Introduce exponential notation with a question: Which would you rather - $1 Million or a Penny a Day, Doubled for a Month? A 3 act math task for exponents.

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]]>In Ontario, exponential notation is introduced in grade 8 in order to pave way for topics such as area of a cirlce and Pythagorean Theorem. As students reach secondary, exponential notation becomes increasingly more important as more complex functions are introduced in each course. Recently, I had a number of teachers emailing me for an interesting 3 act style problem to introduce exponents. While Double Sunglasses by Dan Meyer and Dark Side by Jon Orr are two great tasks involving exponents, I’ve found that they can be pretty difficult for students in grade 8 to wrap their heads around when they are just being introduced to exponential notation.

I think many are familiar with the Wheat and Chessboard Problem and some have even taken their own spin on that to make it more relevant to current times. Dave Bracken from my previous school, Belle River District High School used to tell students a story that went something like this:

I was speaking with your parents last night and they were all complaining that you weren’t doing your chores around the house. After some brainstorming, we came up with an offer for you. If you do your chores every day for the next month, your parents will give you $10,000 or a penny on the first day total, two pennies total on the second, four on the third, and so on. Which would you pick?

So while the story alone will lead to a pretty cool introductory task, I thought I would try to put something together that might help with the delivery and hook.

Here’s a good starter to lower the floor and get kids talking. My expectation is you shouldn’t require more than 10 minutes for this quick minds on.

Show students this video.

This can be some interesting discussion because the video does not give you details for how long. When would one be better than another? What if this was for the rest of your life? Does that change things?

Show students this video.

Or, here’s a screenshot:

Now, students are given the question:

How long will it take before the penny a day is your best option?

My expectation is that it won’t take students too long to realize that there are 1,000 pennies in $10, so you may not even need to show the Act 3 Video.

Or the screenshot:

Now, the scenario gets a bit more complex. However, I would suggest using this task again more for discussion and not spend much time on it.

Even though there is an Act 1 video (here), I might recommend jumping straight to the question by showing the Act 2 video.

Or the screenshot:

So students are now confronted with this question:

How long before the “penny doubled” option is best?

*You may want to reiterate that students are getting one penny on the first day, then the original one penny turns into two pennies on the second day, it turns into four pennies on the 3rd day, etc.*

Again, students will probably figure out pretty quickly which option is best.

Now, show the Act 3 Video.

Screenshot:

In just over a week, students will begin to benefit from the penny doubling option.

As mentioned previously, tasks 1 and 2 were created as a way to get kids thinking, talking and discussing. Now, we move on to the new learning goal we intend to hit: introducing the need for **exponential notation**.

Start off by showing the Act 1 video.

Screenshot:

In Act 1, students are asked:

Would you rather take $1 Million or the “penny doubled” for a month?

*Again, reiterating that students are getting one penny on the first day, then the original one penny turns into two pennies on the second day, it turns into four pennies on the 3rd day, etc.*

I’d try to let kids get going on their own at this point, even without showing Act 2.

If some students are struggling to get started, you may choose to give students the visual provided in the Act 2 video.

Check out the answer here.

Screenshot:

Show students this video.

Or, the screenshot:

After a short amount of thinking time, we introduce the idea of **exponents** and **exponential notation** for the first time using a direct instruction approach starting with this act 3 video.

Screenshot:

So, give it a shot and let me know how it goes in the comments!

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

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]]>Man. Time FLIES! I feel like it was just yesterday when I made a commitment to myself to do a “Week In Review” series that summarized what I had been up to in the classroom each week. I had all the momentum on my side up until week 6, but then I was off to […]

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]]>Man. Time FLIES!

I feel like it was just yesterday when I made a commitment to myself to do a “Week In Review” series that summarized what I had been up to in the classroom each week. I had all the momentum on my side up until week 6, but then I was off to Norway for the NORCAN Project for over a week. Talk about falling off the wagon hard!

Then, we hit the busy “before Christmas Break” stretch. I spent a much enjoyed chunk of time with my family over the holidays, but next thing you know and we’re at the end of our first semester with the EQAO Assessment of Mathematics standardized test wrapping things up. Can’t believe it.

