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Posts Tagged ‘Student Engagement’

I take no credit for this idea at all. I was in a classroom this morning, and the teacher had the students play a game of Radical SNAP. The students were totally engaged, and were enthusiastically converting between mixed and entire radicals. It’s pretty simple to set up.

Materials: You need one deck of cards with the 10, J, Q and K removed for each pair of students, and one giant square root symbol per pair of students. This one should do the trick: Giant Root

Pair off the students in your class. Each pair gets a deck of cards, and should remove the 10, J, Q and K. Shuffle the remaining cards, and deal them so that each person has half the deck, face down.

Mixed to Entire

The students flip over their top cards. The student on the left puts his in front of the radical, and the student on the right puts hers under the radical. The first student to correctly convert the mixed radical to an entire radical wins the round.

Photo 2-12-2014, 11 01 43 AM

Entire to Mixed

The students flip over their top cards, and put them both under the radical. The first student to correctly simplify the radical or to identify that it can’t be simplified wins the round.

Photo 2-12-2014, 11 11 48 AM

 

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@dandersod posted the following video on his blog last week.

He asked, of course, What Can You Do With This?

I decided that there was a lot I could do with it, so I worked on some editing of the video, and then I rolled it out with a group of teachers this morning to see where it would go.

Before I describe the lesson, I should point out that my first edit of the video involved crossing out some of the measurements the original video contained, as well as beeping out the commentary that mentioned the measurements.  I was limited by my video editing skill, and the software I was using. It ended up being awkward and kind of annoying, so I re-did it simply by deleting the parts I had originally wanted obscured.  The new video was much cleaner, and it had the extra benefit of not being so obvious about what I wanted students to explore.  With the beeps and blocked out numbers visible in the first edit, it was painfully evident what I wanted people to find.  The second edit allows for many more directions to be taken in the exploration, and it’s not even obvious that I have deleted anything.

Here was my lesson plan.

  1. Provide each group a ruler and a 60 g bag of gummy bears.
  2. Play the question video.
  3. Ask the students what they wonder about after seeing the video.  In this edit, they will wonder about a whole bunch of things.  I’m hoping they get to, “How many small gummy bears are equivalent to the giant bear, and what are the  dimensions of the giant gummy bear?”
  4. Elicit guesses, lower bounds, and upper bounds of reasonable answers.
  5. Ask them if they need any clarification or information that might help
  6. Turn them loose.
  7. Work the room.  Help those who are struggling.  Provide extensions for those who hammered through it.
  8. Have students share their answers.  They will be all over the place here.  Those that work with the calorie count will be closest to the “right answer”.  Those that worked with the mass will be a bit farther out.
  9. Play the answer video.
  10. Discuss discrepancies.  Is it measurement error?  Problems with the calculations?  False advertising?
  11. Eat the gummy bears.

The lesson is fun, engaging, and has great curricular fit to Alberta’s Math 20-2 course in the measurement and proportional reasoning units.

At step #3 above, some members of the group I was working with really wanted to go a different direction.  Their suggestions became cool extensions for those that got done quickly.

  1. How tall is the man in the video, who is the same height as the gummy bear from 30 feet away?
  2. How many times would you have to walk around the school to burn off the giant gummy bear?

Enjoy

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When I was in high school, I had a teacher who used something other than boring old “Name: __________” at the top of his tests.  He’d put things like, “Hello, my name is: _______” or “_____________ is going to ace this test.”

When I started teaching, I did the same thing.  The kids really liked it, and any time it left room for creativity, they did some neat stuff.  Over the years, I acquired a pretty long list of them.  Whenever I created a new test or handout, I would open up the document with all of them in it, and pick one.  Sometimes I asked students to write their own. There is nothing pedagogically brilliant about this.  It just amused me.

Here’s the document.

 

 

 

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Thanks to this post on Dan Meyer’s blog, and an ensuing conversation between Dan and Curmudgeon, I was pointed to an article that I think would make a pretty compelling problem in Math 10C or Math 10-3 measurement.

The article describes a 17 year old driver who was given a $190 ticket for going 62 miles an hour in a 45 mile an hour zone. His parents, however, had installed a GPS system in his car to track his speed and driving habits, and they claim the GPS proves their son was only going 45 miles an hour at the time the ticket was issued. It appears to have taken two years of legal wrangling, before the ticket was finally upheld, and he had to pay the fine.  I wouldn’t tell the students that yet, though.

Here’s a link to the article: Speeding Teenager

Lesson Plan

1.  Present the problem.

Give the students the following excerpt from the article:

Shaun Malone was 17 when a Petaluma police officer pulled him over on Lakeville Highway the morning of July 4, 2007, and wrote him a ticket for going 62 mph in a 45-mph zone.

Malone, now 19, was ordered to pay a $190 fine, but his parents appealed the decision, saying data from a GPS system they installed in his car to monitor his driving proved he was not speeding.

What ensued was the longest court battle over a speeding ticket in county history.

In her five-page ruling, Commissioner Carla Bonilla noted the accuracy of the GPS system was not challenged by either side in the dispute, but rather they had different interpretations of the data.

