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# QR Code Scavenger Hunt

Test review days.  You can’t live with them, you can’t live without them.

In an effort to make a recent geometry test review day a little more interesting, I decided to try an idea I had heard from another teacher:  making a QR code scavenger hunt.  I was really pleased with the way it went.  Here is what I did:

1.  I created a set of 10 geometry problems and made each one a separate Google drawing (most of them had diagrams).

2.  I used a free online QR code generator to generate a QR code for each question.  I printed out these QR codes and posted them in semi-sneaky locations around the school library.

3.  I paired up my class and created a Google form that

a) sent each pair to a different starting question

b) for each question, told the student where to look for the QR code

c) once they found the QR code, they scanned it and got the question.  Then, they had to input their answer into the Google form.  If they got it right, it told them where to look for the next code.  If they got it wrong, it told them to try again until they got it right.  The questions looped around until each pair had answered every question.

Things that I liked

1) It got the class up and moving.  I read an article a while back about how students need to move more during class, and I’ve been trying to think of ways to make that happen.

2. It fostered good team work.  One student was responsible for managing the form, the other for managing the QR scanner, and I saw a lot of conversations about answering the questions.

3. It left room for surprises.  I put one QR code on the inside of a wide window sill, and when my students started the scavenger hunt, a girl had sat down in the window to read with her back to QR code.  One pair found it eventually and tipped the rest off, but it definitely added a little twist to the morning!

I would definitely do that again.

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# And you can’t beat the colors!

Margaret’s love for Desmos is fully endorsed by the other half of this blog!

If you aren’t convinced, here’s some additional classroom action:

Yesterday in pre-calc, my students did an investigation about power functions.  They graphed groups of these functions and made generalizations about their characteristics.

Here’s what a group of power functions looks like on a graphing calculator:

Here’s what the same group of power functions looks like graphed on Desmos:

Which one makes it easier to tell that all the functions in this group are symmetric about the y-axis?  A picture is worth a thousand words.

# Desmos Graphing App

Graphing calculators are good, but the Graphing Calculator app by Desmos is better.  Graphing calculators are expensive. (The Desmos app is free).   Graphing calculators require several clicks to change the ‘window’ of a graph.  (The Desmos app is interactive and I can zoom in with my fingers).  Graphing calculators can be finicky when entering complicated equations. (The Desmos app points out your error).

I could go on an on about why I think Desmos makes a better graphing calculator for my students, but instead I’ll tell you about my Trigonometry students.

We are headed towards proving trigonometric identities, but before start simplifying them by had, I had them graph pairs of equations whose equations looked very different but graphs were identical.

Two equivalent equations graphed at the same time.

Imagine their surprise when only one graph showed up!  Several were concerned that they had done something wrong, but au contraire, they are equivalent equations!  We had a lot of fun entering pairs of equations and deciding whether or not they were equivalent.

My students have started calling these trigonometric identities “same, same, but different” because they look the same on the graph, but they have different forms when written.

When I did this same activity last year with graphing calculators, it took forever to enter the equations and then find their mistakes if they forgot parentheses.  The Desmos app saved us a lot of time and therefore allowed us to try lots of different pairs of equations.

Entering complicated equations is easy with this list of functions.

You can change the x- and y-axis to radians too!

Desmos also has a web based calculator that is just as fun!

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# The Downside of Digital Textbooks

This year, my Algebra 1 students have digital textbooks, and my Pre-Calc and Geometry students have hardback textbooks.  Back in September, I wrote a post about how I didn’t think it made sense for my Algebra students to use their iPads as notebooks like I was planning have my other students do.  My reasoning was that they needed to be able to work on problems from the book at the same time that they are looking at their textbooks, and I was worried that this much multi-tasking was going to be a recipe for disaster.

A couple of months into the school year, I don’t regret that decision, but I regret that I had to make it because my Algebra 1 students need to spend a significant amount of time using their powerful mobile devices to view Algebra problems that they then work out in their notebooks.  This is not very different at all from what my classes did with a hardback book last year.

On the flip side, I just posted about how my geometry students were able to use their iPads to collect and pool some data last week, and they have also used them to access Google Earth, find pictures of things on the internet to add to their digital notes, draw better, more colorful pictures, and more. They rarely touch a piece of paper.

Next year, these geometry students will have digital textbooks, and I’m not sure if this is going to mean that I am going to ask them to switch back to paper for notes and homework.  I don’t want to.  I am being prompted to try activities this year that I don’t think I would have tried if I had this class working in notebooks and binders.  I am at the point where I would rather have no textbook than a digital textbook.

Why?  I wasn’t exactly sure until I read a post on Dan Meyer’s blog called The Digital Networked Textbook:  Is it any different? about a month ago which said everything I had been thinking.

Meyer contends that digital textbooks aren’t different enough from their paper cousins, and I agree with him.  I think this is because that their main function is still to be a vehicle for content.  They are not a work space or, ideally, a collaborative work space.  Because they are just vehicles for content delivery, I think digital textbooks actually limit the power of the mobile devices being used to view them because students have to use the mobile to look at something, not to do something.

If my geometry students had been able to enter that data they collected last week into their digital textbook, see the data entered by their classmates (and maybe people in other geometry classes?), and then use that to draw conclusions and do other work (all in the
“book”, THAT would be different, and THAT would be worthwhile.

Until then, I can write my own geometry problems, and I don’t mind the extra work if it means my students can use their devices to actually do something instead of just looking at slightly more interactive textbook pages.

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# Pooling our Data

Last Monday in Geometry, it was time for my students to ‘discover’ that when two parallel lines are cut by a transversal, corresponding angles are congruent, etc.  I think its pretty typical for geometry teachers to have students construct parallel lines and a transversal and measure pairs of angles to determine special relationships.  Here’s the activity as suggested by a geometry textbook I have:

I think this is a good activity, and I’ve done it before, but I’ve never been entirely satisfied with it.  First of all, invariably someone starts shouting out the conclusions before everyone is done measuring, and students start making assumptions about their own results, and the magic is lost.  Second of all, I feel like the teacher usually ends up saying something like, “and every time you draw parallel lines and a transversal, alternate interior angles will be congruent.”  I don’t want my students to believe everything I say without evaluating its reasonableness first.  They need more evidence than that.  I am trying to teach my geometry students to adopt an attitude of skepticism; they shouldn’t be drawing conclusions unless they can explain them.

In an attempt to improve this activity this year, I had students work with partners, but I imposed a strict ban on speaking while they were working, so that no pair’s work would be influenced by that of others.  Some students asked me if they could assume certain results would be the case, and I reminded them of the dangers of assuming.  I had them submit all of their measurements via a Google Form, and then we looked at the pooled results as a class to see if we could establish patterns.  I did this with a class of students that need a lot of direction, and it did not exactly go smoothly: some students measured the wrong angles, some students measured the right angles incorrectly, some students entered their data in the wrong place, but we got it done eventually, and I was still happy I did it.

Why?

1) It was a struggle.  I wouldn’t confirm or deny anything my students were thinking and saying for most of the activity, so it forced some actual thinking.

2) Our examples and data were student created.  They weren’t perfect, but they were real.  Not all angles in life are 60 degrees, and sometimes that makes them hard to measure, but you might still have to measure them.

3) There were mistakes.  Students didn’t only see their results, but they saw those of their classmates.  When something didn’t look right, we could have a conversation about whether someone made a mistake, or whether it was actually the case that the pattern people thought they were seeing wasn’t a pattern at all.

I liked this activity, and I liked how my students’ iPads made it relatively easy to execute.  But it got me thinking about something I’m starting to not like about my students having iPads, but that’s a topic for another post…