another student or the teacher has shared. It ties into those mathematical practices (#1 & #3, just to name a couple):

  • Make sense of problems and persevere in solving them
  • Construct viable arguments and critique the reasoning of others

But, this type of engagement, discourse and collaboration with and among students doesn’t just happen. Here are what I consider the three basic elements:

1. Planning

Planning entails thinking about the structures you want to use with students (so pairs, small groups, whole class) and the types of discussions and work you want to students to engage in. There is more to it than this, but some things to think about are

  • What task are students working on and what is the goal (a worksheet of 40 problems is NOT going to promote student discussion). Provide a rich task that fosters critical thinking, questioning, problem-solving.
  • How do you want students to engage? Are they talking in pairs first and then sharing with the small group? Does each pair/group need to show some product (i.e. their work, their thinking, the end result).
  • How will you bring the whole class together at the end? Will each group share out? Will you hang work and have a ‘gallery walk’ and come together to share?
  • How will you know that students have learned or reached the goal? What should students be able to do?

You need to think of these things ahead of time, most importantly because without an engaging, rich, though provoking problem, the conversations students have won’t be productive (and can lead to all the issues mentioned previously).

2. Training

How do you get students to talk about math (or any subject?) How do you get students to work in pairs or small groups and stay focused on a task? How do you get students to listen to each other and to provide critiques without insult (i.e. no ‘that’s stupid’ or “you’re an idiot”). It takes training.  I mean that literally. You have to show and model what it is you expect of them and practice, practice, practice.  Again, there is more to this than what I am listing, but here are some ideas:

  • Start those first few days/weeks of school with non-content related activities that are non-threatening, fun, and where everyone feels comfortable sharing (so talk about ‘the best horror movie’ or argue for/against a ‘beach is the best place to vacation’)
  • Set up group norms – i.e. if someone is talking, everyone else is listening; everyone makes mistakes, and that’s okay, you can support them and provide alternatives, but never insult them; everyone must contribute one idea; everyone’s idea should be heard; you can disagree but must provide a reason why; etc.
  • Show them how to get into small groups (so physically moving desks back and forth – it’s fun to do this a timed game); show them and practice how to talk with elbow partners, or face-partners, or the people next to them.  Practice sharing talk-time (a time works here).
  • Show them and practice group ‘roles’ – i.e. timer, recorder, controller, group spokesperson, etc. Switch roles up.
  • Practice different ways of calling on students (so they know they are all responsible at any time) – so person in the group/pair with the shortest hair, or the darkest colored shirt, or blue eyes….really anything works.

There are obviously lots more ways to set up these collaborative processes, but the idea behind training is that there are some expectations for talking, sharing, and working together, and if we practice these and adhere to these, then our time learning is going to be more positive and productive. Practice, practice, practice.  Which leads to consistency.

3. Consistency

I know teachers here this all the time – if you set boundaries for your classroom, you need to be consistent or students will not follow them (heck, this is true for parents as well!). Again – those first few days and weeks of school are where you set these boundaries up and start practicing with students and modeling both behaviors and actions. More importantly, follow through on any consequences. For classroom culture, this means if you have an expectation that students listen when others are talking, whether that be student or teacher, then be consistent.  If you are talking and they are not listening, stop – call it out – and then talk again. Same thing for students talking. Acknowledge when something is not adhering to expectations and call it out and then refer back to your expectations. Students very quickly learn what is expected, and if they realize that you are going to consistently hold them to these expectations, such as listening, allowing for mistakes, everyone’s ideas matter, etc., then they are going to feel comfortable speaking up and sharing their questions and their solutions/ideas. It becomes a classroom where learning is up front and center and ‘we are in this together’ becomes the norm.

CHALLENGE

I plan to do some more specific posts about classroom culture and provide some resources connected to planning and training. For now, I brought this idea of classroom culture up at the end of a school year because as teachers, you are about to embark on a summer of rest and relaxation. For most teachers I know, it is also a time where we do some personal learning and planning for next year. I would like to challenge all of you to really think about how you want your classroom culture to be next year. You need to start on day one of school creating this classroom culture, so spend some time this summer planning for that. What structures do you feel you could incorporate (i.e. pair work, small groups, etc.) and learn about those structures. What are rich tasks and go find some that would work for the content you teach. What do you want students doing when they are learning together? Go find some tips and ideas for how to create those collaborative discussions and problem-solving environments.

