Explore partial variation linear relations by giving students two points from a linear relation and challenge them to determine the initial value and slope.

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]]>Here’s another task that is a good next step once you’ve tackled the Tech Weigh In 3 act math task that covers direct and partial variation linear relations. This task gives students another chance to get some exposure to partial variation linear relations and could provide an opportunity for the teacher to begin consolidating the topic by moving towards some more abstract concepts like the slope formula and finding linear equations given two points. Similar tasks to check out would be Stacking Paper, Stacking Paper Sequel and Thick Stacks.

Special thanks to Justin Levack again for coming up with the “weigh in” idea and pushing me to actually record this with him when we are all running out of steam at the end of the school year.

As stated above, I’d suggest tackling the Tech Weigh In 3 act math task prior to doing this task. Because I would do Tech Weigh In first, I feel that an act 1 is not really necessary for this particular problem. Tech Weigh In sets the stage nicely and this is more of a sequel than anything else. This photo would likely take care of it:

**What’s the question?**

As always, get your students talking about what they think this math task is going to focus on. Writing the questions out is always helpful. In this case, since they’ve already done Tech Weigh In, my students are pretty confident we’re going to be finding out how much the camera case weighs (or initial value). However, I use this task to get a bit more specific and focus on questions along these lines:

- How much does the camera case weigh and what do we call this number? (i.e.: initial value)
- How much does each pad of paper weigh and what do we call this number? (i.e.: slope/rate of change)
- What is an equation that could represent this linear relation?
- What would the weight be if we stacked _____ pads of paper?
- How many pads of paper would it take to get a weight of ____?

Making predictions is always a good practice after some questions have been shared out.

Show your students this:

Here’s two exemplars of how students may approach this through an inquiry approach:

Many teachers might consider using a procedure to find the equation of a line given two points using the slope formula as the next logical step. However, I have witnessed a few students essentially use substitution to solve this type of problem. It might not look as organized as how students are instructed to solve a system of linear equations, but the thinking is much the same. Here’s an example of what it might look like (but this is probably too organized for a real case):

I’d suggest that **after** solving a simple system of equations using substitution, you might want to move towards consolidating the exemplars above to the slope formula and solving *y = mx + b* algebraically for the initial value, b:

Check out all of the resources here. Or, you can grab what you want individually below:

Be sure to share your student exemplars in the comments!

Have you tried the task? Let us know how to make it better in the comments!

Click on the button below to grab all the media files for use in your own classroom:

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]]>Watch as different combinations of tech devices are piled on a scale. Using linear relations, students will determine how much each device weighs.

The post Tech Weigh In appeared first on Tap Into Teen Minds.

]]>In the Ontario grade 9 applied and academic math courses, students do a lot of work with direct (proportional) and partial variation linear relations. This task was created to assist in adding context to these types of relations and help students build an understanding of both by using intuition, logic, and prior knowledge.

Special thanks to Justin Levack for coming up with the idea and pushing me to actually record this with him when I was running out of steam at the end of the school year!

Show this video:

**What’s the question?**

Get your students talking about what they think this math task is going to focus on. Writing the questions out is always helpful.

Here are just a few of the questions that came up today when we used this task for the first time:

- How much does 3 iPads weigh?
- How much does 1 iPad weigh?
- How many scales would weigh the same as the stack of iPads on the table?
- What is the cost per gram/ounce/kg/etc.?

All great questions that should be recognized! While we could try to answer as many questions as possible, today our focus was on the weight of 1 iPad.

Time to make some predictions!

After students are happy with their predictions, start asking students what information they want. In this case, I have pretty specific information, but my students can usually come up with something similar that could help us out.

Show them this video:

Now we can set the students free to work out the problem. At the beginning of the semester, my grade 9 applied students might struggle to get started due to a low level of confidence in math, but today they were done in a matter of 20 seconds or so. They’ve come a real long way!

I also created a Custom Gameshow in Knowledgehook to allow me to get some instant feedback as students worked. The Gameshow Tool now has a feature that allows students to upload their work and then I can display student work samples to consolidate thinking. It was pretty rad!

You can grab a PDF copy of the Custom Gameshow here.

Although this is a simple proportion, I try to get students to see the other connections that can be made to linear relations including direct variation. Some additional extension questions could include:

- Is this relationship an example of a direct or partial variation? How do you know?
- Find the initial value and rate of change.
- Determine an equation that relates the
*weight*and*number of iPad 2s* - How Many iPads would weigh 27,066 grams?