If that isn’t enough, I’m just now *finally* getting around to posting my first blog post for the 2016 #MTBoS Blogging Initiative when I should already be wrapping up my second. Yikes!

Well, enough excuses. Let’s get to it!

In the first blogging challenge, we were able to pick between two options:

I’ve decided to talk about **One Good Thing**.

I picked the first option because it is so easy to focus on one or two negative experiences through each day and completely miss all of the positive we could be enjoying instead. This is especially true for me at this time of year when I’m completely exhausted physically and mentally as I try to “fix” mathematics education with another group of students. Many who know me are well aware of my passion (addiction) to creating math tasks, trying new ideas and sharing innovative strategies for use in the math classroom. However, only a handful of people know how I get when I haven’t reached every learner in my classroom. My wife knows when it is EQAO time because I get extremely down on myself when I haven’t found a way to inspire a student to want to maximize their potential in math class. I think all teachers feel this same sense of disappointment. But for me, I struggle letting it go. As one who constantly promotes the idea of learning from failure and celebrating that experience, I seem to be the one who needs the advice most.

I know what you’re thinking: “I thought this was supposed to be One GOOD Thing?”

Don’t worry. It is.

For the first time in my 10 year teaching career, I feel like I have finally identified that this negativity is a problem and I am working to confront it as such.

In order to use my own advice and learn from failure, I spent a lot of time over the past couple of weeks thinking about some of the good things that happened this semester as well as some of the things I’d like to improve. I could probably write a book about all of the tweaks, modifications and complete revamps I would like to make as I prepare to enter second semester, I think my One Good Thing could be summed up in one word: **balance**.

Everything in this universe comes down to balance and I don’t think learning (or teaching) mathematics is any different. These past few years I have really been stretching my thinking beyond direct instruction and a largely lecture-style approach. While my assessment would say that my students and I both enjoy math class much more, I also think that it is easy to shift too far to one side. For the first 8 years of my career, I was of the belief that direct instruction was best. After some great learning at conferences, these past two years managed to shift my beliefs to include inquiry/discovery learning. However, my attempts to get better at teaching with an inquiry/discovery approach has led me to almost banish direct instruction from my classroom completely. It wasn’t something I intended to do, but it happened. However, there is a place for both direct instruction and inquiry based learning and I realize this is an area I need to work on.

One of the most challenging questions we as math teachers get to wrestle with is when to use each approach for the greatest effect on learning. After much thought in this area, I believe that there is no right answer.

In my case, this shift in thinking has made me try to envision a math classroom where I hope to better combine the use of the inquiry process when introducing a topic and direct instruction when consolidating a topic.

I’m excited to dive in and share how things go by the end of next semester.

I just hope someone is nice enough to remind me of what I always say about failure.

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]]>Convenient & FREE Practice Options For Your Students A few folks were interested in the Free EQAO Practice via Knowledgehook’s Gameshow tool, but felt they didn’t have the time to experiment with a new tool during “crunch time” in the semester. I know the feeling! Now, Knowledgehook has made it easy for students to practice […]

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]]>A few folks were interested in the **Free EQAO Practice** via Knowledgehook’s Gameshow tool, but felt they didn’t have the time to experiment with a new tool during “crunch time” in the semester. I know the feeling!

Now, Knowledgehook has made it easy for students to practice any Gameshow independently without any setup, registration, or other hassles.

- Student go to a simple website address to play the gameshow.
- They receive instant feedback.
- Done.

This is a great way to give students the option to practice what they need to work on in a fun, interactive way.

When students access Knowledgehook Gameshow activities via a link instead of through the website, there are some drawbacks including:

- Upload solution is disabled since they are playing without an account.
- Teacher cannot track student progress.
- Students cannot reflect on the work they have done because once they close the link, the information is lost.

So, in my opinion, I would go with teacher and student accounts, however if you are in a time-crunch at the end of the semester, this is still a great way to offer students an additional way to prepare for the EQAO Grade 9 Assessment of Mathematics.