Only YOU can change the classroom culture in your own classroom – so think about what you want that to look like and sound like, and spend some of your summer learning and finding ways to foster this culture in your classroom when school starts in September (or August).

The Last Five Minutes of Class

You teachers out there know that those last five minutes of class – when students are ‘packing up’ even if you are not quite finished with the class activities, or, you’ve finished and they are suppose to be working on their assignments or reviewing – are often  a ‘wasted’ five minutes. In my many years at schools, I saw teachers use that time in various ways – but more often than not, it was simply time to get ready to leave, basically chat time and get your stuff together and wait time. Not productive learning time at all.

It’s easy enough to make these moments into fun, engaging, mathematics problem-solving that students, believe it or not, actually come to enjoy and request. I use to have a few different things that I would pull out – focusing on either logical thinking or number-sense or puzzles. Here are just a couple of things:

  1. I had the 24-game – several different versions.  I(If you have never played this or seen this, you should explore it). So, in those last 5 minutes, I would pull out a card, write the 4 numbers on the board and students would try to reach the target of 24. As an example: 2, 3, 4, 4 and you can add, subtract, multiply or divide using each number one time, to make 24. I often had candy for anyone who could come up with a strategy.
  2. If you don’t have actual cards, you can create your own version of ‘reach the target’.  So, pick 4 random numbers using a calculator, and give students a target number to try to reach (so 24). Or, choose 2, 3, or 4 random numbers with a calculator (or have students give you numbers) and ask students to use all the operations and come up with the smallest outcome and/or the largest outcome.  This is a lot of fun – you get some interesting problems and students have to explain their answers and defend their solutions.
  3. Give the students a logic puzzle.  I actually purchased several logic books, and so would read one out to the students or draw/show the picture on the screen and they could work in pairs/small groups to try to come up with a solution. Great critical thinking and collaboration going on here – and if we couldn’t get the solution before the bell rang, we would take it up the next day with most of them working on it overnight. Here are some good resources for logic puzzles:
  4. Read a story.  Yep. Even with my high school students, I would read stories.  Math related of course. You would be amazed at how they actually enjoyed listening, and of course, once the ‘story’ was finished (which might take a couple days depending on our actual time at the end of each class) we’d discuss the ‘math’. Some of my favorite books:

Students loved the challenge of these last 5 minutes (sometimes it would be more). It was a very competitive yet non-threatening time where they could test their math skills or thinking skills, work together, and have fun with numbers and logic. That time was no longer wasted – it became a time students actually looked forward to and often requested.

As you are nearing the winter break, there is probably a bit more time to spare or a bit more time needed to keep students attention.  Use that time in an engaging way that allows for some critical thinking, collaboration and a game-like atmosphere that challenges students and keeps those last five minutes productive.

Math and The Electoral College

With the election looming, and yet another Presidential Debate this evening (anyone else dreading it?) and more polls than you can shake a stick at, it seems appropriate to think about the math behind the Electoral College. I admit to really not understanding this whole system – and I know I am not alone. With the rampant conspiracy theories about the November 8 election, and a ‘rigged election’ and cries to eliminate the Electoral College and go to a popular vote only, it had me diving into “what does the Electoral College mean, why do we vote this way, and is it fair?” I think this is a GREAT conversation and critical thinking activity to have with students, especially in classes like statistics where you can actually study and do ‘mock votes’ and see what the outcomes are with or without the Electoral College.

A quick summary of what the Electoral College is – and please note, I still am a little iffy about whether I truly get it. In 1787 the delegates of the Constitutional Congress made the decision to do this indirect way of voting for the President of the USA. It was a compromise between those who wanted a) individual citizens to vote for President (1 person, 1 vote, majority wins); b) letting State legislators choose the President; or c) letting congress choose the next President. The idea was to create a method where the best candidate was chosen. Individuals in a state vote for President – the winner in that state gets all the states electoral votes (though some split the electoral votes now), and the electors (who are elected by voters),  put in the final vote for President. The person who gets the majority of Electoral Votes (270 or more) wins. Still confused? How is this fair?  Bear with me….I am hoping I can figure that out myself!

