Lollipop Lollipop oh la la Lollipop! — & Rates of Change

September 21, 2015 by Jon Orr

Last year on twitter I saw that Alex Overwijk and Janice Bernstein with their grade 12 advanced functions classes did this lollipop activity!

How does licking change things? Using Tootsie Pops, measuring tapes and dental floss to investigate IROC and AROC. pic.twitter.com/j9KF6h8H5K

— Alex Overwijk (@AlexOverwijk) October 1, 2014

I knew that I wanted to give this a try for this semester! What I especially love about this activity other than students experiencing rates of change is that this is an activity that can span multi-grades!

Here is what we did,

Generating Curiosity

I found this video on YouTube and asked the class to think of great questions we could ask about what we see!

Great questions from the kids and we all agreed to look at

How does the sucking time affect the radius, circumference, volume, and surface area?
How long will it take until the lollipop is all gone?

Let’s investigate those relationships starting with the easy to measure (circumference) and also estimate how long it will take until the lollipop is no more!

We had guesses : ranging from 10 minutes through to 35 minutes.

Gathering Data

I handed out one lollipop per pair of students, along with some dental floss for measuring circumference. We set our timer for 30 seconds and began sucking and capturing data!
We recorded the circumference every 30 seconds up to 7 minutes like Al’s and Janice’s instruct in their lesson Plan.

They also have a great handout for tracking the circumference over the 30 second intervals.

Analyzing the Data

So we first looked at the Time vs. Circumference and Time vs. Radius relationship

We discussed its linearity and why. Students predicted with more accuracy when their lollipop would run out.
Up to this point this task is great for grades 7, 8, 9, or 10!! (Just edit the file to exclude the average and instantaneous rates of change).

Grade 7 & 8: Practice plotting points and reading/interpreting graphs.
Grade 9 & 10: Find lines of best fit and first differences.

We found the average rate of change for each 30 second interval and discussed what this meant. We used the last column to talk about narrowing the interval down to estimate the instantaneous rate of change, and noticed that it’s about the same for all values. Why does this make sense???

We moved on to looking at Time vs. Volume and Time vs. Surface Area

Great talks around how Volume and Surface aren’t deceasing at a constant rate! It changes! Students can see these changes and see in their tables where the volume is changing the fastest.

Overall a great intro activity to get students thinking about narrowing intervals to approximate instantaneous rates of change.

Next up: We’ll relate what we did here with the tables to the graphical interpretation of rates of change (secant and tangent lines) and then on to the algebraic!

Desmos Challenges in iTunesU, Multi-Touch Book, and Web Version

August 28, 2015October 31, 2015 by Jon Orr

For many years now my classes have been completing a course wide project on Picture Modelling. Before Desmos (B.D.) I use to send home copies of Geometer’s Sketchpad for students to generate a picture using only functions. Screen Shot 2015-08-28 at 12.41.47 PM
After Desmos showed up it was now super easy for students to generate art and access graphing software from any device.

The project has been so successful at engaging students to learn about various functions and their transformations I extended it to all grades! For the last few years the project spans grades 9 through 12. Each year learning new functions and creating art.

Screen Shot 2015-06-10 at 1.49.50 PM This summer while at the Apple Distinguished Educator Institute in Miami I started a project that would create a digital resource that would link the Modelling Functions with Art Project with function challenges created by Michael Fenton, Dylan Kane, and myself.

If you are in an one-to-one iPad room or have access to iPads the resources are in an iTunesU course and multi-touch book for iPad otherwise they are linked on this site for any device (see below).

Each chapter starts with linking patterns, tables, graphs and equations in pre-made Desmos graphs or in pre-made Desmos activities made using Activity Builder. Screen Shot 2015-08-17 at 7.49.53 PM
Following that, activities ask students to match functions to specific criteria like Michael Fenton’s Match My Line or in my Match My Trig Function. Again the teacher can choose to use the activities in the Multi-touch book or from the pre-made Desmos activity.

Every so often in the challenges students are asked to show their thinking by uploading a picture of their work on a Padlet page. Students can crowd source different ways to solve the same problem.

Finally, at the end of each chapter students are to create a working piece of art and share it on a Padlet gallery page! Students can see each others work and comment.