Since I do these problems back-to-back, students already have a feel for what we’ll likely be exploring. You could try to pull out some more question ideas, but I usually find that the students are already hooked in and are actually more interested in getting to the math. I do, however, try to get some predictions out there just to ensure that they have some way to judge how realistic their answers are.

Show them this video:

The question is: How much does the MacBook Pro weigh in at?

Again, students are now ready to be set free to solve the problem. There is no pre-teaching necessary here. Most students will intuitively be able to determine the weight of 1 iPad Mini and ultimately use the formula for slope of a line by accident as they usually do in Thick Stacks. Let them do it on their own and consolidate later.

Surprisingly, one student even wrote out their solution as a system of linear equations and used elimination to eliminate the MacBook Pro completely:

I found this to be fascinating because I had never even considered this as a potential problem to introduce the concept of elimination to a group of students working with systems. Not my intent at all with this problem, but you bet I’ll be using it in that case from now on!

Here are some extension questions to complement this partial variation relation:

- Is this relationship an example of a direct or partial variation? How do you know?
- Find the initial value and rate of change.
- Determine an equation that relates the
*Weight*and*Number of iPad Minis* - Determine the approximate number of iPad Minis it would take for the entire stack (including the MacBook) to weigh 29,005 grams?

Check out all of the resources here. Or, you can grab what you want individually below:

- Task #1 – iPad 2 Weigh In – Act 1 [VIDEO]
- Task #1 – iPad 2 Weigh In – Act 2 [VIDEO]
- Task #1 – iPad 2 Weigh In – Act 3 [VIDEO]
- Task #2 – MacBook Pro and iPad Mini Weigh In – Act 2 [VIDEO]
- Task #2 – MacBook Pro and iPad Mini Weigh In – Act 3.1 [IMAGE]
- Task #2 – MacBook Pro and iPad Mini Weigh In – Act 3.2 [VIDEO]
- Slide Deck for Both Tasks [KEYNOTE]

I only managed to grab one photo of student work today (ooops!) so please send your student work my way or add the images in the comments (yes, you can add images!) so others can learn from your students!

Have you tried the task? Let us know how to make it better in the comments!

Click on the button below to grab all the media files for use in your own classroom:

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]]>I’d like to take 5 minutes of your time to talk about one of the most commonly used, yet misunderstood buzzwords thrown around in education today.

The post Unmasking Education’s Biggest Buzzword appeared first on Tap Into Teen Minds.

]]>Earlier this month, I participated in my first ever Ignite Session at the OAME 2015 Annual Conference. If you’ve never watched an Ignite Session, they are essentially short talks where the speaker has exactly 5 minutes to get their point across. Seems pretty simple, but they also throw in this twist that you are also restricted to **exactly** 20 slides that automatically advance every 15 seconds. I’ve seen some pretty awesome Ignite Sessions online, so I was pretty nervous to put my own together for my first go.

My Ignite focused on * Unmasking Education’s Biggest Buzzword* and you can check out the footage below or jump to the slides and presenter notes.

I’d like to take 5 minutes of your time to talk about one of the most commonly used, yet misunderstood buzzwords thrown around in education today. Most of us believe we understand it, but what the word represents is so complex, it’s often difficult to define.

If you haven’t guessed, the buzzword is “Engagement”. When it comes to student engagement, there are many different types, but unfortunately there are no clear answers as to which types may impact student learning or which factors increase different types of engagement.

What I can tell you is that student engagement doesn’t look like this. However, I didn’t realize that back on Tuesday September 5th, 2006 when I began the long journey to bore my first cohort of math students for a full 89-day semester.

It took less than two weeks before everyone in the room, including myself, wanted out. While I may not have been able to define what student engagement looked like at the time, I definitely knew – that – was not it.

With the daily reading on the student engagement richter scale at or below zero, I turned to my familiarity with technology to help. While using technology allowed me to spend more time on classroom management than on writing a note on the board, math class was still a drag.

I believed that if I could better manage my room, students would be engaged in my lessons. If I could get students to “do what they’re supposed to do”, then then everything would be better. While using technology to present material improved the behavioural engagement of my students, it did little to nothing intellectually.

Unfortunately, the “VANITY METRIC” I was using to measure was the behavioural improvement observed when I used what I now call “BORING” slideshows misled me to believe that the technology was the magic pill to solve all the problems in my classroom and in mathematics education.