If you look at the image above, which outlines the number of Electoral votes per state, you can see a huge difference – some states have an enormous number of Electoral Votes, and some very few. As you can see – size might matter (CA, TX, FL), but not always – VA is relatively small and yet has 13 Electoral Votes compared to say Montana, a larger state with only 3 Electoral Votes. So – how is the number of Electoral Votes determined? Hawaii gets 4 vs the very large state of Alaska only 3. So – it must have something to do with population numbers, which in fact is the case. The number of Electoral Votes is the number of state representatives in Congress (both Senate and House of Representatives), which are based on the population of the state. Every state will have at least 3 Electoral Votes (2 Senators, 1 Congressman). Obviously you now see why winning states like CA, TX, FL, PA, and NY are so crucial because of their large populations and large number of Electoral Votes.

I have been reading a lot and searching for good websites that might be helpful for teachers wanting to figure this out with their students. There are several sites that talk about the Electoral College and what it is – I didn’t find these too helpful from a teaching perspective, but they may be of interest to some of you from a historical, “why do we do this” perspective.

  1. Nice interactive map – http://www.270towin.com/
  2. Article about the ‘fair or unfair’ aspect of Electoral College and the funding – not sure it answers the questions but makes you think: https://blogs.scientificamerican.com/guest-blog/the-funky-math-of-the-electoral-college/
  3. This is a nice site with lots of historical perspective and answers to questions, like does my vote count? http://www.learnnc.org/lp/media/lessons/davidwalbert7232004-02/electoralcollege.html
  4. This article makes a case for the Electoral College system being fair: http://www.politico.com/story/2012/12/keep-electoral-college-for-fair-presidential-votes-084651

Here are some sites I found that would be helpful for doing some simulations and having interesting conversations with students. Many of these are interactive, with the ability to create election results (or simulated) to get a better understanding of how the Electoral College system works, and hopefully make a determination about whether it is fair or not.

  1. This was my favorite – be sure to check out the “Play Presidential Politics” link, as it has a simulation vote where you can create your own populations for states.  Would be great for students. http://www.sciencebuzz.org/topics/electoral-college-math
  2. Lots of information (some of which I used) in kid-friendly language: http://www.congressforkids.net/Elections_electoralcollege.htm
  3. Nice lesson here – some interaction/lesson plan info as well: http://www.scholastic.com/teachers/article/math-majority-rules
  4. Yummy Math – nice lesson here (using the picture above!) http://www.yummymath.com/2016/electoral-college-vs-the-popular-vote/
  5. From NCTM – a lesson on the “fairness” of the elections – Love Illuminations! https://illuminations.nctm.org/lesson.aspx?id=2825

So – is it fair or not fair? Does your vote count? I am not sure I can give you a definitive answer. It probably depends who you are, who you want to win, and where you live. But, in my readings looking at several charts that compared the ‘weights’ of individual votes toward the outcome (i.e. Does your vote count?), I think my personal opinion is yes, your vote does count, and yes, it is fair.

Notice Alaska, with a smaller population, has a much more weighted vote compared to CA. This may not seem fair – but, Alaska, a huge state with many diverse needs and interests but with a small population, deserves an equal representation in the government, which may not happen in a one-vote majority rule election, if we look at populations sizes of CA or NY, with their enormous populations. This is why the Electoral College was created in the first place – so every state gets a fair share of representation for their interests in the outcome, no matter their populations size, and those ‘states’ with larger populations don’t end up  deciding everything. NY’s interests are vastly different than Alaska’s, after all. A popular vote would be unfair because those larger states, who lean more one way or another, would control the outcome, leaving those states with fewer people, left out of the equation, and their interests not accounted for or lost in the process. My personal conclusion – I am actually for the Electoral College, after all my reading and my still foggy, but much better, understanding of the system.

One final note – look at the overall United States (in chart above) – the total population, the total Electoral votes, and the weight of each individual vote.  It’s 1.

So YES – your vote counts – get out and VOTE!  (And make it an educated vote, based on candidates proposed policies and plans – not based on emotion).

