Sharing Out Our Sinusoidal Function Task

Lindsay Santos-Cox ( and I were excited to get an innovation grant to look at what ways we could support the infusion of ADST into the mathematics classroom.  We were hoping to increase the use of the Library Learning Commons area and to have students be exposed to 3D printing as well.

To introduce 3D printers, we had students create a design in Desmos and then 3D print their design with the TinkerCad website and Tinkerine software.

To support students with the ADST process we designed a task asking students to create a tool to graph a sinusoidal function.

We’ve shared our project and results here for those that are interested!

We felt that it was a worthwhile project and are looking forward to more math projects with the Library Learning Commons!

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Phones During Assessments?! WHAT?!

One of my students figured out a way to securely use their phones during assessments – and I just had to share!  🙂

It use to be that I couldn’t allow students to have their phones out because they could use it for communicating between each other, taking pictures, or just plain googling things.  ALL THAT HAS CHANGED!  It’s now possible to restrict how students use their phone through a “Guided Access” or “Screen Pinning” feature on iPhones and for Android. WOO HOO!!!!  It’s EXCITING!!!

Students really don’t need to buy a graphing calculator these days… they’re expensive, easy to leave at home or on a table somewhere, and have a way steeper learning curve then just using an intuitive app like Desmos.  (I have NEVER seen a student walk off without their cell phone – that’s pretty much like walking out without a limb…)

My husband is an Iphone user, and I’m an Android user, so I have successfully tested and tried this “lock down of features” trick on 2 operating systems.  Here’s how:

iPhones, iPads, and iPods – Guided Access

The feature is called “guided access” and a detailed description of how to do it can be found on Apple Support by following this link.  To use this with students, you have to have them allow you to set the passcode for “Guided Access” on their phone, and then watch them get into the app you would like to restrict them to.  When they’re done, you can enter your secret code and they’ll have access to all of the phone’s features.

The one note I would add to this is to have the student turn off “Guided Access” in the settings… I would hate to have a student turn it on by accident and then not be able to access their phone until we saw each other again!  I’ve never had this happen, but it sure is better safe than to be sorry!

I filmed my student showing me how to do it though (if you want the silent play-by-play… 🙂 )

She also showed me that you can use guided access to block out a portion of the screen you don’t want them to access.  Super cool!

Android Phones – Screen Pinning

This is a little less slick than the Apple version, but still do-able and great!  Android phones have some great app options like Desmos and the Graphing Calculator Emulator App that’s out there.

Step 1)  Students have to allow you to change their security code, or to set a passcode.  This can be done by going to the security settings on their phone.  (A 2 finger swipe down from the main screen, and then clicking on the Settings Gear icon will quickly get you to settings window.)  To get to the Passcode window, click on Settings –> Security –> Screen Lock –> PIN.

Step 2)  Enable Screen Pinning.  There are many tutorials online.  Here’s one that I found handy!  Be sure to turn the “Require password” setting on when turning on Screen Pinning!

Step 3)  After disabling Screen Pinning, be sure to have the student set their password back (or to disable a password if they didn’t have one in the first place).  Again, to get to the Passcode window, click on Settings –> Security –> Screen Lock –> and have the student select either “None” or whichever screen lock they choose.

A final note:

There are a few down sides to this process.  First off, it takes a little organization and a few minutes to set-up and put away at the end of a task, so you’ll need to budget in some extra time for that.  Secondly, it does involve a little bit of trust that you are going to restore the student’s phone back to its original condition (with no weird passwords or locks on it).  I would make sure to be really aware and cautious of both of these issues, and make sure that students know what is happening to their phone when you’re setting this up.  (Also – just do it in front of them or even have THEM press all the buttons (except the password) so that they know exactly what was happening.)

Overall, I think this is a fantastic way to incorporate technology that some (most?) students already have!  If you have any suggestions or questions, feel free to comment below!


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A Number Talk about Radian Measure

On Tuesday, my Pre-Calculus 12 class used our classroom clothesline to explore the magnitudes of radian measures.