Because I was blinded by the behavioural changes in my students when I introduced technology, I was quickly on a path to implement the next tech tool in my classroom. I was completely ignorant to all of the interesting parts of mathematics, likely because they had never been shown to me.

So in came the SMART Boards, the clickers, laptop carts, iPads and Apple TV’s in order to supposedly “engage” my students. I wasn’t the only one tricked – my technology use earned me the label of “good” teacher by most simply because of the technology and not the teaching practice.

By this point, I was observing improvements to success rates and believed technology was playing a key role. I had seemingly found a working formula for high test scores, but were students actually engaged in math and enjoying the process or were they just being compliant?

It wasn’t until 2012 when I attended the OAME Conference in Kingston that I was able to attend a session that completely changed my approach to teaching. My eyes were open to new ideas I never knew existed and I’ve been building on them for students to better engage AND enjoy the process.

Before long, I joined Twitter and began learning from the “Math Twitter Blogosphere” or #MTBoS, as most know it as. Now, I’m learning from a global professional learning network consisting of thousands of math teachers willing to stretch my thinking.

While I still believe that innovative uses of technology CAN increase intellectual engagement, my blinders have been lifted to see that focusing on one small piece of the puzzle is merely a band-aid solution that can hide the underlying problems.

When I came to the conclusion that the traditional lesson format I had always used was due to familiarity rather than efficiency, I knew I had to make a change. I was tired of being the gatekeeper of math knowledge and wanted my students to have a role in the learning process.

Trying to teach math by giving students all of the answers through a list of definitions, an algorithm and 8 examples is like giving someone a crossword puzzle with all of the answers written on the page. We’ve sucked out any opportunity for curiosity or thinking.

I don’t think that anyone would argue that algorithms alone are the key to engaging our students and we would likely agree that successfully following the steps of an algorithm does not necessarily mean they understand math.

Unfortunately, it took me 8 years to realize that the traditional lesson structure I was using that focused on steps and procedures over inquiry, was promoting students to memorize math rather than build a deep understanding of how it all connected.

Now, lessons are delivered in a task based format allowing students to use the inquiry process to make connections to their prior knowledge. When students prove to themselves that they can solve a problem independently, we can extend thinking to a new learning goal with greater ease.

What I’ve realized only recently is that maximizing intellectual engagement of our students has less to do with making math tasks real world or relevant, but rather, how we ask those questions.

So, if I’ve learned anything about student engagement, it is this – never stop trying to find new ways to leverage the natural human curiosity we all have in order to expose the beauty of mathematics to our students. And, If we can find a way to do it daily, student engagement will be a buzzword of the past.

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]]>Knowledgehook's Gameshow Beta Tool is a FREE Gamified Online Assessment Tool that can do what Socrative and Kahoot do, but offering much more!

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]]>Knowledgehook’s Gameshow Beta Tool is a FREE Gamified Online Assessment Tool that does more than what Google Forms, Socrative and Kahoot can do by pushing the bar up with level-up experience (XP) points as well as FREE content teachers can use to run ready-made gameshows or customize their own!

While this is just the beta version, I am impressed with the look, feel and roadmap for this new tool to join the online assessment party.

Let’s have a closer look…

See below for a quick written summary with screenshots of the experience:

Signing up for a free teacher/administrator account was simple and painless. Only a few details including your school email address to avoid the possibility of students signing up as a teacher.

You must pick your province next and unfortunately it only has Canadian provinces listed (so far?). Since this is the beta version, I would assume that other locations outside of Canada simply have not been added (yet). Since this took can be useful for any teacher in any subject area around the world, I’d probably select a province for now and hopefully more locations will be added shortly.

I’m unsure of the different course options available depending on your location. In Ontario, it appears that grades 7-10 math have been covered. If I was in another subject area, I would just select any courses (maybe all) and then move on. There is a custom gameshow creation tool where you can construct your own questions, so this tool will be useful regardless of whether you have selected your correct course.

From here, you can now select your desired course from the pull down menu in the main navigation bar at the top of the screen.

Click on the VIEW button to preview the questions, add them individually to a custom gameshow, or edit the questions directly.

Press PLAY on a ready-made gameshow, or customize your own gameshow by interleaving content or creating your own problem sets.

Students head to playkh.com and enter in your gameshow room PIN to begin. No student accounts necessary – Just a device and a connection!

Using a minimalist and modern approach, the platform is appealing to the eye.

With all of the work that I’ve been doing on Gamifying my assessment practices this year, the experience points seem to fit in nicely with my thinking.