 

Multiple Entry Points and Rich Math Tasks

I was reading this article the other day about how a strength-based approach to learning math (and learning in general) redefines who is “smart” and allows all students to succeed. In her article, Katrina Schwartz has some quotes and reflections from former students who learned math using the complex instruction method, and who were all successful.  They talked about how “math class made them feel safe, heard and able to express their ideas without fear”.  Wow – how often do you hear something like that?!!

Complex instruction is based on the idea that learning is collaborative, where students are learning using rich tasks with multiple entry points and pathways, and each student has a role and accountability. This isimage15 not a post about complex instruction however. What I was thinking about while reading the article was in fact about the Common Core Standards for Mathematical Practice and how they support what the students were expressing in the article – that math class “was a process and it required other people. It wasn’t just you and your work and not talking.”

If you actually read the 8 mathematical practices, you will notice over and over again words like communicate, justify, analyze, plan, make sense, look for entry points, reason, ask questions, make viable arguments, apply.  The practices are all about communicating and talking and finding multiple entry ways to solve problems. And working and talking with others to get there. Like complex instruction, these problems should be rich, where in fact, there are multiple entry points and possible solution pathways. Where each students strengths can support the process and help build the understanding of others. Learning is collaborative, NOT an isolating experience that a worksheet or a lecture so often create.

The Common Core gets a bad rap because so many publishers and testing companies have standardized it – by providing ‘common core problems/strategies’ that are in fact limiting and narrowly focused so they can be graded easily. When I see parents and students and teachers complaining about “common core problems”, I get so angry because what I am actually seeing are ‘forced entry points’ – meaning, rather than allowing all students to approach a problem from their mathematical strength and understanding, they are forced to choose between 1, 2 maybe 3, ways to solve a problem, which may NOT be understandable methods for them.  Therefore, NOT Common Core (or Complex Instruction). As it says in the practices: “Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution”. It does not say mathematically proficient students are given specific entry points to solve a problem.

image16My hope is that with the changes in standardized testing on the horizon under the Every Student Succeeds Act, that math teachers and classrooms can truly begin to focus on students strengths and learning, not preparing for a test. To actually provide learning experiences focused on allowing students to work from their strengths. But it requires a willingness to have a noisy classroom with students talking and collaborating.  It requires  rich mathematical tasks, not standardized worksheets and drill and practice,  that truly provide multiple entry points. This in turn requires teachers who are willing to accept multiple solutions from students rather than the traditional one-way, algorithmic approach we tend to focus on. And it requires support for teachers – in resources, training, time, and expectations.

Read the article by Katrina Schwartz – it also has links to information about Complex Instruction and great feedback from San Francisco Unified School District who has made a concerted effort to teach mathematics this way. Read the Common Core Standards for Mathematical Practice. If you are not already doing so, try to incorporate some of these practices into your math instruction. It’s not what you teach, but HOW you teach, that has an impact on students.  Every student can learn math – it’s up to you to create a culture that helps them believe that.

More than Calculators – Teacher Support & Resources

I received a message the other day from a reader who commented on how much he liked the Prizm, but because 2016-05-13_12-52-22Casio didn’t have any resources to support the learning of the Prizm, he was a little reluctant to try it.  My first reaction was “What?!! We have a TON of resources!!”  My second reaction was to ask myself why might he think this? I was able to answer my own question when I searched for our resources – the issue being they are a bit hidden among all of Casio’s other products, (which, just so you know, is of course in the process of changing as we create a more user-friendly web-page).

In the meantime, I want you to see the great teacher/student resources we have! Let me share with you the resources we have that supports teachers (and students), from complete subject-specific or grade-specific resource books (i.e. complete lessons), so sample lessons and activities (free), to online course for Prizm (free) to webinars (free).  There are teacher-created resources and quick-start guides.  Casio WANTS teachers and students to use their calculators and get the help and support they need to use them appropriately.