When graphing sinusoidal functions, students have noticed that we can divide the period into four pieces (minimum, center, maximum, center) to help determine the location of a given function or to check the accuracy of our function after having graphed it.  That said, they were also having trouble dividing a period into 4 equal parts, and if given a graph and asked to find points A to D as shown below, they struggled to find them.  To get them to play around and explore strategies to find these points on our graph, it was clothesline time.  🙂

trig graph

To play around with this concept, I selected random students and gave them each different values like pi/6, pi/2, 3pi/2, etc..  They were then asked to place them on our number line (as shown below).  They were told that if they needed help or just wanted to feel like they were on the Price Is Right, they could ask for crowd input as well.  🙂  We then used the values to discuss if they were appropriately placed on the clothesline.  Were they placed using the appropriate proportions?  What values would fall between them?  Were there any benchmark values that would have made placing their values easier?

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The students shared their thought process and explained their reasoning in thoughtful ways.  There were disagreements that were turned to agreements when students explained their reasoning in convincing ways.  After playing with the values we had placed together, I then called attention to 2 values in particular: the value between pi/2 and pi/3, and the value between 0 and pi/6.  (Notice that these are the x-values of points A and C on the trig function above.)  After our number line discussion, students had many strategies for finding these and were much more confident in determining the value.

Once they had found these values (5pi/12 and pi/12), we then tried to find the midpoint of these values.  The strategies shared were FANTASTIC!  They had surprising ways to find the values, and it was overall a super worthwhile discussion.

The activity made me super curious what other strategies are out there, so if you have time I would love to know: How would YOU find point B on the trig function shown?  I would love to hear your feedback and/or strategy in the comment section below!  🙂

I’ll gather my students’ strategies from yesterday and add them to a future blog post!  🙂

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Building Number Sense with Clothesline Activities

One of the many great take-aways from the recent Professional Development day in October was an activity that begins with a clothesline (thanks to Estimation180 and Andrew Stadel).  Students are shown an image or given a question and asked to estimate their solution.  As the teacher circulates, they ask some students for estimates that they think are too high or too low. Students write these estimates on red (or pink) pieces of paper, and add them to the clothesline.  Other students are given green pieces of paper and asked to write an estimate that they think is the correct solution.  These are also added to the clothesline.

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The result is a collection of numbers that can be used to develop students’ number sense around the magnitude of numbers and proportional reasoning. Inevitably, students will place their numbers on the clothesline in a way that doesn’t accurately depict the relationship between each number. The number talk around how the values can be arranged differently and how we can appropriately space the numbers is a great sense-making activity! The conversation inevitably comes around to the fact that using benchmarks would make the adjustments to the number line much easier to figure out. There were some excellent observations and conversations around what benchmarks would be most useful, and which ones might not be helpful.

I’ve been trying it for the past couple of weeks and have found it really neat how students asked for benchmark numbers at first, and how it’s evolved even in a short time span. In the picture above, my students initially asked for benchmark numbers like 20 and 15 (rather than what I thought would be easiest, 0).
I left it up during class and allowed students to rearrange the numbers thoughout the class if they wanted to… with 10 minutes to spare, one student asked if she could have another benchmark number… she wanted a 30, placed it at the opposite edge of the wall and began rearranging. It was such a GREAT teacher moment to see that she had been thinking about it all class and wanted to make that change!

I will definitely be using Estimation 180 and my surroundings to come up with other images for students to make predictions about. I would like to find some that would have estimates that stretch student’s thinking to other place values (such as the thousands, millions, etc.). Overall this is a great activity with MANY extensions! (In fact, at the conference we were using it to solve equations… it was cool.)

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Our Math Vocabulary Wall – November 10th, 2015

Here’s a snapshot of our vocabulary wall as of today!  It’s loaded with the math vocabulary that we’re also hearing in our classes.

On the back of each cue card there is a brief definition of each word, so if students aren’t sure about a term they can always go and take a peek!  🙂

It’s always neat to see students checking it out by either taking pictures of it, reading the cards, or suggesting other terms to add to the chart.

