There are candies on the table. How many candies should each of four people receive if you know how many there are in two thirds of the whole?

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]]>In this task, students see a bunch of candies poured on the table. How many candies should each of four people receive if you know how many there are in two thirds of the whole?

What’s the question?

In this case, we’re looking at:

How many candies should you receive if they are divided evenly amongst 4 people?

Students now know how many candies there are in 2/3 of the total. How many should each person get if the total is split amongst 4 people evenly?

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

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]]>This is just the beginning of what we believe to be an exciting project to redefine what it means to assess students in the 21st century - JOIN US!

The post Let’s Make An Online Assessment Tool That Rocks! appeared first on Tap Into Teen Minds.

]]>Back in January, with only a few days until semester 2 was set to begin, I was lucky to have come across a post by Jon Orr and a new idea he was going to implement to improve the assessment process in his classroom based on Alice Keeler’s original work around Levelling Up and Awarding Badges. I was quickly convinced that what Jon was aiming to do with his Google Sheet Skill Evidence Record could mean a huge step in the right direction for grading my own students.

Over the next couple of days, I had spent some serious time adding new features to the sheet for better tracking, opportunities to leave feedback, links to additional tasks for improvement, and functionality to write report card comments in one spot. These features have not only made my life easier, but have also encouraged my students to take responsibility for their own learning and strive for improvement like I have never seen before.

While our students can see a very detailed list of their progress through the course in an organized fashion, understanding how the formula-heavy Google Sheet works can be tricky. There is absolutely no programming or spreadsheet knowledge necessary to implement this assessment strategy, but the Master Assessment Sheet can be intimidating when you are unsure how it all works behind the scenes.

Recently, Jon and I were discussing our experience using the Google Sheet and came to the same conclusions: this assessment strategy has completely changed the way our students are responding in the classroom in a very positive way, however most teachers are overwhelmed when we try to show them how it all works.

Although the hours of planning, researching, and creating this dynamic Google Sheet to transform the way we assess our students has paid off in our own classrooms, we want to stretch this idea to a web-based assessment tool that is accessible for all teachers globally.

**But we can’t do it alone.**

We have a system that is more effective and more complete than anything offered by the assessment tools currently offered on the web. And, we want to do it for free. In order to make this happen, we are actively searching for a web programmer that can dream with us as we create a completely unique online assessment tool that teachers and students will love.

This online assessment platform will allow students and parents to login and clearly understand where they are having success and areas where they are not there yet. View an overview of student progress or view your growth over time related to a specific learning goal – it can all be seen with the click of a button. A student wishes to demonstrate their newly acquired understanding of a concept? They can upload their new work from any device to a specific learning goal for organizational ease and an ability to track growth over time.

Teachers will not only be able to track student progress by individual learning goal, assign mastery badges, provide feedback, and differentiated next steps for every student, while also being able to post resources for students and share course material with other teachers in the community.

This is just the beginning of what we believe to be an exciting project to redefine what it means to assess students in the 21st century.

Be sure to fill out our form below if you are a web programmer who is passionate about transforming assessment in education and are willing to embark on this incredible journey with us.

Check out what Jon has to say about this exciting opportunity on his site, Mr. Orr is a Geek!

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]]>Today, I experienced first-hand why I should not have been teaching math by talking during the first 8 years of my career. Let me explain why...

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]]>A few weeks back, I was reading a book called Teaching Minds (Kindle/Hardcover/Paperback or Audible Audiobook) by Roger Schank and really enjoyed it. As a Professor Emeritus at Northwestern University after his faculty experience at Stanford and then Yale, he is known for the quote:

There are only two things wrong with the education system –

- What we teach; and,
- How we teach it.

When I read great books on education, learning, or motivation, I will tweet out quotes that I may want to go back to at a later date. Today, during my grade 9 applied math lesson, I was immediately brought back to the following quote from Teaching Minds:

"Once you move to teaching large groups of 10 or more students, you must teach by talking and hope someone was listening." ~ Teaching Minds

— Kyle Pearce (@MathletePearce) March 25, 2015

It was this book that inspired me to completely break free from note templates that I had been making for my students to complete on their iPad. I consider them pretty nifty and are more interactive than what you’d think of when someone says “worksheet“, but I realized that much of it was me scaffolding them along and that can quickly turn to disengagement and even just “copying” once it goes up on the screen.