  1. Free online activities and sample questions: http://www.casioeducation.com/educators/activities
    • These include grade-level activities and specific Casio Prizm-vs-TI 84 activities
    • Scrolling down the page you will find sports activities for use with five different calculators
    • Keep scrolling to our Quick Start Guides for 6 of our calculators (including Prizm)
    • Keep scrolling to Subject-specific Teacher Resource Guides and Calculator Tips
    • Scroll further to see all our grade-level and subject-level resource books that contain complete lessons
  2. If you look at our products page, under Software & Additional Products, you will be able to scroll through all our grade-specific/subject-specific resource books: http://www.casioeducation.com/products/Calculators_%26_Dictionaries/Software_%26_Additional_Products/ED-WKBK-PRECALC
  3. Here’s a short-link to our Casio Lesson Library (with teacher created activities): http://www.casioeducation.com/lesson_library
  4. Short-link to Guided tours for the Prizm: http://www.casioeducation.com/resource/prizm/features/index.html
  5. 2016-05-13_12-56-04If you are interested in the Prizm, we have a whole webpage dedicated to Prizm activities and support, which includes lessons, videos, and also has the OS updates. http://www.casioeducation.com/prizm 
  6. We have a free online course for the Prizm (self-paced).  If you complete the course, you get the Prizm (fx-CG) emulator software for free. http://www.casioeducation.com/educators/online_training
  7. Free webinars on many math topics (statistics, geometry, algebra, calculus, etc.)(you do have to register your email to view these, but they are free): http://www.casioeducation.com/educators/webinars
  8. Links to manuals for specific calculators: http://www.casioeducation.com/support/manuals
  9. And let’s not forget the videos showing you how-to’s and comparisons! https://www.youtube.com/user/CasioPrizm/videos?view=0&sort=dd&shelf_id=2  and http://www.casioeducation.com/resource/HTML/edu_videoPage.html

As you can see, we have a ton of support for teachers and students wanting to use and learn-to-use Casio calculators to support their instruction and/or math learning. We hope those of you out there excited to start working with Casio calculators start using these supports. We are educators here at Casio and want you to love the calculators as much as we do!!

Spring Is In The Air – The Sweet Smell of Testing….

Don’t you just love spring? The flowers blooming, trees bursting with new leaves, bees buzzing around, IMG_2650and the weather turning warmer.  Walking around town this morning looking at all the beautiful trees and flowers certainly reminded me how much I love the spring.  Then, as I walked past the local high school, I was reminded of what spring means to most students, (students who were probably staring out at the beautiful weather right that moment.).  Testing.  Spring doesn’t smell so sweet to them, I imagine.

I remember when I was teaching back in Virginia, where we test-prep-posterhad the Standards of Learning End-of-Course tests every April/May (the S.O.L.’s….appropriate acronym!)  (They still have these of course).  What I remember is how the whole month of April leading up to the tests was focused on test prep — review, review, practice test, practice test, pep rally to pump kids up, more review, etc.  By the time the actual tests rolled around, students were so tired of “practicing” that they probably didn’t even care about the tests. Then, those that had to take the AP tests as well still had those to look forward to.  As a teacher, I HATED this time of the year as much as the kids because it felt like learning was forced to stop so kids could “get ready for the test’.  I would much rather have kept on with teaching new and exciting things – applying the math by making bridges out of toothpicks or tetrahedron kites, using technology, etc.  I knew my students were ready because they’d been learning and applying all along – they didn’t need all this down-time for test prep. But ‘preparing for the test’ was a district/school/department mandate. I had no choice. The computer labs were taken over for testing, so no more Sketchpad. The days on the calendar had required test prep mandates and there were weekly department meetings to look at the practice test data and pick the review  materials for continued preparation.  The whole school was focused on getting kids excited about taking a test.  Students hated it.  Teachers hated it.  And we all forgot that it was spring. We were all too stressed about passing the test so that the school met AYP (Adequate Yearly Progress from No Child Left Behind) and we stressed about getting at least 70% of our students to pass the test and students to get at least 70% ON the tests, so we would get good evaluations (teachers) or graduate (students).  Spring was a time of anxiety, not beauty.

Hopefully, if not this year, by next year, all this will change. With the passage of the Every Student imagesSucceeds Act (ESSA) there may be a spring again. Yes, there will still be testing.  Assessment is important obviously, to determine where changes need to be made in instruction, to ensure students are learning and meeting standards, to ensure that teachers and schools are educating students.  But testing is going to change and it won’t be this punitive system (I hope) that NCLB created.  And hopefully, it won’t be a constant thing where months of a school year are taken up with test prep and test taking. That’s a good thing. School should be about learning, not just testing, which is what it often feels like, especially this time of year.