Each chapter covers different functions but many chapters can be done in the same course:

Ontario curriculum suggested chapters:

Chapter 1 – Linear Functions – grade 9 & 10
Chapter 2 – Quadratic Functions – Grades 10 & 11 & 12
Chapter 3 – Various Functions (function notation, cubic, square root, reciprocal, non-functions). – Grades 11 & 12
Chapter 4 – Trigonometric Functions – Grades 11 & 12
Chapter 5 – Exponential & Logarithmic Functions – Grades 11 & 12 (Coming soon!).

The project page has more details on how to access the course, book, and web resources.

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”none” text=”Go to the Project page” relationship=”dofollow” url=”http://wp.me/P3az6g-14y”]

R2D2 – Pear Deck/Desmos Mash Up!

August 20, 2015October 31, 2015 by Jon Orr

School is just right around the corner for us up here in Ontario and I can’t stop thinking about that first day. As for my grade 9 applied class’ first day I have ran the R2D2 problem in the past with great success.
Now, over the summer I’ve seen great improvements in Pear Deck and wanted to get into it! Also Desmos has been busy and released Activity Builder!! So let’s mash these two apps up with some R2D2!!

So here is the R2D2 problem presented with Pear Deck and an extensions with Desmos….

Act 1: The video

and this is what Pear Deck will show after you insert the video…..love how the video will be displayed on the projector and not on each individual device!!!

I like using Pear Deck here for asking for wonderings and notices because it allows students who normally won’t shout out answers to have a voice in the room. Students get to input their responses and the teacher can show them on the projector.

For generating estimates I absolutely love how they put our Too high and Too low guess on a number line…..it gives us the visual of where our actual estimates will lie.

Act 2: Gathering the Info

In the new version here I get students to draw their estimates of the dimensions of both the board and the post it note…..this pushes them into drawing diagrams.

Revealing the dimensions….

Students are ready to solve….

Act 3: Revealing The answer

The Extension: How many rectangles can we make that have an area of 609 post it notes?
To extend I want students draw out different rectangles and label their dimensions! They can use Pear Deck’s white board!

But then they can enter them into Desmos through a pre-made activity I created in Activity Builder. (the Pear Deck file links to the Desmos activity).

For each rectangle the student can come up with they find the perimeter and plot the length vs. perimeter in the Desmos graph. The teacher on the projector can use the Overlay function and show all the different rectangles students are coming up with…essentially showing the pattern that emerges! Using the pattern students can read off the minimum perimeter!

If you have a Pear Deck account Grab and download the file below!

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”star” text=”Pear Deck File” relationship=”dofollow” url=”https://drive.google.com/file/d/0B9g0jeaVwshveDVhWktzdTRudE0/view?usp=sharing”]

Link to the Desmos Activity

Final Assignment – Estimation Challenge

June 18, 2015January 28, 2016 by Jon Orr

For our final activity I started the off with this……

we filled in too high, too low, and best guesses! Then we checked the answer…..

Completing this challenge got the students pumped and hooked into doing some math on our very last days of class (especially with some students exempted from the final exam). Our final assignment is to …

We got out the iPads and I let the kids work….. here is what a few came up with:

A lot of kids did water filling or post it note covering estimates. Some kids ended up making an all-out 3 Act math problem.

Zack

How many caps will fill the marker?

Estimate & Answer

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Alexis

How many cups to fill the shape?

Answer:

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Meghan

A 3- act task in Explain Everything:

How many post-its will cover this triangular wall:

Act 1: She put a photo and a small video in Explain Everything to start us off.

Act 2: She provided us with a little more info after we made some guesses.

and

Act 3: Made a time lapse video and provided a screen shot with the answer

Grab her Explain Everything File here

[aio_button align=”center” animation=”none” color=”blue” size=”medium” icon=”download-alt” text=”Grab the EE File” relationship=”dofollow” url=”https://drive.google.com/file/d/0B3zQp-gapBCeVmU2anF4Ty1DOUE/view?usp=sharing”]

—————————————————————————–

Tiana

How many stickies to fill the door window?

And hit us up with a time lapse video for the answer:

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Celina

How many water bottles will fill the hexagonal prism?

and the answer

Watch the water fill up by grabbing her Explain Everything File

A fun last few days….and I’ve got some new estimates for class next year.

Class Activities

Lollipop Lollipop oh la la Lollipop! — & Rates of Change

Generating Curiosity

Gathering Data

Analyzing the Data

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