Today, my students were working on Dan Meyer’s Hot Coffee 3 Act Math Task to introduce the volume of a cylinder with my goal being that we show the **interconnectivity of math** by connecting this **new knowledge** to **prior knowledge** involving proportional reasoning. What I’ve taken away from Teaching Minds and other books like Make It Stick that discuss interleaving with spaced practice is that **students learn by doing – not by listening**. While this might be difficult to deconstruct in certain subjects that are content heavy like Geography or History, it seems fairly obvious in math class. As I’ve outlined in a recent post called The Two Groups of Math Students I Created In My Classroom, I spent the better part of my career rewarding students who could memorize through mass practice, rather than rewarding them for being good at math.

It can be difficult to convince math teachers that scrapping a formal note that outlines definitions, formulas and an extensive list of examples if I expect them to “get through the curriculum”. After all, many students are successful when lessons are delivered primarily in a lecture format where a note is given and students sit back passively listening to the teacher while copying down the important points. But how many of us have actually engaged in some serious thinking about what made those students successful? Was it because they copied a note and listened to you? Unlikely.

I’ve learned to be pretty honest with myself when it comes to reflecting on my lessons. When my lesson sucks, I know it and am not ashamed to say it. Thinking back to my days delivering a traditional note as mentioned in the previous paragraph, my successful students were those who did their homework and crammed the night before a test. Those who were not successful, likely did neither. Sure, firing off a couple examples would help some make connections, but how did they do when it came to problem solving questions that appeared to be unfamiliar? Not so great.

Listening is tough. It is even tougher when you don’t care about what you’re listening to. When strong students seem engaged in your lesson, it is more likely the need to get the note down and maintain a high average that is motivating them rather than the words coming out of your mouth. For struggling students, they learned long ago that school isn’t so bad when you aren’t paying attention. Many would say that today’s generation has a lot more Attention Deficit Disorder (ADD), while I believe they just aren’t afraid of teachers or parents anymore and don’t feel a need to comply. That isn’t a bad thing, either.

I have ensured that each and every class this semester has focused on students solving problems through discovery/inquiry, connecting them to new learning goals, and finding ways to extend them to a variety of other concepts in the course. There is not a whole lot of direct instruction coming from me and the kids are doing great. Now that I’m not up there for 75 minutes talking while oblivious to who is or is not paying attention, I can tell quickly when students are not listening. Only once or twice a class do I ask them for 50 seconds of their time (even though it is for more like 5 minutes) and during that time, I tell students to stop and have their eyes on me. Wow, do they struggle with it. I typically have to individually ask certain students for “eyes up” and by then, the ones who were looking are now looking through me and a few others are now starting to lose focus.

Today, I wanted to clarify an issue that every student in the classroom was having. The question was an extension that Dan Meyer provided with the task:

If you were going to try to triple the Gourmet Gift Basket worlds largest coffee record, what kind of coffee cup would you have to build?

Since the students had to convert the volume of 269.255 cubic-feet to approximately 2010 gallons, every student had substituted 2010 in for V in the volume of a cylinder formula. Usually, I talk with a small group of students who are working collaboratively, however I thought I could save some time and address the whole class.

So I started:

Ladies and Gentlemen,

After circulating the room, it appears that we are all having a similar issue. Can you all stop for 50 seconds and look this way…

I went on to ask students what had gone wrong and when there was nothing, I thought this is a great spot for some direct instruction. I explained why using gallons was not possible and that they should use their measurement in cubic-feet and sent them on their way.

I then began walking around again to each group and quickly realized that none of the students had made the adjustment. So, I discussed it with the first group and they were off. Went to the next group and explained it again. The third… and so on. It actually took a matter of 10-15 seconds talking with groups individually and they were off to the races.

What I realized rather quickly today was that speaking to a large group appears to be the most efficient method, but it actually hurts more than it helps. After taking about 3 minutes to explain the gallons/cubic-feet issue, there were literally **zero** students who had absorbed what I had said at the front of the room and yet each student understood in under 20 seconds when I spoke to them directly.

Today, the lesson I learned about learning by doing instead of listening was much more important than the lesson my students learned about volume of a cylinder. In order for me to ensure that I won’t forget it, I thought I should probably apply my own advice of “learning by doing” somehow.

