Repurposed Bottle Cap Fractions

When we were testing in our tech room the other day, I noticed a bucket of bottle caps.  I asked the instructional technologist about them and she said that she enters the codes from them and then has just been saving them because she felt bad throwing them away. I asked if I could have them and she said sure!

I did a google search on ways to use them for math games and found a sort with decimals, percents, and fractions.  I was talking to one of our 4th grade teachers about modifying it for her class and we decided on equivalent fractions.  When I started making them, I looked up the standards to make sure I set it up with the correct fraction ranges and I found that many of the other NF standards could be made into games for practice using bottle caps too!  I got distracted and pumped out 4 different tasks in about 30 minutes.  I wrote the standard on the front of the Solo cups she gave me to store them and I took pictures of the games for task cards by putting 4 images on a piece of cardstock and cutting them apart.  They fit really well in the cups.  I am going to ask teachers to start saving the mini Pringles containers for the future!

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The funny part is, I hadn’t even made the original game we discussed yet!

Later in the day, our Kindergarten teachers used them for making ordering number games and missing number games.  Our 2nd grade teachers used them for repeated addition through skip counting.

I know this idea has been around for a long time…but we were excited to re-purpose these caps into useful tools for individual practice!

I’ll try to post more pics as we create them.  Please share your ideas!

Are You Educated? Or Are You a Learner?

I’ve been really reflecting on the state of our educational system lately.  In part because of the big changes that have been happening in my district.  Changes that involve the fostering of 21st Century Skills, Problem-Based Learning, and the integration of technology.  It has led me down some really philosophical paths in my spare time and caused me to evaluate my personal teaching philosophy more than once.

Sometimes I think the phrase “educated” gets used interchangeably with the the word learner, when in fact, the words mean very different things.

To be educated implies that someone has undergone a formal education program.  They have sat through the classes, done the work (or not), and passed the final exam (or not). They have been taught at and they have taken in information.

Being educated seems to imply that there is nothing left to learn.  That since the person has participated in a formal educational program, they are done.  They get a stamped diploma and they can go out into the world and be successful. (Is it bad that I get a mental image of prep school jackets and golf polos?)

I would argue that being a learner is a much more fluid thing, a constantly evolving journey that continues indefinitely.

Being a learner is being engaged in the process of education; either formal or otherwise. People are learners because they have a need to know.  They need to know because they are interested in the topic, or they need to know to get a job done or a problem solved.  That does not mean that what they are learning has to be a favorite subject.  It just means they have a reason for learning it.

These situations call for ingenuity in finding information.  It may take the form of an instruction manual, a YouTube video, a phone call or video conference with a colleague or friend or family member.  Sometimes it might start with a Google search and end by falling down the rabbit hole into the world of blogs and help centers.  It might be researching scholarly articles or scientific journals, calling a tech call center or doing an image search.  Learners know how to find information not because they are smarter, but because they never give up.  They NEED to know.

I’ve heard the term “ungoogle-able questions” pop up a lot lately in education and I understand from where this stems.  However, I don’t agree that we should always be looking for “ungoogle-able” questions.  Most problems we face in daily life are google-able…and that is a great thing!  I also don’t think we should discourage students from using google (or calculators…but that is a story for another time) as a resource when solving problems.

What we need to be doing is finding a way to connect with students so that they have a need to know about whatever they are studying so that they are actively engaged in their education.  So that hopefully, we have transformed them into learners; not educated people.

We also must ditch the idea that all students are university bound.  Our world is changing yet we are still teaching students as if university is the finish line.  Many very successful people I know never attended college.  Some are entrepreneurs, some self-taught, some are builders or makers or tech gurus.  Universities cannot keep up with the rate at which new career fields are being invented.  We must teach students to be thinkers and doers, but most importantly; learners.

Flipping Review and Anchor Videos

One of our 5th grade teachers was talking to me the other day about how she had about a week to review before our state standardized test.  We have been talking about and trying to iron out the details to start flipping our math classrooms in 4-5 since we got our devices in September.  To me, this sounded like the perfect opportunity!

A Kindergarten teacher I work with recently told me she has been using a website called Blendspace with her students to better organize her PBL units.  I really liked the visual layout of the program and have been milling around in my head what application it might have for math.

I decided this was definitely one!  I played with a couple of possibilities and ended up deciding on creating a Blendspace lesson per chapter in the Math textbook we use to organize anchor video lessons for students to use for review of concepts they aren’t firm on, but we could also very easily use next year when we start fully implementing flipped classrooms.

The coolest feature I found was the collaboration button under the share option.  I can enter in the email addresses of all of the teachers that teach that grade-level and they will have instant access to the videos to embed in their own Canvas pages, but will also be able to add videos of their own.

I mentioned to this to my Math Coach colleagues today at coaches meeting and we decided this would be a great way to collaborate on lessons we or our teachers create so we aren’t re-creating the wheel each time we want to flip a lesson.

Each of my teachers share their Canvas page with me, so I created a page that would be very easy to navigate for students and embedded the Blendspace lessons in each page that is linked to the main anchor video page.