The custom gameshow and question creation tool is really versatile offering the most customization I’ve experienced thus far in the online assessment / clicker quiz market. I’m really excited to dig in and play with all of the options including HTML tags to add links and other great features.

Have you tried this new free online assessment tool? If so, let me know how it went for you!

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]]>Dan Meyer, Buzzmath and a variety of math teachers created a series of Graphing Stories Math Videos that are great! Here they are in 3 act math task format!

The post Graphing Stories – 3 Act Math Style! appeared first on Tap Into Teen Minds.

]]>Dan Meyer and BuzzMath worked collaboratively with a group of math teachers to create some really impressive resources for distance-time and many other relationships comparing a dependent variable over time. For the past couple years I have been using the videos on the Graphing Stories website and really enjoying how the videos engage my students in ways I had never considered. However, over time, I have been trying to do a better job developing the question as Dan Meyer and many others discussed here. My thinking was that we could develop the question more effectively if we chunked the Graphing Stories videos into 3 acts.

So that’s what I did and I’d like to share those videos chunked into 3 acts with you below.

Quick Tip: I’d recommend only using a few of these graphing stories each day as anything too repetitive will lose effectiveness. Spacing out your distance-time work with Graphing Stories over a few weeks seems to work well in my own classroom.

In Bum Height off the Ground, Carey Lehner submits a video of a child sliding down a large theme park slide. What does the graphing story look like when you compare bum height and time?

In Act 1, Kenneth Lawler submits a video of a weight lifter bench pressing. What does the graphing story look like when you compare the distance of the bar from the bench and time?

Watch the other acts below:

In Act 1, Adam Poetzel submits a video of a man sitting on the edge of a playground ride. What does the graphing story look like when you compare distance from camera and time?

Watch the other acts below:

In Act 1, Paul Reimer submits a video of a man pumping a football with an air pump. What does the graphing story look like when you compare air pressure and time?

Watch the other acts below:

John Golden submits a video of a man blowing up a balloon. What does the graphing story look like when you compare balloon length and time?

Watch the other acts below:

Adam Poetzel submits a video of a man sitting on the edge of a carousel. What does the graphing story look like when you compare the distance from centre of the carousel and time?

Watch the other acts below:

Liam Johnston submits a video of a man running the bases of a baseball diamond. What does the graphing story look like when you compare distance from home plate and time?

Watch the other acts below:

Arianna Hoshino submits a video of a man rolling down a hill. What does the graphing story look like when you compare elevation and time?

Watch the other acts below:

Jose Luis Ibarra submits a video of a person flying a paper plane from the second floor of a building. What does the graphing story look like when you compare elevation and time?

Watch the other acts below:

Jean Phillipe Choiniere submits a video of a person zip-lining in the rain forrest. What does the graphing story look like when you compare height off ground and time?

Watch the other acts below:

Rachel Falknor submits a video of a person bouncing a ball on the ground. What does the graphing story look like when you compare height and time?

Watch the other acts below:

Mark Sloan submits a video of a person stacking styrofoam cups. What does the graphing story look like when you compare height of stack and time?

Watch the other acts below:

Adam Poetzel submits a video of a person climbing up a slide and then sliding down. What does the graphing story look like when you compare height of waist off ground and time?

Watch the other acts below:

Dan Meyer submits a video of himself swinging on a swing. What does the graphing story look like when you compare height of waist off ground and time?

Watch the other acts below:

Bowen Kerins submits a video of a video game character using a teleport on the screen. What does the graphing story look like when you compare height off ground and time?

Watch the other acts below:

Christopher Danielson submits a video of a person adding pony figurines to the frame. What does the graphing story look like when you compare the number of ponies in the frame and time?

Watch the other acts below:

David Cox submits a video of a person dealing out a deck of cards. What does the graphing story look like when you compare the size of hand and time?

Watch the other acts below:

Mariah Thompson submits a video of a person holding a clock and watching the time go by. What does the graphing story look like when you compare the time on the clock and the time on the timer?

Watch the other acts below:

Esteban Diaz Ibarra submits a video of a person filling a cylinder with water. What does the graphing story look like when you compare the volume of water and time?

Watch the other acts below:

Mark Sloan submits a video of a person stacking cups on a scale. What does the graphing story look like when you compare the weight of the stack and time?

Watch the other acts below:

Mark Sloan submits a video of a person un-stacking cups on a scale. What does the graphing story look like when you compare the weight of the stack and time?