And now, you’re reading it.

The post We Can Teach By Talking, But Are They Listening? appeared first on Tap Into Teen Minds.

]]>Creating Your Own Interactive Content WITHOUT Bookry Many educators using iPads as a tool in their classrooms are turning to iBooks Author to create interactive multi-touch books that bring life and enjoyment to learning. iBooks Author is filled with many great tools and widgets to embed photos, video, self-assessment tools, and many others to load […]

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]]>

Many educators using iPads as a tool in their classrooms are turning to iBooks Author to create interactive multi-touch books that bring life and enjoyment to learning. iBooks Author is filled with many great tools and widgets to embed photos, video, self-assessment tools, and many others to load teachers up with tools to improve learning in the classroom. For those looking to reach beyond the default widgets in iBooks Author, there are companies like Bookry who have made it easy to include all kinds of other interactive widgets in your multi-touch interactive content created for iBooks.

But what if iBooks Author and Bookry don’t have what you’re looking for? Hack a widget yourself!

While it might seem a bit scary at first, I will help provide you with the steps to do what you want to do in your interactive multi-touch books created in iBooks Author. You heard me correctly; the teacher who is against teaching students steps, procedures, and algorithms without a deep conceptual understanding is going to make an exception just for you. Let’s be honest – it is unlikely you are interested in building an iBooks Author Widget empire. Rather, you’re looking for a quick way to get your multi-touch book to do what you want.

Let’s get started!

Download the iBooks Author Hacked Widget Template to your harddrive.

Extract the zip file. You should see a file with the extension .wdgt

Right-click on the HackiBookWidgetTemplate.wdgt file and select **Show Package Contents**.

You should now see the contents of the widget:

Don’t worry, you don’t have to do much from here.

Open **main.html** in TextEdit. You should see some HTML Code. Don’t worry, nothing for you to do here. The file should have the following content:

All you need to do is paste the embed code from YouTube, Padlet, or any other website that allows you to embed code on a website.

Paste the code under the line that says *INSERT YOUR IFRAME / EMBED CODE HERE* and save the file.

Now, just replace the default.png image with the photo you’d like displayed in your interactive multi-touch book and you’re set. Be sure to keep the file named default.png or else it will not work.

Drag it into your iBooks Author file and you’re all good! Note that you can only test the widget by previewing your iBook.

How’d it work out for you? Did I miss something? Please let me know in the comments!

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]]>Jump into another Explain Everything Math Learning Journey. This time, we explore opposite angle theorem and interior/exterior angles of a triangle!

The post Explain Everything Angle & Triangle Journey (Part 2) appeared first on Tap Into Teen Minds.

]]>Yesterday, I posted about my first attempt at creating an Explain Everything Math Learning Journey by providing students with an Explain Everything Project File with some questions intended to have them discover some angle theorems. We began the journey today and I hope that we will have some video footage to share in the coming days. The student iPads did not have an updated version of Explain Everything which made it a bit more difficult to navigate, but we should be good to go with a little practice using the app.

Just as we did with the first EE Learning Journey, my hope is for students to create tutorial videos that explain what they have discovered along the way to share with a global audience. My thinking is that we can take some topics that can tend to be dry (i.e.: HS Exterior Angle of a Triangle Theorem) and make the learning experience more engaging and enjoyable.

This new Explain Everything Learning Journey explores the Angle Sum of a Triangle and Exterior Angle of a Triangle with moving angles that students can use to help them “prove” their discovery. Check out the new project file, a quick exemplar video (sorry, it is SILENT…) and some screenshots from the Explain Everything Math Journey.

The post Explain Everything Angle & Triangle Journey (Part 2) appeared first on Tap Into Teen Minds.

]]>This Explain Everything Math Learning Journey sends students on an inquiry/discovery interactive task where they record their findings along the way.

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]]>*Wed Apr 8, 2015* – The Explain Everything Project File has been updated to correct an error.

The Geometry portion of the grade 9 applied course is one that I have always struggled to make meaningful for my students. The curriculum has students exploring angle theorems, but really never goes deep enough for finding these angles to be interesting or useful. While I’ve spent a significant amount of time trying to improve other areas of the course, this is one that I haven’t moved forwards as much as I would like. It probably doesn’t help that I usually teach this portion of the course last when everyone (including myself) is pretty burnt out. With the spiralled approach I’ve been taking this semester, I have been focusing a lot of attention to this portion of the curriculum with some high hopes for more opportunities for inquiry and curiosity.

