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,
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.
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!
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.
How many caps will fill the marker?
Estimate & Answer
How many cups to fill the shape?
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.
Act 3: Made a time lapse video and provided a screen shot with the answer