ESSA obviously is new and it will take time for changes to be implemented.  Though even as early as this year, there are states who have changed their testing or eliminated testing this year.  The ESSA (from 5 ways ESSA Impacts Standardized Testing, by Anne O’Brien):

  • Allows districts to use a locally determined, nationally recognized test like the ACT or SAT instead of the state test in high schools, which could have huge implications for classroom practice
  • Allows states to institute a cap limiting the amount of time that students spend taking tests, which could reduce that time (and the time educators spend administering them)
  • Funds states in auditing and streamlining assessment systems, eliminating unnecessary and duplicative assessments
  • Establishes a pilot program in up to seven states (or consortia of states) that allows for the complete revamping of their assessment system, meaning that it’s possible that summative state tests as we know them will be eliminated, replaced by competency-based assessments, performance-based assessments, interim assessments, or something else entirely
  • Allows for the use of computer-adaptive testing in state and local assessments (NCLB did not), a process that could allow for much more accurate data on student performance

IMG_2649I think one of my most favorite things about ESSA is that it requires states to use more than academic factors (i.e. standardized test scores) as indicators of accountability and school/student success. A test score is no longer the be-all and end-all, allowing education to focus on learning, not test prep and testing.

Maybe now both teachers and students can start enjoying spring again.

Power bills as sources of math questions.

I’ve been thinking a lot about graphs lately, and how in general, many people are deceived by graphs because they don’t understand numbers, scale, sampling size, etc.  In this very contentious political time, it seems many people are fooled by the statistics they “see” graphically.  In my last post, I quoted Dan Finkel’s line “when we are not comfortable with math, we don’t question the authority of numbers”, specifically referencing people’s willingness to believe statistics they see or hear because they don’t really understand where these numbers came from or what they represent.

We can help our students get a better sense of statistics and numbers by providing them as many opportunities to explore, in context, graphs and statistics and ask questions and make sense of these. That could mean exploring all the statistics and poll results currently happening with the presidential election.  Or looking at weather predictions. As I looked at my power bill yesterday, I realized how easy this type of access to real numbers can be, as I stared at the graphical representation of my gas and electric over the past 13 months. (There is also a numerical table showing daily use of kilowat hours (kWh) and 100 (C) cubic feet volume of gas (Ccf). There alone is a whole bunch of mathematical calculation/conversions/ratios).  What I love about my graphical representations is there is a 13 month trend – so I can see where my usage was last year at the same month, and then see how my usage has changed throughout the year.  Below are my December & January graphical representations for both gas and electric usage.

ELECTRIC:

December Electric

December Electric

January electric

January Electric

 

GAS:

December Gas

December Gas

January Gas

January Gas

 

Just from these graphs, there are a lot of assumptions that can be made, and questions that could be asked, that would then lead to more exploration.  For example, December electric from 2014 and 2015 is about the same, but January 2015 is significantly less than January 2016 – why is that? (hint: my children are home for break, so we use more electricity). Gas use in December of 2015 was much lower – was this because it was warmer in December? Are we having a warmer winter than last year? The gas bills seem to show that – but, we could then go look at the weather temperatures for the same time frames in the area I live and see if there is a correlation between temperature and gas usage (i.e. heat). Why is the electric so much more in the spring/summer months and gas is lower? There are so many questions, and, if we brought in the tables of daily usage, cost of kWh and Ccf (volume) we could be doing math calculations, comparing costs, etc. Maybe compare bills from last year to this year and see if the price in oil/gas has had an impact on the overall monthly charge. I like the idea of bringing in the weather and comparing to the electric/gas usage. You can get average weather for the area you live in pretty easily, but it would be even better for students to collect actual temperatures over time and make their own graphs and comparisons.

2016-02-26_12-00-35

Average Climate Chart

The point I am making here is that a simple thing like a power bill can be a powerful tool for visualizing math, doing math, making connections, and asking questions. Or try looking at some statistics from car sales or stocks or polls on the presidential election. It leads kids to ask interesting questions, explore mathematics they care about, and opens them to the real-world aspect of mathematics and how numbers can be used to inform, deceive, and help make decisions.  These types of explorations are interesting and help students become involved in the world around them as well and better prepared for the realities of things like gas bills! Anyway, just another suggestion on how to bring some context into your math instruction in a relatively easy way.