Here’s a video summary of what I’ve created in Explain Everything for a portion of my lesson tomorrow. Feel free to jump down to screenshots if you’d prefer.

In order to allow students to do some exploration, I have created an Explain Everything project file that is preloaded with slides for students to work on like you see below:

Students are prompted to find some angles using a transparent protractor. They are later asked to record their solutions and justify as if they are creating their own tutorial video. I have *tried* to get my students to create tutorial videos in the past, but always found that there is a much steeper learning curve than I had anticipated – especially when dealing with secondary students. In order to scaffold students to a place where they are more comfortable creating their own videos from scratch, I am hoping these project files will slowly move them closer to gaining some confidence recording their thinking.

Throughout the Explain Everything project file, students are encouraged to ditch the protractor by finding rules (or theorems) that could help them save time and effort. This is my whole focus on inquiry – to get students to want the more efficient method.

At the end of the exploration, the “New Browser” option in Explain Everything allows me to embed a web browser right inside the project file. In this case, I’m going to try a Socrative multiple choice assessment that students will include in their screencast video to promote consciously verbalizing why they are selecting each response.

My hope is that students will not only make connections related to angle theorems, but I will also gain some insight as to how deeply each student understands the concepts. Often times this portion of the course can have students jumping to solutions without clearly communicating their thinking. Are they on track or are they simply guessing/estimating? If that isn’t enough, I’m hoping this will be a great screencasting ice-breaker for my students moving forward. With the progress we are making due to the spiralling of content, it is my hope that students will have some time at the end of the semester to compile their own MFM1P Grade 9 Applied Tutorial Resources site that students around the world can access.

Grab the project file here and Explain Everything on the App Store.

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]]>An Example of Tricks and Quick Fixes Leading to a Dead End Recently, my students were just starting their weekly assessment that interleaves/spirals our math learning goals from the year. The first problem was taken directly from an EQAO Standardized Test open response release question about unit rate: My students have been working with ratios, […]

The post Why We Must Model The Interconnections in Math appeared first on Tap Into Teen Minds.

]]>Recently, my students were just starting their weekly assessment that interleaves/spirals our math learning goals from the year. The first problem was taken directly from an EQAO Standardized Test open response release question about unit rate:

My students have been working with ratios, rates, and proportional reasoning delivered in various contextual problems throughout the year including some unit rate problems sprinkled in. As soon as my students began solving this problem, they went straight for the strategy that they’ve likely been using since grade 6 and the strategy that I used to teach for years – division. While division does work, it is only useful when there is an understanding of “why” and I find that most struggling students (and even some strong students) are unsure of that “why”.

Here’s what I witnessed most students doing at their desks:

This is a fairly common mistake I see often when students are dealing with unit rate and comparing the best deal. The worst part is that it isn’t even a mistake at all – students can use this information to solve the problem. The issue here is that students aren’t sure what the result represents relative to the problem. What students have found is the number of oranges you can purchase for $1, which is definitely a unit rate! However, most students believe what they have found is the cost per 1 orange.

In Ontario, students in grade 9 applied have difficulty using proportional reasoning skills and I can understand why. Proportional Reasoning is one of five strands in the Ontario Math Curriculum and a common trend I have noticed is that once it is completed, it is not intentionally addressed with other strands throughout the school year. Textbooks commonly silo topics into sections and units to suit the organizational needs of the teacher, while hurting the learner in the process. It is also common to think that re-introducing topics will derail the entire lesson that was intended to introduce a new concept.

Only recently have I intentionally been spiralling content to re-introduce concepts that students haven’t used recently. This definitely does do a bit of derailing, but if that is the case, doesn’t it mean that students do not have a deep understanding of the concepts? Rather than avoiding topics that students struggle with like fractions, proportions, or calculating percentages, why not show students how all of these topics are actually interconnected? By avoiding the use of these seemingly difficult concepts whenever possible and substituting their use with tricks, rules, and algorithms, students are sure to hit a wall at some point.

