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Monthly Archives: March 2013

Why I Like Geology

If I could do it all over again, I’d be a geologist!

Earth science is fascinating to me. I like thinking about the Earth that used to be, the Earth that might be in the future.  I like looking closely at the rocks and imagining what kind of world created them, and thinking about how they’re currently dying and being destroyed to start the cycle over.  My daughter wanted to study plate tectonics for her science fair project, so I suggested we drive around and look for evidence of tectonic activity just outside town.  In northern Colorado, there are rich and interesting places to study geology and I thought it would be a shame for her to do an earth science project at a desk!  So we drove around and looked at rocks.

We found marine fossils embedded in the limestone near home.

Sea creatures

Sea creatures

We dug into the shale at a roadcut.

Uplifted shale

Uplifted shale and Dakota Sandstone

We ran our fingers over the conglomerate at a rock climbing area.  I marveled at the Morrison Formation under our feet, which has yielded a very rich trove of dinosaur fossils over the years.  Who knows what could be right under us!

Conglomerate. Once, there was a mountain. Pieces of it washed away and got cemented into a new rock, then that rock got uplifted and became.. a new mountain

Conglomerate. Once, there was a mountain. Pieces of it washed away and got cemented into a new rock, then that rock got uplifted and became.. a new mountain

We felt the gritty sandstone at base of the red cliffs of the Fountain Formation, like bookends on either side of a mountain.

IMG_1845

 

We visited Horsetooth Mountain Park and examined the ancient schist and pegmatite.

Schist

It’s all metamorphic and schist.

Pegmatite granite. Igneous

Pegmatite granite. Igneous rock

 

We downloaded a free geologic map from the USGS for the project.  What a wonderful resource!  My kid organized her rock information and made a presentation board, and of course I keep thinking and thinking and thinking about rocks.  It made me understand the reasons I like geology as much as I do.  As a “math person”, it appeals to me because it has logic-puzzle features.  I like looking at the evidence around me and reasoning out the history of the area.  As with all logic puzzles, there are a few simple rules and likely only one correct solution.

– Sedimentary rocks are created in more-or-less flat layers.  Newer layers are always created over the top of older layers.
– Igneous rocks can intrude into other rocks.  If an igneous formation cuts through another rock formation, it’s newer than the surrounding rock.
– Faults can cut through other rocks.  A fault is newer than the rock it cuts through. Rock that overlays and covers a fault is newer than the fault itself.  Uplift happens after the sedimentary rock has been deposited.

I know less about the formation of metamorphic rocks and so my rules for them are incomplete.  But using what I know, I can look at the map and at rocks around me and build a geologic history of the area.  The rocks had to have been created in a certain order, and so a story starts to weave itself.  First there was rock, and then metamorphism, and then igneous intrusions, and then came the sandstone, then some faulting, then the shale and the dinosaurs, then more sandstone and then more dinosaurs, and then there must have been a time of erosion, and then more faulting and so on and so on.  I like to look at the map to see if I came to the same conclusion as the geologists who made it.

As much as I want to help my kid learn about the scientific method, all I keep thinking about is what a cool puzzle it is to piece together the history of northern Colorado!  Is that science, or more mathematics?

 

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Posted by on March 26, 2013 in Outside the Classroom

 

Cooperative Learning – a good lesson for me

I got a reminder this week on the importance of cooperative learning!  I’m a little embarrassed that I needed the reminder, but I think during busy times, we tend to forget about what’s important.

The students have been learning about circles. (Anticipating Pi Day!! Yahoo!)  We’ve watched video tutorials on circles, done whole-class instruction, worked drills online and on paper.  I wanted them to start synthesizing what they’ve learned by combining it with their problem-solving skills and their previous knowledge of area and perimeter.  So, one day, instead of our usual warm-up problems, I distributed this problem set and told the kids to work them solo.

circle_problems1

 

I gave the students a few minutes of struggle time and then told them to share out their answers.

The results were so disheartening!  Students didn’t know whether to calculate area or circumference – or do neither.  Very few students made any progress with the pizza problem.  The most common mistake by far was to just divide the price by the diameter.  We JUST finished studying unit prices, too! They had learned about area in the past, and about perimeter, and I could not understand why this was giving them so much trouble.  The cognitive effort was low and engagement was low as well – so I could also not understand if it was a difficult task or if the problem was more one of effort and engagement.  I made a note to come back to these topics.

I did not do any additional teaching between that set of problems and today.  We reviewed formulas, but did not tackle the idea of problem solving in whole-class instruction.  Today, I decided the kids have the skills necessary to solve the problems. They just needed to explore the ideas and discuss them with a group to sort out their misunderstandings.  I created a new problem set:

circle_problems3

 

I realize the picture is hard to see, but they’re basically circle problem-solving questions along the same vein as the pizza and basketball problems.  I don’t tell them whether to use circumference or area or both or neither – the students need to analyze the problems and develop a strategy.  Exactly the same skill set.  However, I set it up differently this time.  I did not give the kids a few minutes of solo work time followed by going over answers.  I said:

As a group, you will need to analyze these problems and figure out how to solve them.  By now, you know my expectations for group work.
– Select a leader.  This person will read the questions and make sure everyone is doing the same problem together.
– Give everyone a chance to contribute, and everyone must also have a chance to listen.
– Thinking out loud while you’re working will help you solve the problems successfully.
– Stay on the same problem at the same time.