Share the following useful links with your students. Jump to grade 9 academic or grade 9 applied content.

EQAO Release Material From Previous Years:

Content By Course Expectation/Learning Goal:

- NA2.01 Simplify numerical expressions involving integers and rational numbers
- NA2.03 relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations
- NA2.04 Add and subtract polynomials with up to two variables, using a variety of tools
- NA2.05 Multiply a polynomial by a monomial involving the same variable, using a variety of tools
- NA2.06 Expand and simplify polynomial expressions involving one variable

EQAO Release Material From Previous Years:

Content By Course Expectation/Learning Goal:

- NA1.01 Illustrate equivalent ratios, using a variety of tools
- NA1.02 Represent, using equivalent ratios and proportions, directly proportional relationships arising from realistic situations
- NA1.03 Solve for the unknown value in a proportion, using a variety of methods
- NA1.04 Make comparisons using unit rates
- NA1.05 Solve problems involving ratios, rates, and directly proportional relationships in various contexts, using a variety of methods
- NA1.06 Solve problems requiring the expression of percents, fractions, and decimals in their equivalent forms

Need more practice? Let me know in the comments and I’ll add more!

The post Grade 9 EQAO Math Practice Links for @Knowledgehook Gameshow! appeared first on Tap Into Teen Minds.

]]>This 3 act math task is a great way to introduce the concepts of parallel and perpendicular lines with context by using two graphing stories that produce distance-time graphs.

The post Walk Out Sequel feat. @Desmos Activity & @Knowledgehook Gameshow! appeared first on Tap Into Teen Minds.

]]>This 3 act math task was created using video clips from the Walk Out 3 Act Math Task as a way to get students wondering about parallel and perpendicular lines. Here’s the expectation from the grade 9 academic course in Ontario:

- AG2.04 – identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicularity), using graphing technology to facilitate investigations, where appropriate.

After spending some time asking folks on Twitter about how they introduce the concept of parallel and perpendicular lines, I found that we were all doing something pretty similar.

To investigate parallel lines:

- Give students two lines with the same slope in slope/y-intercept form;
- ask them to graph the lines; and,
- ask them what they notice.

The process was pretty similar for perpendicular lines:

- Give students two lines with negative reciprocal slopes in slope/y-intercept form;
- ask them to graph the lines; and,
- ask them what they notice.

After students complete the two investigations, a consolidation would take place. I’ve been doing something similar to this for about 10 years and while it does appropriately address the parallel and perpendicular portions of the expectation through investigation, it felt more like I spoon fed the investigation a bit too much.

While it is pretty easy to find a contextual situation where comparing two parallel lines makes logical sense, I really struggled to find a useful case for comparing two perpendicular lines. You can compare the linear relations representing the cost of two different taxi companies as parallel lines, but it makes absolutely no sense if you try to make a case where the linear relations are perpendicular.

When distance-time graphs came up in my course, I created the Walk Out tasks and finally found a way to at least spark the conversation about parallel and perpendicular lines.

Here it is:

Show this video.

If you have already used the Walk Out 3 Act Math Task with your class, you could probably just show this image:

Ask students what they wonder? What questions come to mind?

Write down some of the questions/ideas that students share.

Hopefully one or more students come up with something like “are they perpendicular or not?”

Once sharing out those questions that come up as a group, I ask them:

Are the lines parallel, perpendicular, or neither? How do you know?

I give them a minute to discuss with their groups.

In grade 9 academic, it might be a good idea to ask the group what it means for two lines to be parallel or perpendicular. What does it look like? What are some examples? This is the first time those concepts come up in the math curriculum in Ontario, so I never assume everyone has an understanding.

**Teacher Move:** It should be noted that my intention with the video/image is that the lines do *appear* to be perpendicular, but the scale on the x- and y-axis’ are not equivalent. This gives the viewer the impression that the lines are parallel, but as you’ll see in the next few videos/images, they are not.

After allowing students to argue it out a bit, I play this video.