Watch the other acts below:

Mark Sloan submits a video of a person stacking different kinds of cups on a scale. What does the graphing story look like when you compare the weight of the stack and time?

Watch the other acts below:

All of the video content originally licensed CC BY 3.0 US on the Graphing Stories website by Dan Meyer, BuzzMath and a group of excellent teachers.

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]]>How much would it cost to build the Big Nickel in Sudbury, Ontario out of real nickels? A task using volume, proportional reasoning and trigonometry!

The post Big Nickel appeared first on Tap Into Teen Minds.

]]>So earlier this month, I was in Sudbury, Ontario delivering an Apple Professional Development session for the Sudbury Catholic District School Board. I had always heard about the “Big Nickel” monument and thought I should search it out. On my way, Justin Levack sent me a text saying I should see what kind of 3 Act Math Task I could think of. This time, rather than trying to develop a question on my own, I tossed it out to the Twitterverse:

Thoughts on what to do with this one? @ddmeyer @mathycathy @robertkaplinsky @mr_stadel @Ryan7Read #maths #mathchat pic.twitter.com/qQlh8oTW3p

— Kyle Pearce (@MathletePearce) September 19, 2014

As expected, I had some ideas coming to me within minutes including these:

@MathletePearce @ddmeyer Get the roasted red pepper soup, whatever you do! And..how many nickels would have to be rendered to make THIS one?

— Cheryl Geoghegan (@mathsuds) September 19, 2014

@MathletePearce If that was made of nickel how much would it be worth? How many nickels?

— Dan Meyer (@ddmeyer) September 19, 2014

@mr_stadel My favorite question so far, Andrew! No rest for me until I know the answer @MathletePearce @ddmeyer @robertkaplinsky @Ryan7Read

— Cathy Yenca (@mathycathy) September 20, 2014

So, just like that, Cathy Yenca went and solved Dan Meyer and Andrew Stadel‘s question and was kind enough to share her work with us so we can all use this task when a related learning goal comes up.

Show your students this video or the photo below:

The approach you choose to have your students answer whether constructing the Big Nickel with actual Canadian Nickels vs. using the material they actually used to build the monument would be more cost effective will depend on the level of your mathematics students. Here, I’ll give two approaches to make this task accessible by more students.

All students would benefit from these two photos:

**Diameter of the Big Nickel in Sudbury, Ontario**

**Big Nickel Divided into 12 Triangles**

**Thickness of the Big Nickel**

The thickness of the Big Nickel will serve as the height of the prism in order to calculate the volume. By taking the area of the base and multiplying by the thickness (height), students will know how much space the Big Nickel occupies:

**Thickness of a 1951 Canadian Nickel**

The thickness of a 1951 Canadian Nickel will serve as the “height” in the volume formula when calculating how much space is occupied by an actual nickel:

If your students have not covered trigonometry or primary trigonometric ratios yet, you’ll want to give the students a little more information. Here are some details you can give your students:

**Base and Height of One (1) Triangular Section of Big Nickel**

Students can use these dimensions to determine the area of one triangular section of Big Nickel, then multiply by 12 to get the **area of the base** in order to help them find the total volume:

**Base and Height of One (1) Triangular Section of a 1951 Canadian Nickel**

Students can use these dimensions to determine the area of one triangular section of a 1951 Canadian Nickel as they work towards finding the volume:

If your students have covered the **primary trigonometric ratios**, you can opt to use the following images that force students to use trig ratios to find a working solution:

**Height of a Right Angle Triangle in Big Nickel**

Students know that the diameter of Big Nickel is 9.1 m and thus the height of the right angle triangle we can form in one of the 12 triangular sections

is 4.55 m. From here, students must use their knowledge of primary trigonometric ratios to find the base of the triangular section:

Using a similar approach to the above image, students must also use their knowledge of primary trigonometric ratios to find the base of a triangular section of a 1951 Canadian Nickel shown below:

Once students determine the volume of Big Nickel and a 1951 Canadian Nickel, they can determine how many nickels it would take to build the monument as well as the total cost to do so.

The Big Nickel was completed in 1964 for approximately $35,000 according to Wikipedia. Information about the 1951 Canadian Nickel also according to Wikipedia.

My assumption is that the nickels would be melted down to create the monument, but some students may assume you’re just “dropping the nickels in” or something along those lines. Great discussion to be had there.