The difference was truly amazing, and it reinforced that my students DID have the necessary skills to solve these problems, and they COULD synthesize ideas – but they had to discuss their ideas and explore them together.  Our group work isn’t perfect, and I know many teachers do a much nicer job at coordinating cooperative learning than I do.  But I looked around my noisy, busy classroom and there was great math going on.  They were engaged in the task and vigorously debating the solutions.  They were excited to share their answers and give feedback to their peers.

Group work didn’t always look like this.  Early in the year, the focus was much more on how to behave properly in a group setting and not as much on the math.  It took lots of practice for the students to settle into it!  But now, we’re a little more of a community and the kids have expectations of each other.  They know what good group work looks and feels like.  They have come a long way.
I needed that reminder – that even during busy times, when you don’t think you have the time or energy for the messiness of cooperative learning, it’s a key ingredient for anyone to really do any complex thinking.  I feel my students gave me a great gift by reminding me of what they are capable of!

 

 

 
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Posted by on March 12, 2013 in Uncategorized

 

Probability Pi Day Carnival, Part II!

Here’s how the Pi Day preparations are going and what the students are up to.  There is some great math going on, and every year I enjoy this project more and more.  I always finish the unit wondering why I don’t do more project-based learning.

First:  Students need to create a game, and write the rules for it.  They have to determine how much you pay to play, and include how much you win for various levels of prizes.  The math has to contain multiple probabilities or multiple events to get an advanced grade.  This group of students has a game where you pick a card, which has a fraction on it from 1/5 to 4/5.  You turn around, and they put pigs under the buckets such that the fraction represents your probability of revealing a pig.  When you choose a bucket, you win a prize if you find a pig.

Sort of a Monty Hall idea?

Sort of a Monty Hall idea?

Second: Students need to calculate the theoretical probability of winning.  They need to show how they arrived at the probability.

This group used a counting tree to determine the probability of drawing two matching puzzle pieces.

This group used a counting tree to determine the probability of drawing two matching puzzle pieces.

This student uses Area = pi x r^2 to figure out the probability of throwing a ball through a precisely measured circular hole.

This student uses Area = pi x r^2 to figure out the probability of throwing a ball through a precisely measured circular hole.

Third: Students have to test their game 100 times to determine the experimental probability, and discuss differences between experimental and theoretical probability.  Games of skill often have a big difference between experimental and theoretical, while pure chance games are very close!

A student intern tries to put these 5 jars of candy in the right order, blindfolded.

A student intern tries to put these 5 jars of candy in the right order, blindfolded.

 

These students roll marbles onto their target area.

These students roll marbles onto their target area.

Fourth: Students have to make predictions based on their probabilities, to help the carnival organizers determine how many prizes they’ll need to buy – and to make sure their project will make a profit!

These students say the buckets will be full of prizes for their duck game. How full though?

These students say the buckets will be full of prizes for their duck game. How full though?

 

Lastly, the students make a presentation pitching their game to the carnival committee, and the committee determines which games make the cut.  We pick about a third of the games to represent the school in the big Pi Day carnival after school.  The rest of the games will be played in the class mini-carnival on the day before Spring Break.

This young man couldn't decide on a name for this spinner game, but thought "The Wheel of Awesomeness" would help in his sales pitch.

This young man couldn’t decide on a name for this spinner game, but thought “The Wheel of Awesomeness” would help in his sales pitch.

These students collaborate on their presentation using Google Docs.  Their game is called "Flash Dice".

These students collaborate on their presentation using Google Docs. Their game is called “Flash Dice”.

 

On March 14, after school, we reserve the gym.  We set up a table for each group and allow them to come set up their project.  We sell tickets for ten cents each, and provide each group with some tickets and a small bag of candy to give away.  If tickets are given as prizes, they can be entered in a big raffle drawing.  We also have food, drinks, and a silent auction.  It ends up being one of the biggest events of the year, and it’s a celebration of math!

 

Photos of the big day coming soon.  I will also post a grading rubric for the projects!

 

 

 

 

 

 

 
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Posted by on March 7, 2013 in Uncategorized

 

Probability Pi Day Carnival

It’s that time of year again!  A few years ago, one of my colleagues finished a probability unit by having a mini-carnival with student-created games.  The next year, the entire seventh-grade team took part, and now, the mini-carnival has turned into the capstone math event of the year – the Probability Pi Day Carnival.  Hundreds of students attend, and it is a terrific celebration of learning and math.

Students create their own carnival game, calculate the probability of winning, do an experiment, make some predictions, and pitch their game to the carnival committee.

I described the project to students by creating a video describing the requirements and going over an exemplar.

Youtube screen capture

Youtube screen capture

 

The kids came up with some clever and creative games!  They’re currently working hard on calculating the probability of winning, both theoretically and experimentally.  Then they will need to predict how many prizes they need to give out, so the carnival committee knows what supplies are needed.  I’ll post more about the games they’re creating tomorrow.

Their final project will be a model of their game, and a media presentation describing their game and the math behind it.  It can be a document, presentation, video, or anything they wish.

The best part is the school carnival, which is on Pi Day.  It’s awesome to see hundreds of kids in the building, celebrating their learning in math.  Kids talk about their projects for years to come. The community supports us by donating prizes to give away, and we sell circular treats such as pizza, fruit, and cookies.

I will update more as we get closer!

 

 
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Posted by on March 6, 2013 in School and Unit Planning