Alternatively, here’s the image:

Then, I show them this video to give a bit more information.

Give students more time to discuss and share out. I usually ask students to share out who feels confident in their original guess and who wants to update their prediction.

Now, I play this video.

Alternatively, here’s the image:

Here are a couple more videos you might want to show as they change the scale to 1:1, but aren’t necessary:

While many math teachers have been using the very powerful Desmos Graphing Calculator, the new Desmos Activity Builder is an awesome way to leverage the power of Desmos in a more structured activity. In the past, creating an activity using multiple Desmos graphs involved linking a series of graphs from one to the other. Took quite a bit of time and planning. Now, creating an interactive Desmos Activity takes only a few minutes and it is easy to share with your students and colleagues.

Or, make a copy of the activity so you can edit to your liking!

Here’s some screenshots from the Desmos Parallel and Perpendicular Lines Activity Builder Activity:

After students finish the Desmos Activity Builder Activity and you’ve taken some time to consolidate the new learning about parallel and perpendicular lines, students can now work on some practice to reenforce the new learning. Check out a Knowledgehook Custom Gameshow that I created with some practice questions related to parallel and perpendicular lines:

Or, just try out the gameshow yourself.

*Note that if you run this Knowledgehook Gameshow with a class account, students have the ability to upload solutions which you can then share via the projector in real-time. The only way to go if you choose to run the activity in class.*

Here’s all the links in one convenient spot for this activity to go off without a hitch:

Act 1 [video]

Act 2 [scene 1 video | scene 2 video]

Act 3 [scene 1 video | scene 2 video (optional) | scene 3 video (optional)]

YouTube Playlist [All Videos]

Desmos Activity Builder [Try It | Copy It]

Knowledgehook Custom Gameshow [Try It | Copy It]

Make sure to leave a comment if you try out the task! Would love to get some tips on how to make this better.

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]]>Extending the concept of solving systems of linear equations, here are contextual tasks for practicing solving algebraically with substitution & elimination

The post Piling Up Systems of Linear Equations appeared first on Tap Into Teen Minds.

]]>There has been a lot of requests for more contextual and/or 3 act math tasks related to solving systems of linear equations when I work with teachers. A big realization I’ve come to this past year is that making students curious with contextual tasks doesn’t necessarily have to involve a relevant question. Dan Meyer has discussed it multiple times (like here and here), but it still takes a lot of reflection to start identifying what is important when trying to hook your students in.

Continuing the series of Tech Weight and the Tech Weight Sequel, we take the same context of weighing random items to give us some additional practice. You’ll quickly notice that these tasks are definitely **contrived**, but I still find tasks like these useful if introduced as a challenge to my students. Even though they REALLY don’t care how much each item weighs, they DO enjoy the challenge of solving the problem. The media and 3 act format gives them an easy entry into the task. After allowing students to intuitively solve simple systems of linear equations like in the Counting Candy Sequel or the Tech Weight Sequel, you can use these tasks as a way to practice substitution and/or elimination as a way to solve algebraically.

Show students this video.

Ask students what they are wondering? What questions come to mind?

After discussing with a group, help direct the focus to the question:

How much does each weigh?

Students can make predictions and argue why they believe their guess is best.

Show students scene 1.

Alternatively, you can show students the following images:

The weight of 4 bottles of glue and 5 glue sticks is 679 grams.

The Weight of 3 bottles of glue and 12 glue sticks is 680 grams.

Now, students can try to solve this system intuitively, by graphing or algebraically with substitution or elimination.

Show students the solution video.

Alternatively, you can show students these images:

The weight of one glue bottle is 145 grams:

The weight of one glue stick is 21 grams:

At this point, your students should notice that their answers are close to these weights, but not exact.

Why might that be?

What extraneous variables could influence the results?

Show students this video.

They will already know the question, so move on to Act 2…

Show students scene 1.

Alternatively, you can show students the following images:

The weight of 13 pens and 5 packs of correction tape is 166 grams:

The weight of 6 pens and 3 packs of correction tape is 88 grams:

Now, students can try to solve this system intuitively, by graphing or algebraically with substitution or elimination.