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McMath’s Math Club

This year McMath students have started a Math Club… and it’s been wonderful to be a part of!

Students have spent their club days working on different mathematics activities such as Waterloo contests and famous puzzles.  Today, students tried to find ways to create a solution of 24 when given 4 random cards from a modified deck of cards.  The students’ energy was exciting to see… there is nothing better than watching students enjoy mathematics!

If you’re a student… please come join us in Room B202 on Fridays!  We would love to see you!  You can also check out our McMath Math Club blog!

If you’re a parent… let your son/daughter know that new members are always welcome!

If you’re a teacher… I would love to hear what your math clubs are like, so if you have any ideas, please get in touch!  🙂

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A fun spatial reasoning problem…

My students went CRAZY for this video… it’s pretty cool!  Enjoy!  🙂

If you’re dying to know how this “math miracle” is done, then here’s a great explanation…

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Calculating Marks for Report Cards…

Even though my classes receive feedback on each learning outcome using standards based grading, my school district still requires a percentage for reporting purposes.

Luckily I have a brother who’s a software engineer and who is currently working on a program that will make reporting out the learning outcomes, and calculating a mark, a super easy task.  He’s hoping to have it done for second semester, so check back to this site for a copy of it!  🙂

In the meantime, I calculate students’ marks using an excel spreadsheet and I weight each learning outcome based on their importance.  I also attach a percentage to each of the standards (Fully Meeting/Meeting/Minimally Meeting/Not Yet Meeting).  Students can also figure out their mark by going to their course website and clicking “Calculate Your Mark“.  I like that they can determine this on their own because it really helps with their own personal goal setting and also gives them an exact snapshot of where they’re at.

The details of this spreadsheet are explained in this quick video… if you have any other questions about it, please don’t hesitate to ask!  🙂

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Creating my Class Set of Inexpensive Whiteboards

I had been meaning to “up my game” when it came to students using whiteboards… For the longest time I have been using these mini whiteboards from Spectrum, but students often each had their own and it wasn’t as collaborative as I would have liked.  (They had to squeeze their work into a much smaller and less visible space).

I really love using whiteboards with students – it allows for a kind of risk taking that just isn’t always happening with paper and pencil. Fred Harwood had showed off his awesome set of whiteboards at last year’s BCAMT conference in 2014, and it had been on my to-do list ever since!

I decided to make mine with some particle board as the backing, and a piece of laminated poster board as the whiteboard surface. Home Depot was awesome about cutting the board down to size for me… and when they heard what it was for, they didn’t even charge me for the cuts!  For the poster board, I put a grid on one side so that students can use it for both graphing and problem solving. Here’s a link to the grid paper… it’s meant to be printed on an 11×17 sheet of paper.  The great thing about just using laminated poster board is that when it starts to get all scuffed up, I can easily (and cheaply) replace them.

The students loved it and had fun working together to graph various functions… I’m going to start using them all the time though… the uses are endless!

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The one thing I noticed is that most students preferred writing on them on top of their desks and not as a vertical surface… but that might be because I don’t have a great way to prop them up yet… Suggestions are welcome!

How do YOU use whiteboards in your classroom?  I would love to hear about it!  (Feel free to comment below or to send me an email!)  🙂

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Mobius Strip Fun!

At the Northwest Conference on Friday, Trevor Brown reminded us of all the neat things we can explore with Mobius strips!

Here’s a quick video of the first few cases my classes explored (they tried to predict what would happen in different scenarios – a mobius strip with one twist, 2 twists, etc)… the Ooooh’s an Ahhh’s had to be muted to ensure that my students’ names weren’t in there, but it was super fun!

My favourite moment was when students wanted to extend the question to see what would happen if we twisted the mobius strip 10 times… and many of them grabbed paper, tape, and scissors to try it themselves… they were hooked!

It was also great to be able to share that this is a branch of mathematics called Topology… they were excited at the idea that they could find out more and study those big ideas some day (and started the journey today)!

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