All GPS systems in vehicles calculate speed and location, but the tracking device Malone’s parents installed in his 2000 Toyota Celica GTS downloaded the information to their computer. The system sent out a data signal every 30 seconds that reported the car’s speed, location and direction. If Malone ever hit 70 mph, his parents received an e-mail alert.

Malone was on his way to Infineon Raceway when Officer Steve Johnson said he clocked Malone’s car going 62 mph about 400 feet west of South McDowell Boulevard.

The teen’s GPS, however, pegged the car at 45 mph in virtually the same location.

At issue was the distance from the stoplight at Freitas Road — site of the first GPS “ping” that showed Malone stopped — to the second ping 30 seconds later, when he was going 45 mph. Bonilla said the distance between those two points was 1,980 feet.

2.  Ask the students to discuss the article.  In the end they will come to the question we want explored.  Was young Shaun guilty of speeding?

3.  Let them answer the question.  Have them prepare a defense for Shaun, or an argument for the prosecution.

4.  Show them the Commissioner’s conclusion, based on mathematics.

Bonilla said the distance between those two points was 1,980 feet, and the GPS data confirmed the prosecution’s contention that Malone had to have exceeded the speed limit.

“The mathematics confirm this,” she wrote.

Teacher Resource

A possible solution

An extension, eventually.

I have been attempting to contact the person mentioned in this local article, but so far he hasn’t responded to me.  Similar mathematics could prove he wasn’t driving as excessively fast as the red light camera claimed, but I would need to get a copy of his ticket to show that.

Red Light Camera

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October’s issue of the NCTM Mathematics Teacher magazine included an excerpt from an interesting article in their Media Clips section.  They used a Forbes article that dealt with tween earnings, and the portion they included is:

Hollywood’s 10 top-earning tweens collectively pulled down $107 million between June 1, 2007 and June 1, 2008.   According to Alloy Media and Marketing, it’s a rabid and often indulgent fan base: America’s 20 million kids aged 8 to 12 spend $51 billion of their own money annually and influence $150 billion more in spending by their doting parents. Tied for the top spot: Hannah Montana star Miley Cyrus and Harry Potter lead Daniel Radcliffe. The young talents each banked a cool $25 million in the last year.

I love this article for the questions it could elicit.  The problem with the Mathematics Teacher Magazine treatment of this is that it follows the article with 8 questions we are supposed to ask kids.  Teachers might see this, and defer to the questions provided, thereby missing a great opportunity.  I’d much rather show students the article, and have the kids decide what would be interesting to explore further.  There are lots of potential rate and ratio questions that could come from student exploration here.

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This is an activity a group of teachers I was working with fleshed out based on ideas on Mark Wahl’s website, and here.  This activity is appropriate for Math 10-3 (Measurement) and Math 10C (Measurement or Real Numbers).

Statues of human bodies that the ancient Greeks considered most “perfect” embodied many Golden Ratios. It turns out that the “perfect” human face also contains many Golden Ratios.  This task allows students to take measurements of an ancient statue, and check whether these measurements approach the Golden Ratio.  Then two celebrity photos are provided and the students check how beautiful the celebrities are based on these calculations.  Finally, students can use pictures of their own faces and GeoGebra to check how they match the Golden Ratio.

Part 1 Students perform the measurements on a photo of a statue, and calculate the ratios requested.  These measurements could be made by printing the picture and physically measuring, or by inserting the picture into GeoGebra and using the software to measure.

Part 2 Students complete the same measurements, either on a provided celebrity photo, or one of their own choice.

Part 3 Students then take their own picture and insert it into GeoGebra.  They can then measure, and check how closely the ratios in their own faces match the Golden Ratio.  Students who are not comfortable using their own pictures can choose other celebrities from the internet. (I didn’t teach Cameron Diaz, but her face is much more likely to be beautiful using this test than my own…)

The complete student package in Word format is available for download here.

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I saw this episode of Seinfeld a couple of days ago.  Now that my WCYDWT radar is finely tuned, I realized that it would be a good clip to show in a Math 10-3 class in the unit on rate and ratios.  I know it’s a little dated (who would use a Wizard now?), but it’s still one of my favorite shows.  Click on Morty to play the clip.

The one question kids need to ask will be apparent to them, but the math will be tricky for Math 10-3 students.  In the end, it’s still not a particularly compelling problem, but maybe this is a better way of presenting it to students.

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This morning, as I was making my toast and about to put peanut butter on it, I was reminded of something I did early in my career in a Math 31 (Calculus) class.  It was at least 15 years ago, and way before we had digital cameras or Dan Meyer, but I think it definitely qualified as a WCYDWT.

One morning in the early 1990s, I was having peanut butter and toast, and had gotten near the bottom of the jar.  While scooping peanut butter out, I got it all over the handle of the knife, my hand, and then of course, my pants.

It occurred to me that the jar really was taller and narrower than it should be, and in a rare moment where everything came together for me, I realized that the shape of the jar was probably significant and we just happened to be working on Maximization and Minimization problems in Math 31.  Since digital cameras hadn’t been invented yet, the only multi-media artifact I could take into my classroom was the jar itself.