Here are some additional extensions and images that are included in the slide deck available for download:

- The City of Windsor wants to build a “Double Big Nickel” where the total volume is doubled. Can you just double the dimensions?
- The WFCU Arena in Windsor cost a total of $71 Million to build. What percentage of that cost would it take to construct the Big Nickel?
- When constructing the Big Nickel, construction workers need to know the interior angle measures in order to build it. What are they?
- If the Big Nickel needs to be taken off-side for repair, what would the interior angles be for the supports needed?
- If resurfacing the entire Big Nickel, how much would it cost?

Cathy Yenca was the first to answer Dan Meyer and Andrew Stadel’s question(s) and she was kind enough to share her work via a TACKK! Click here or on the image below to see the full solution:

Cathy also blogged about our co-creation of this task from a great distance over a very short period of time! Read about it here!

- Act 1 [VIDEO]
- Slide Deck Images [JPG FILES]
- Slide Deck Presentation [KEYNOTE FILE]

Be sure to share your experience in the COMMENTS!

Click on the button below to grab all the media files for use in your own classroom:

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]]>Gas Guzzler shows Mr. Pearce filling his gas tank. Act 1 shows the price of gas covered up. Students must find the rate of change using the cost for 20 L.

The post Gas Guzzler appeared first on Tap Into Teen Minds.

]]>This 3 Act Math Task focuses on the rate of change for proportional reasoning / linear patterning / direct variation linear relations problem.

In the first act, students watch a 30 second video that shows someone pre-paying for gas, selecting the grade of fuel and start pumping. You’ll notice in the video that the cost per litre (rate of change) is blanked out on the pump.

Students will then be asked:

What is the price of gas?

Here are a few images in the case you don’t want to load a video / have a slow connection:

We then watch the gas being pumped in fast-forward and then at about the $20 mark, we see an image showing the price for a specific amount of fuel in Litres.

Students can then use the given information to determine the cost of fuel.

At this point, you can also ask the students to determine:

How much will it cost to pump _____ litres of fuel into the tank?

In this video, the total number of litres is 38.264 L. Suggesting they find the cost for exactly 38 L might lead to a good discussion about why the video doesn’t stop at exactly 38 L to fill the tank, etc.

This video shows both the cost of gas on the pump and on the Petro Canada sign.

The video also show how much gas was pumped into my 2011 Dodge Grand Caravan.

- Did the 38.264 L fill the tank from empty? If not, what fraction or percent of the tank did it fill?
- Is this scenario a direct or partial variation? How do you know?
- Will you ever encounter a partial variation when filling up your vehicle like we viewed in this video?
- What other 2-variable relationship could we explore in this situation other than Volume of Gas and Time?

Grab them all here or, individually below:

Act 1 [VIDEO]

Act 2 [VIDEO]

Act 3 [VIDEO]

Presentation [KEYNOTE SLIDE DECK]

Here’s a quick look at what the slide deck looks like:

Click on the button below to grab all the media files for use in your own classroom:

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]]>Get your Twitter account ready to join in the #OAMEchat that will be going on throughout (and after) the OAME Annual Conference with questions Tweeted daily

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]]>A couple weeks ago, Jim Pai tossed out the idea of creating a Twitter Chat that will run in the style of #slowmathchat by Michael Fenton. A group of Ontario Math Educators including Jon Orr, Matthew Oldridge, Amy Lin, Mary Bourassa and myself jumped on-board.

If you are unfamiliar with #slowmathchat, be sure to check out Michael Fenton’s post outlining how it works.

As mentioned, we will be following the #slowmathchat model by Tweeting out questions throughout the OAME Annual Conference to encourage:

- People sharing their experiences from OAME
- People sharing their thoughts on their experiences from OAME
- People sharing their reflections on their thoughts on their experiences from OAME
- People not attending sharing their reflections on the thoughts of the experiences of others from OAME

While the intent was to connect mathematics educators during the conference, it is possible that we continue with the same format after the conference comes to an end.

Use the hashtag #OAMEchat to engage in conversation related to the four (4) questions that will be tweeted out from Tuesday to Saturday during the OAME 2015 conference. The hashtag #OAME2015 is for general conversation about the conference that is not specific to the chat.

However, consider using **BOTH** hashtags when participating in the chat to inspire others following the #OAME2015 hashtag to join in!