Using division alone to find unit rate is a trick that can cause problems like I witnessed in my classroom. This does not mean that students are discouraged from using division, however if they cannot explain why they are doing what they are doing, then a red flag goes up. Rather than simply having them divide because “that’s how you do it”, why not build a deeper conceptual understanding and also gain some practice working with proportions at the same time? What students have ultimately done in the example above (without knowing it) is this:

Digging deeper here, if we think ahead to graphing relationships with independent and dependent variables, we can see that the student has opted to use the independent variable in the numerator. When we get into rates of change and slope of linear relations, students will need to find the difference in the dependent over the difference in the independent. It might be beneficial to help students make this connection early when working with rates to avoid this misconception altogether.

By focusing on identifying the independent and dependent variables, students can determine that we are likely more interested in how much (dependent) per 1 orange (independent) than the other way around.

Using proportions on a regular basis for direct variation linear relationships not only strengthens student ability to work with proportions, but also sets them up for success when they begin finding unknowns using a table, graph, and equations. Let’s not forget that we are ultimately working with fractions as well; something I think all students could benefit from.

I will also mention that using a proportion should be more than cross-multiplication. Similar problems that prompted me to write this post when dealing with unit rate will also come up when students are instructed to multiply across an equal sign and divide. Again, I did it for the majority of my career, but I now realize that this is only a trick that will be forgotten or butchered in the future.

What this post ultimately means for us as math teachers is that our job will be more difficult. For years, I depended on tricks to make math easy for students and was always considered a “good teacher” because of it. Unfortunately, what I was really doing was making students believe that they were good at math when they were really just good at remembering my tricks and catchy ways of teaching them.

The post Why We Must Model The Interconnections in Math appeared first on Tap Into Teen Minds.

]]>Dive into a bag of Doritos Roulette and determine whether there are really 1 hot chip for every 6 regular chips like the image on the bag suggests.

The post Doritos Roulette: Hot or Not? appeared first on Tap Into Teen Minds.

]]>Today, I was finally able to record some footage involving the mysterious Doritos Roulette chips when I was working with some colleagues from Tecumseh Vista Academy. If you haven’t heard of the new Doritos flavour, here is the commercial:

Special thanks to: Joey Demarse, Dan Frezell, Diane Gardin, Craig Guthrie, Jeff Hillman, Dee Kruc, and Justin Levack for volunteering to eat a bag of chips with me while I recorded the footage.

Show your students this video:

**What questions come to mind?**

Some questions students might have:

- How many doritos in a bag?
- Is the ratio of “hot to not” chips really 1:6 or 1 out of 7?
- How many hot chips should you expect in a bag?

Some student exemplars from my first go with this task:

- Clayton Edwards shared some resources and student exemplars.

Let me know in the comments what you did with this task and how it turned out!

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

The post Doritos Roulette: Hot or Not? appeared first on Tap Into Teen Minds.

]]>There are two groups of students I used to see forming in my math classroom and my teaching & assessment practices were the main reason why they formed.

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]]>Check out a recent talk I gave in regards to the two groups of students I used to see forming in my math classroom each year or jump to a written summary:

When I was in school, I can remember a distinct lesson framework that I could recognize in most every math course:

- Take up homework;
- Learn New Definitions, Formulae, Procedures/Algorithms;
- Do a bunch of examples; and,
- Do a bunch of homework problems.

It seems only natural that teachers would likely deliver the math curriculum in a way familiar to them such as the way they were taught.

If we open a textbook, it won’t take long to figure out that many of them follow a similar format. More recent releases also tend to include an investigation or activity to try and address the inquiry/discovery requirements of many curriculum expectations, but the activities are written in a series of steps and without much to pique student curiosity.

Because much of my teaching looked something like what I’ve described above for the first 8 years of my career, I noticed that there were two groups of students forming in my classroom: those who are good at math and those who are not. Even though nobody said it, most students would probably identify themselves as being in one of those two groups if asked by a teacher, parent or friend.

I would typically consider students in the **Good at Math** group those who know:

- terminology, definitions, math language; and,
- procedures, steps, algorithms.

While students in the **Not Good at Math** group tend to have neither.

I need to be really careful here because I don’t think we intentionally aim for students to only be proficient in these areas, but it would seem that most math classrooms tend to assess based primarily on these particular skills.