So I took my jar of peanut butter into class, slammed it down on the table in front of the class, ranted for about 5 minutes about how mad I was at Mr. Kraft for getting peanut butter on my hand and pants, and then told the class that we wouldn’t be doing Calculus that day, because I had to write a complaint letter to Mr. Kraft.  I sat down at my desk, and pretended to write, and hoped.  It took a couple minutes, but then it happened.  One student said something like, “Mr. Scammell, there must be a reason it is made in that shape.”  Another jumped in with, “It’s probably the shape that uses the least material but still has 1 kg of peanut butter in it.”  Then they argued for a bit, and decided on their own to figure it all out.  They measured, calculated, argued some more, and then told me to write my letter, because you could hold 1 kg of peanut butter in a container that was wider and shorter so my hand wouldn’t get peanut butter on it.

Again, I pretended to write while I waited and hoped.  And then they extended.  One kid stopped the whole thing, and said that there must be a reason it was the shape it was.  He observed that the lid was thicker than the other plastic, and therefore must cost more.  They re-ran their calculations based on an estimate that the lid cost twice as much as the other plastic, and then concluded that the shape was logical if we assumed the lid cost more.  It’s too bad that this was all done years before the internet hit our schools, or perhaps we could have quickly researched further to find out costs and contact numbers for Kraft.

I tried the Peanut Butter Rant several more times over the years, with varying degrees of success.  Some classes got right to the one important question, while others took some prompting.

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After attending a session on our revised curriculum by Dr. Peter Liljedahl, several teachers have told me that they have been inspired to spend the first week of Math 10 Combined on  establishing collaborative and problem solving practices in their classrooms.  Since we will be teaching math in a different manner than teachers and students are used to, it is important to create a safe environment in which students can explore and construct meaning through rich problems.

The idea that we will spend the first week on processes and exploration, rather than on checking off the first few curricular outcomes is frightening to some teachers.  Several have asked me what types of problems they should give students during that first week.  Below are three of my favorites.  They have loose curricular fit, but all allow for rich discussion, debate, exploration and invite multiple methods of solution.  The idea is to throw these out to students before any teaching has happened, and allow them to use any method they can to solve them.  Feel free to give me feedback, and share your own favorite problems.

Problem 1 Fred’s aunt is twice as old as Fred was when she was as old as Fred is now.  How old is Fred and how old is his aunt?

Problem 2 Three businessmen check into a hotel (in the olden days, when hotels were cheaper).  The desk clerk charged them $30, so they each paid $10.  Later on, the desk clerk realized he had made a mistake, and the room charge should only have been $25.  The desk clerk sent a bellboy up to the room with $5 change.  Unsure how to divide the $5 evenly among the three men, the bellboy gave each man $1 back, and kept $2 for himself.  Now each man has paid $9, for a total of $27.  The bellboy has $2 which brings the total money up to $29.  But the men originally paid $30.  Where is the missing dollar?

Problem 3 – The Jail Cell Problem In a prison, there are 100 cells numbered 1 to 100.  On day 1, a guard turns the key in all 100, unlocking them.  On day 2, the guard turns the key in all the even-numbered cells, thereby locking them.  On day 3, the guard turns the key in all the cells numbered with multiples of 3, thereby altering their state.  For example, if the cell was unlocked, he locks it.  If it was locked, he unlocks it.  On day 4, he turns the key in all the cells that are numbered with multiples of 4, thereby changing their state.  He continues this process for 100 days, at which time all the prisoners in unlocked cells are set free.  Which prisoners are set free?

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Here’s a WCYDWT for Alberta’s Math 10-3 on Ratios and Rates.

This fish, a 60 pound sturgeon, was recently caught and released in a small self-contained pond on a golf course near the Red Deer River.  When local biologists heard about the catch, they decided to investigate.  They surmise he (or she) came into the pond when the river flooded five years ago, and then spent the next five years feeding happily on the stocked trout.  Since sturgeon are endangered, it was important to return him (or her) to the river, which they were able to do.

This story reminded me that about ten years ago, I was fortunate enough to be present when a team of biologists surveyed a cutthroat trout population on a remote mountain stream.  Biologists typically use a method called electroshock fishing to stun fish so they can be tagged and released. They had a boat with a generator on it and a long metal prod which they poked around in the water.  When the current got near enough to a fish, it would be momentarily stunned, and float to the surface.  The biologists then weighed, measured and tagged the fish before returning it to the stream.  Any fish that had been previously tagged had its number recorded and it was again weighed and measured.  It was a humbling experience to see that there were actually abundant numbers of fish in that stream, because I had been unable to catch any earlier that day with my fly rod, but I digress.

I have used the story of watching the biologists electroshock fish several times in my classes as a ratio problem and asked students determine the population of fish in that stream.  Sometimes I gave my students the number of fish tagged on the first day, and then the number of tagged fish caught on a second run of the same stretch of river later on.  Other times (and probably a better problem), I had my students design an experiment to predict the population of fish before providing them the actual numbers.

Red Deer Advocate story about the fisherman who first caught the fish

Red Deer Advocate story about the biologists capturing and releasing the fish back to the river

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