#OAMEchat will consist of four (4) questions that will be tweeted out throughout the OAME 2015 Annual Conference. Here’s the schedule:

- Tuesday May 5th & Wednesday May 6th – Question #1 (Q1)
- Thursday May 7th – Question #2 (Q2)
- Friday May 8th – Question #3 (Q3)
- Saturday May 9th – Question #4 (Q4) & Question Summary

Each question tweet will begin with the letter “Q” and the question number (e.g.: Q1 for question #1). In order to help those in the chat understand which question your tweet corresponds to, we suggest that you begin your tweets with the letter “A” and the question number (e.g.: A1 for answer #1).

Many grew up writing notes in a binder that would get tucked away – often never to be read again.

Recently, I began using Twitter as a way to document some of my learning at conferences by quoting speakers and sharing big ideas acquired from sessions. Not only does this provide me with a digital filing system that I can go back through to refresh on some key learnings, but it also prompts interaction from my Twitter Professional Learning Network.

Here is a recent (short) conversation prompted by a reflective Tweet:

I *try* to include my direct instruction during consolidation rather than prior to the task, building on strategies observed. #springsimk12

— Kyle Pearce (@MathletePearce) April 23, 2015

@MathletePearce #springsimk12 letting students construct their own understanding and struggle if necessary rather than telling/over scaffold

— LMS-Campbell (@lstrangway) April 23, 2015

@lstrangway exactly – then, that leaves little for the teacher to clarify/extend throughout.

— Kyle Pearce (@MathletePearce) April 23, 2015

@MathletePearce we have a BINGO!

— Alex Overwijk (@AlexOverwijk) April 23, 2015

During the OAME Annual Conference, we will:

- Post four (4) questions throughout the conference;
- OAME Attendees and those following via Twitter can share their experiences from the conference, while sharing their responses to the questions; and,
- At the end of the conference, we will archive the conversation for future reference.

Disclaimer: These ideas are stolen from Michael Fenton’s post:

- Add a #OAMEchat column to your Twitter client. I’ve been a fan of Tweetdeck for quite some time, but there are others that will allow you to do the same. If on a mobile device, be sure that you continue checking the hashtag via the search field in the Twitter app.
- Spread the word about #OAMEchat by retweeting questions, answers, and any other interesting Tweets with the hashtag.
- Toss out some interesting questions during the conference to keep the chat lively!

Do you have ideas to make the chat awesome? Please let us know in the comments! Looking forward to your Tweets at the conference!

The post Join the Circle! #OAMEchat During @OAME2015 appeared first on Tap Into Teen Minds.

]]>An Education Officer from EQAO has confirmed that the new Desmos Test Mode app can be used on the Grade 9 Assessment of Mathematics in Ontario Classrooms.

The post EQAO Guidelines Allow Use of @Desmos Test Mode App appeared first on Tap Into Teen Minds.

]]>Recently, I came across a post by Carl Hooker explaining how the Eanes Independent School District managed to get Desmos Test Mode approved for students writing the Texas State math tests (also check out Cathy Yenca’s post here). I’ll be honest and say I never really read too deeply into these posts until I heard from Jon Orr that a school district near Toronto was approved by the Educational Quality and Accountability Office (EQAO) to use this brand new app on the upcoming Grade 9 Assessment of Mathematics in June. I immediately made a phone call and also sent off an email to EQAO in order to learn more about the possibility of allowing my district to do the same.

A representative from EQAO responded to my email today and stated:

…Students can use calculator applications on iPads, as long as the calculator applications have the same functionality as a regular scientific or graphing calculator, with or without computer algebra systems. For example, it must not contain a glossary or be instructional in nature (e.g. provide tutorials or definitions), as scientific/graphing calculators do not have glossaries or provide instructions. Students can also choose to use the virtual manipulatives on the iPad. However, any applications and software which require internet connectivity in order to function are not permitted during the assessment. As well, they should not have access to other applications or the internet during the assessment.

All provisions outlined in the Administration and Accommodation Guides must be adhered to. Any instructional materials, including applications of an instructional nature, that facilitate responses to questions cannot be used. We rely on the professional judgment of educators to administer the assessments in accordance with EQAO guidelines…

With Jon cc’ed on the email, we were both very excited to be able to share this news with our colleagues and Twitter PLN from other parts of Ontario.

**PLEASE NOTE – THERE IS NO APPLICATION OR REQUIREMENT TO CONTACT EQAO TO USE DESMOS TEST MODE APP ON THE GRADE 9 ASSESSMENT OF MATHEMATICS; FOLLOW THE STEPS BELOW AND YOU WILL BE COMPLYING WITH THE RULES/REGULATIONS SET OUT BY EQAO.**

If you plan on allowing students writing the Grade 9 Assessment of Mathematics to use the Desmos Test Mode iOS App on an iPad, iPhone, or iPod Touch, the EQAO provisions state that students must not be able to access the internet and must not be able to access other apps on the device.