Show students the solution video.

Alternatively, you can show students these images:

The weight of one pen is 4 grams:

The weight of one package of correction tape is 20 grams:

Again, the actual weight may differ from what students found algebraically.

I find that sequel tasks like these often don’t require the “hook” as we’ve already engaged the learners to come towards the math. This task is simply additional practice prior to moving on to more traditional word problems and/or abstract problems. Thus, there is no act 1 video for this extension task.

Show students scene 1.

Alternatively, you can show students the following images:

The weight of 5 large notepads and 7 small notepads is 882 grams:

The weight of 3 large notepads and 5 small notepads is 563 grams:

Now, students can try to solve this system intuitively, by graphing or algebraically with substitution or elimination.

Show students the solution video.

Alternatively, you can show students these images:

The weight of one large notepad is 116 grams:

The weight of one small notepad is 43 grams:

Again, the actual weight may differ from what students found algebraically.

Try it out and let us know how it goes in the comments!

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]]>We are back to weighing laptops and iPads. You're given the weight of 3 different piles of technology. How much does each item weigh?

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

]]>Recently, I’ve shared a few tasks related to linear relations with a push to explore multiple strategies including simple systems of equations. The intention of this post is to take students from working with partial variation linear relations to systems of linear equations.

While I’m excited to share the sequel to the Tech Weigh In task, I think it is important that you explore some of the following tasks prior to introducing systems of equations. Check these out with your students as suggested prerequisites prior to introducing the new tasks from this post:

- Stacking Paper – Proportional Reasoning / Direct Variation Linear Relations
- Stacking Paper Sequel – Partial Variation Linear Relation Given Slope and a Point
- Thick Stacks – Partial Variation Linear Relation Given Two Points
- Tech Weigh In – Direct Variation & Partial Variation Linear Relations
- Camera Case & Pads of Paper Weigh In – Partial Variation Linear Relation Given Two Points

Show students this video.

Ask students what they are wondering? What questions come to mind?

After discussing with a group, help direct the focus to the question:

How much does each weigh?

Students can make predictions and argue why they believe their guess is best.

Show students scene 1.

Alternatively, you can show students the following images:

Show students the solution video.

Alternatively, you can show students these images:

Try it out and let us know how it goes in the comments!

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]]>This 3 act math task is a great way to introduce the topic of Distance-Time Graphs before moving on to motion-time & other linear graphs of various contexts

The post Walk Out appeared first on Tap Into Teen Minds.

]]>This 3 act math task was created as a simple, yet powerful way to introduce distance-time graphs and other various graphs of linear and non-linear relationships between two variables. In particular, I’m looking to address the following specific expectations from the grade 9 math courses in Ontario:

**Grade 9 Applied LR4.02 & Grade 9 Academic LR3.02:**

- LR4.02 – describe a situation that would explain the events illustrated by a given graph of a relationship between two variables (Sample problem: The walk of an individual is illustrated in the given graph, produced by a motion detector and a graphing calculator. Describe the walk [e.g., the initial distance from the motion detector, the rate of walk].);

Show this video.

Ask students what they wonder? What questions come to mind?

Write down some of the questions/ideas that students share.

Show this video.

Students are now given the distance of the walk and the amount of time it took me to walk the distance.

By now, either students will have come to the conclusion or you can share the question that we’re hoping to begin with:

What does the distance-time graph look like of my walk?

I usually have my students sketch out a graph on their desks using non-permanent markers, but you might opt to give them a grid like this one that Dan Meyer and the BuzzMath folks shared on their Graphing Stories website.

Then, I’ll get my kids into Knowledgehook Gameshow to do the remainder of the task interactively. I’ll play videos (there are 10 different walks) and students can sketch the graph, select from options I send to their screens, and then upload a solution of their work.

Note that when I embed questions on my blog, the upload solution option does not work.

Here’s the first Knowledgehook question:

After students have responded and you’ve shared out some of their sketches to the projector to discuss as a group, you can play the Act 3 video.