I inserted the Anchor Video link on her Math
Workshop page and it was ready to go!

I can now share these pages to the Canvas Commons and import them into other 5th grade classes very easily.  Since the Blendspace lessons are embedded, they will automatically update each time we add a lesson.

Now on to 4th grade!

Misconceptions in Measurement

I tried out the Gatorade is Thirst Aid task with five classrooms this past week. Three 4th grades (2 were combined) and two 5th grades.

I knew there would be misconceptions about measurement, but the information we gained was invaluable in really pinpointing where students were struggling with conversion.  It was pretty interesting to see that it differed at each grade-level.  Probably because they both just finished units on Measurement and were learning slightly different standards.

Interestingly enough, our 4th grade students had a better grip on how many ounces per cup and the fact that we needed to multiply or divide to find the answer.  They also had a better grip on how to use the remainder.  Many started by writing in cups and ounces and then when asked if there was another way to write it, came up with the mixed number of cups.

Our 5th grade students had the misconception that there were 16 ounces in a cup.  They were no doubt thinking ounces in a pound, but it was interesting that many of the students had this same thought.  What I have noticed with this group of students is that they often try to over-complicate the process when solving 3 act tasks.  They think there is a trick in there somewhere which leads me to believe that they don’t have a firm conceptual basis of how to work with numbers and operations.

I noticed two misconceptions that really stood out to me.  One student wrote his answer as 3.4 cups because there were 3 cups with 4 ounces remaining.  He did not see the remainder as a part of the composite unit 8, but instead wrote it as four tenths in decimal form.  Does this student have a firm understanding of decimal place value?

The other misconception that I thought was really interesting was that the solution could be written as 3/5 cups in fraction from because the decimal notation was 3.5.  This one really got me thinking about how to integrate fractions and decimals more thoroughly as related concepts.

And the part that I love: “What’s the Math?”

Gumball Activity

Today, with those two 5th grade classes, we did the gumball activity I mentioned in a previous post and it was really surprising to see that many of the students did not have firm grip on 36″ in a yard” or “100 cm in a meter.”  They struggled less with visualizing a square meter than the last class, but instead had a difficult time determining how many inches were in a yard, and how to tell how long a meter was.  I did a lot of questioning with these groups like, “how many inches are in a foot?   How many feet in a yard?” and “what do you know about metric measurements?  Why are they easier to work with?  How could you use that to help you?”  A few students were able to tell me that they are in tens, but many then decided that 10 cm was a meter.  I showed them the size of 10 cm and asked, “does that make sense?”  They agreed it didn’t and then were able to tell me it would be 100.  They were pleasantly surprised when they saw that the measurement tape they were using was exactly 100 cm long!

One of the most surprising things I noticed was that many students could not agree on an approach to the question, “how many gumballs across is the sidewalk?”  I saw measuring tapes laid across the sidewalk, I saw gumball lining the edges and I had students asking me how to solve this one.  I assumed (yes I know) that measuring with non-standard units would be the easy one for them, but they were trying to find some way to measure the gumballs and count and couldn’t come up with a solution.  When I asked them to reread the question, I asked, “where would you start?”  They were able to say, “counting the gumballs.” I then asked, “do you need a measurement tool for that?” That’s when it hit home.

We asked students several clarifying questions after we completed the activity.  When we asked students how many centimeters in a meter, they were able to tell us.  When I asked “how do you know?” A student said, “because I saw it on the stick when I was measuring.”

This just firmed up the hypothesis we had that measurement is best taught in context.  The teachers and I discussed how we might change our measurement lessons next year to allow them to have more experiences measuring and converting with objects.

I asked a student, “why do you think we did this activity today?”  I was saddened when the reply was, “because it might be on the MAP test.”

I knew it was time to interject and bring in some examples of when and where they might see this in their daily lives.  I said, “yep, it might be on the MAP test, but let me tell you why I care about what we did today.  I am getting ready to re-seed my lawn and seed bags come by how many square yards the bag of seed will cover.  If I didn’t know how big a square yard was or wasn’t able to calculate about how many square yards in my lawn, I might buy too much seed or not enough.  Those bags are heavy and I only want to buy what I need.  Here is another example: I recently repainted my son’s room.  Paint comes in gallons that tell me how many square feet the paint will cover.  Does anyone know how I would figure that out?”

Student: “that’s area.”

Me: “You’re right, and how would I find the area of the wall?”

Another Student: “length times width.”

Me: “Yep, so how would I find the area of the wall?”

Another student: “The same way.  Measure the length and width of the wall.”

Me: “And then what?”

Student: “multiply it.”

And yes, I did tell them that I don’t want them to know this because it’s gonna be on the MAP test, I want them to know because it will be important to them when they own their own home.

What I gained from this activity is the fact that when planning projects such as this, it is so very important to include many types of question sets that span the grade-levels especially those leading up to the current.  Many times, we as teachers assume that students have a firm grip on a concept because it was taught many grades before, but we really have no way to gauge their experiences before they enter our classroom.

Assume nothing.