My suggestion is that you:

- Put the device in How to use AIRPLANE MODE in ioS to ensure WiFi/Cell Data is OFF;
- Launch Desmos Test Mode; and,
- Use the What is Guided Access in iOS on iPad and iPhone accessibility feature included in iOS to restrict students to the Desmos Test Mode app.

By following the three steps above, you will ensure that you are following all of the EQAO Guidelines for the Grade 9 Assessment of Mathematics.

Personally, I believe that the free Desmos Test Mode app offers students a more intuitive way to leverage the features of a typical graphing calculator. I know that most of my students in grade 9 applied are hesitant to use the TI-83, simply because it is difficult to remember the series of steps necessary to achieve the graphical representation they are looking for. This can be more of a burden for struggling students than an asset.

I’m excited to see whether Desmos Test Mode has an impact on our EQAO Success Rates and to hear what the students have to say about the experience.

The post EQAO Guidelines Allow Use of @Desmos Test Mode App appeared first on Tap Into Teen Minds.

]]>A bunch of candies spill out on the table. Students will explore solving systems of equations to determine how many of each colour there are.

The post Counting Candy Sequel appeared first on Tap Into Teen Minds.

]]>Previously, the Counting Candy 3 Act Math Task that had students problem solving with fractions to determine how many candies each of four people should receive given the number of candies in 2/3 of the container. The Sequel extends this idea and asks students to determine how many of each colour are there using a **system of linear equations**.

While the original Counting Candy task may seem below the level of students who are expected to solve a system of equations, but I’d recommend doing the original task to add to the development of the question.

Supporting images:

**Act 2 – Solving a Single Linear Equation Version**

Not solving systems? Use this version for a single linear equation.

**Supporting image for Single Linear Equation**

**Act 3 – Solving a Single Linear Equation Version**

Not solving systems? Use this version for a single linear equation.

**Supporting Images:**

When I deliver the Counting Candies Sequel, I typically do the Counting Candies task first. It is a very low floor task that hooks students in and gives all learners a feeling of success prior to diving into solving Systems of Linear Equations. Once that is complete, we get the kids using inquiry and prior knowledge to solve the Counting Candies Sequel. When I give this task to teachers, they typically jump straight to algebra and start building a system of equations. However, when we leave students to their own devices, you’re likely to get something simple (and likely more efficient) than a system.

Here’s an exemplar of what a student might come up with prior to the introduction of systems of equations. This is a **GOOD** thing! We want students to build their confidence in math by proving that they can solve problems given their prior knowledge and intuition!

After discussing a solution like this, you might want to start making connections to algebra and consolidating by formalizing the idea of a system of equations and what must be done to solve it. Students have done this intuitively here, so now it could be easier for them to make that connection in the algebraic world.

Most teachers who have taught systems of equations will immediately recognize that a system will do the trick. However, in this case, it seems almost redundant to solve the problem with a system:

WOW. That was a lot of work when a student could solve it in 3 pretty basic steps.

So why would a teacher jump to a system when it could be done more efficiently using simple arithmetic/logic? Could it be that we have built the automaticity to quickly identify problems and match them with the procedural solution?

I don’t know about you, but I would much rather a ___________ (fill in with: student, employee, etc.) to select the most efficient solution for the task. Surprisingly, math doesn’t ALWAYS make things easier. However, a task like this makes it so much easier to then move to a situation where maybe the solution isn’t so easy to do without an algebraic system of equations.

Funny enough, following a procedure like in exemplar #2 can also make things more complex if we don’t stand back and think about the most efficient place to begin. Because we have two equations with an expression of *x + y*, we could skip some steps and immediately isolate *z*:

I hope that you find this task as well as the exemplars useful when you are trying to help your students begin working with systems of linear equations. I find it very helpful and even get students solving this task in younger grades just because they can!

You can access all the resources in a shared Google Drive folder here.

Or, download files individually here:

- Act 1 [VIDEO]
- Act 2 [VIDEO]
- Act 3 [VIDEO]
- Counting Candies & Sequel Slide Deck [KEYNOTE]
- Images [SHARED FOLDER]
- All Resources [SHARED FOLDER]

Click on the button below to grab all the media files for use in your own classroom:

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