My kids had some fun doing this activity in class. Obviously, if you have calculator-based rangers (CBRs) for your TI-83’s or digital versions that connect to your tablets/phones, that is an obvious cool activity to do as well. You can also have students create their own videos with their iPads/tablets like Jon Orr does with his class.

Send your students through an interactive math task with Embedded Gameshow (like the questions you see above). This is similar to the Interactive Math Learning Journeys I have posted in the past.

Here’s all the videos on YouTube for all 10 of the walks:

Task 1 [act 1 | act 2 | act 3]

Task 2 [act 2 | act 3]

Task 3 [act 2 | act 3]

Task 4 [act 2 | act 3]

Task 5 [act 2 | act 3]

Task 6 [act 2 | act 3]

Task 7 [act 2 | act 3]

Task 8 [act 2 | act 3]

Task 9 [act 2 | act 3]

Task 10 [act 2 | act 3]

Here’s a YouTube Playlist with ALL of the walks. Pretty convenient to have all the acts of the ten walks in one, big playlist.

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

The post Walk Out appeared first on Tap Into Teen Minds.

]]>Hot Coffee is a 3 act math task created by Dan Meyer that has students curious to determine how many gallons of coffee will fit using volume of a cylinder.

The post Hot Coffee appeared first on Tap Into Teen Minds.

]]>Dan Meyer’s **Hot Coffee 3 act math task** is my favourite task to use in order to give us a reason to find the volume of a cylinder. Dan has a great summary of this task here, so I’ll just quickly preview what you’ll get when you head to his resource page.

*Please note that all material below was shared by Dan Meyer via a Creative Commons CC BY-NC 3.0 License from his site located here.
*

Show students this video.

What is going on in the video? What questions come to mind? What are you wondering?

The question we are going to head towards is:

How many gallons of coffee will fit in the cup?

I’m sure the discussion around why anyone would want a cup of coffee that big will come up at some point.

Show them this video.

Students will see the old record was 750 gallons of coffee. Let them make their predictions on how many gallons the cup in this record breaking attempt will hold.

The video also discusses how long it took to brew the 750 gallons of coffee used in the old record (4 hours). How long will it take for the new “biggest cup” to fill up?

Here’s some details necessary for students to solve the problem:

And you can use Google to determine the conversion from feet-cubed to gallons (1 ft-cubed = 7.4805 US gallons).

Show the students this video.

Grab all the files here including an Apple Keynote presentation file that has all the videos and images conveniently organized in a slide deck for easy use on your MacBook or iOS (iPad, iPhone) device!

*Please note that all material above was shared by Dan Meyer via a Creative Commons CC BY-NC 3.0 License from his site located here.
*

Click on the button below to grab the full task for use in your own classroom:

The post Hot Coffee appeared first on Tap Into Teen Minds.

]]>Math facts, especially memorizing multiplication tables, is an area of discussion for math teachers that isn't going away. But is this the only problem?

The post Are Math Facts “THE” Urgent Student Learning Need? appeared first on Tap Into Teen Minds.

]]>This past Thursday for our MYCI Planning Meeting WSG Dan Meyer, there was quite a bit of discussion surrounding math facts as a **student learning need**. This is no surprise, as I think we can all agree that this is an area we would like to support our students in. The discussions at each table made it clear to me that we are all passionate about supporting our students in their mathematical journeys. Some of the discussions focused on math facts in general, while others were more specific such as being able to recall multiplication facts or working with fractions. All great discussion with great ideas being carved out along the way.

During our time debriefing the session, Justin Levack threw out a great question that I couldn’t find an answer for.

His question was:

If ______________ (math facts, multiplication tables, fraction fluency, etc.) is the most urgent student learning need in mathematics for a classroom/school/district, what exactly are students being held back from doing?

This was an “ah-ha” moment for me as we often think of our struggling students as those who do not know their math facts. However, maybe we need to zoom out a bit to discuss why these students struggle with math facts in the first place?

