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

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

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!

FullSizeRender-1Great 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.
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They also have a great handout for tracking the circumference over the 30 second intervals. Screen Shot 2015-09-18 at 2.22.08 PM

Analyzing the Data

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

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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???

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

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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!

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Final Assignment – Estimation Challenge

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

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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 …

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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?
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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.
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Act 2: She provided us with a little more info after we made some guesses.
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and
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Act 3: Made a time lapse video and provided a screen shot with the answer

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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”]

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Tiana

How many stickies to fill the door window?

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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?

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and the answer

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Watch the water fill up by grabbing her Explain Everything File

[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-gapBCeZkEtWnA0dWVjZ0k/view?usp=sharing”]

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

Trashketball – A Spiralled Lesson!

This was our multi-day, curriculum-spiralled, activity this week!

Day 1 – Filling the Bin!!

Let’s get curious!!…..I showed this video from Andrew Stadel, and took questions & wonderings:


We settled, (I chose) on the question on how many paper balls would fill a bin! They made predictions, too high, too low and right on!

They made paper balls and found their diameter. We agreed that each ball could be different so we recorded everyone’s diameter and averaged them to give the “average ball size”

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Continue reading

Distance-Time Graphs – Gallery Walk

The last few semesters I ran this two-day lesson on distance-time graphs. Today I added a new twist on Day 2.

Recap: Day 1 – A few prediction videos on water height in a cup vs. time. Then WATERLINE by Desmos!

Day 2:  Today

Warm Up – We reviewed the previous day’s work by choosing one of the cups from the picture and drawing a water-height vs. time graph.

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Not surprisingly, no students chose to draw the graph for the Stanley Cup. After they make their sketches we dove into using the CBR Rangers from Vernier just like on Day 2 from the previous post. They walked in front of the Ranger taking various different walks and we all saw their distance-time graphs in real-time. For each walk the students made prediction graphs on their whiteboards before seeing the live graph.

I wanted more predictions from them so I showed them a video I made. They were to watch the video and make a prediction graph of my distance away from the camera vs. time.


After take up of this graph they were to create their own video on the iPads. Each pair of students we’re given a scenario to film that described motion.

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Here are two motion videos they filmed: Very basic to start!


They had to create their distance-time graph and hide it under the flap on the vertical whiteboards.

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Pairs then went on a gallery walk. They watched each student made video, graphed the matching distance-time graph and then checked the answer under the flap.

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Kids enjoyed it and they practiced lots of different distance-time graphs.

Thanks for reading!!!