Digging deeper here, I feel as though what many math classrooms are really assessing are those students who are **Good at Memorization** and those who are **Not Good at Memorization**.

I know that there are some folks out there who really deeply understood the math when they were learning it in high school, but I was one of the many who learned to play the memorization game early and played it well. Students in the **Not Good at Memorization** group are typically those who are **unable** OR **unwilling** to play that same game.

My thinking here is that if you’ve ever thought that studying the night before a test to be successful in math class was the difference for some of your students, then maybe the same two groups have formed in your own classroom. Only recently have I realized that if a student cannot come into my classroom and problem solve without being notified (i.e.: told to cram the night before), then they may not really know what they’re doing and are unlikely to retain whatever knowledge they have familiarized themselves with for use later.

While it would appear that these groups are completely independent of each other, there is something that most students in both of these groups have in common. In my experience, most students in my classroom tend to **struggle with problems that are unfamiliar**.

I would tend to create assessments with problems that looked fairly similar to those we had explored throughout the unit and then toss one or two “challenging” problems at the end. When I really thought about it, the problems that I had selected to supposedly challenge my students were actually problems that didn’t follow a predictable series of steps or procedures. Essentially, they were problems that students could not memorize from their notes and thus could not manage to solve based purely on familiarity.

Over the years, I have had some students claim that I was being unfair (or insert a variety of other expletive adjectives here) because I had not “taught” them how to do these problems. For quite some time I thought that maybe the students were right. If I clearly set the rules of the game as “memorization” for the majority of my assessments, then is it fair for me to change the rules of the game with 2 minutes left in the 4th quarter?

So I agree that it is unfair to switch the rules late in the game, but also think that solving unfamiliar problems is what math is really all about. Unfortunately for my students, I am now trying to make my assessments more about problem solving rather than reproducing the steps, procedures and algorithms. Don’t get me wrong, I still need students to meet the expectations of the course, but I am trying to emphasize as many unique situations as possible to avoid students falling back on familiarity and “cramming” to assist with retention issues we commonly see over the mathematics learning continuum.

This semester, I have begun assessing my students each Tuesday and the questions relate to any learning goal we have studied previously in the course. Students are not warned what learning goals will be addressed as I want to identify where students are and where we need to improve. If a student struggles on a learning goal, it is indicated in their Skill Evidence Record and they are invited to re-address that learning goal when they are ready.

My hopes are that making some changes to my assessment practices as well as continuing to make tasks contextual, visual and concrete while also promoting the natural interconnectedness of mathematics will help me redefine what it means to be “good” at mathematics and to also maximize the number of students that can join that group when ready.

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]]>Jump into a Desmos Math Journey to explore three of the four Representations of Linear Relations: Tables, Graphs and Equations using this investigation.

The post Desmos Math Journey: Representations of Linear Relations appeared first on Tap Into Teen Minds.

]]>Just recently, I have really been extending the effectiveness of inquiry/discovery based learning in my classroom by having students work at the whiteboards around my room. Students in grade 9 applied math are usually disengaged in math class because they have likely struggled with mathematics in elementary school. While I’m thoroughly enjoying the learning environment and collaborative culture that is developing in my classroom, I also want to ensure I give students access to some great explorations that may not be so easy on a blank whiteboard.

After recently checking out Michael Fenton’s “Match My Line” activity and seeing an innovative way to break an investigation down into a series of Desmos graphs by Jon Orr, I thought I’d try to do something similar with linear relations:

In the activity, students begin using their understanding of linear relations and constant growth to determine missing values in a table:

After students have found the missing values in the table and plotted those points, they can now begin using the sliders for ‘m’ (slope/rate of change) and ‘b’ (initial value). It is important to note here that I will not discuss what these values are – that’s why we’re doing the investigation. Hopefully, as a group, we can consolidate later and settle on what these values might be called based on their characteristics.

Students can then write their equation. While this is a bit redundant, I want to expose my students to as many tools throughout the investigation as possible as this is the first time we are using Desmos this semester. They are also asked to write an explanation/reflection to see if they can recognize what ‘m’ and ‘b’ really do and where we can find them in the table.

After they have completed the first part, they click on the link and move on to the next portion of the Desmos Math Journey:

Click on the graph below to start this Desmos Math Journey:

Here are some direct links to each of the six parts:

Toss the links in the comments!

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