Does knowing times tables actually make students better in other areas of math, or is it a result of the students doing something else? Or just one piece of what makes a student strong in math? Sure, many strong math students know multiplication tables, but can we state without a doubt that knowing multiplication tables is the cause and being strong in math is the effect?

Maybe. Maybe not.

What if knowing multiplication tables is the effect of some other factor?

Could it be that having some other skills/abilities makes multiplication facts easier to recall? If so, can we somehow identify these skills/abilities and then spend some of our time focusing on them as well?

While I don’t have the answer, it could be worth a discussion with your MYCI Team, math department and/or professional learning network to determine whether we need to turn more stones to inform how we move forward.

With this, I’ll end with an article that really helped me better define what I would love for my students to be able to do once they leave my classroom:

Fluency Without Fear: Research Evidence on the Best Ways to Learn Math Facts by Jo Boaler, Stanford University.

I think this article does a great job summarizing some of the pieces of our discussion last Thursday and might serve as a starting point as we continue our journey to support students along the math continuum.

What are your thoughts? Let’s keep the conversation going!

After posting this article on Twitter, I liked this response:

@MathletePearce Word up. Math facts are just the canary in the coal mine. Not that hard to master, so… what's the real problem?

— Tilton's Algebra (@tiltonsalgebra) December 8, 2015

Definitely an analogy I will be using in the future.

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]]>Watch a video clip of a pool draining. How long do you think the pool will take to empty completely? How do you know? Then, watch what REALLY happened!

The post Draining The Pool appeared first on Tap Into Teen Minds.

]]>This Real World 3 Act Math Task will have students **making predictions** via **interpolation** and **extrapolation** using **scatter plots** and a **line of best fit**.

Data management of two-variables including:

- making predictions between two-variables,
- creating scatter plots,
- classifying correlations as positive/negative and strong/weak, and
- interpolating and extrapolating using a line of best fit.

This task can be extended to **linear relations** and **equations** by having students determine an equation of the line of best fit or alternatively, non-linear regression to find an equation of a curve of best fit.

If you haven’t already, I recommend using the Candle Burning 3 Act Math Task prior to using this task, as the data appears to have a stronger linear correlation.

Show students Act 1:

After showing the video clip, I have students discuss with their group some questions that come to mind. Sometimes, I have students focus on two types of questions:

- The first question that comes to mind; and,
- a unique question you don’t think someone will come up with.

This tends to differentiate the question responses rather than seeing a ton of the most obvious one. We discuss these options, then settle on our first question:

How long will it take to empty the pool?

Then, we move on to Act 2.

I personally don’t ask too many questions about what information they want, as most tend to know where this problem is heading.

Show them Act 2:

Although I try to avoid fading out my videos to ensure the information doesn’t go away, here’s a screenshot of the last frame, for your use:

Feel free to save the image.

At this point, students can head off on their merry way. I find most of my students tend to go straight for a scatter plot and extend a line of best fit, while others might choose to try to leverage the initial value/y-intercept and estimate a rate of change/slope to create an equation. At midterm and beyond, I’m hoping that the second option becomes more attractive to my students since we have been working with linear equations quite a bit. If no students head in that direction, I would introduce it during the consolidation of the problem as a potential strategy for future use.

If you’re beyond students drawing scatter plots and want to do something more advanced with this problem, consider using Desmos as a way to manipulate and interpret data.

Click the image below to grab a shared Desmos graph with all the data points plotted from a table of values with regression line/curves:

Once students have updated their prediction based on their mathematical thinking, we can show students Act 3 so they can cheer (or cry) based on what really happened:

Here’s a screenshot of the last frame, if you’d like to use it for some of your consolidation:

Feel free to download the Act 3 image.

- What do you predict the depth of the pool would be after 17 hours of draining? (interpolation)
- What would be a reasonable drain rate for this pool assuming the trend is linear?
- What would be a reasonable equation for a line (or curve) of best fit?

Please comment to let me know how it worked in your classroom!

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

The post Draining The Pool appeared first on Tap Into Teen Minds.

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