Year 13 Inquiry - Rate of change - Lollipop activity

How does licking change things? Using Lolli Pops, measuring tapes and dental floss to investigate

#1.  Raise Māori student achievement through the development of cultural visibility and responsive practices across the pathway as measured against National Standards and agreed targets for reading Years 1-10 and NCEA years 11-13. As a CoL leader within school I  am more interested in inquiring about student learning and my own practice.

Investigation questions

(1) What is the volume of the lollipop?
(2) How many licks to the center?
(3) How long until it has gone?
(4) What is the relationship between Time, Radius, Volume, Circumference and surface area?

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: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!

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

Analyzing data: We first looked at the Time vs Radius relationships? 

LollyPop Table (Radius)

Time (seconds)	Circumference (cm)	Radius (cm)	First differences of radius (cm/30 seconds)	First differences of radius (cm/ second)	Instantaneous rate of change at time ____
0	9.0	1.43
			-0.16	-5.33 x 10-3
30	8.0	1.27
			-0.08	-2.67 x 10-3
60	7.5	1.19
			-0.08	-2.67 x 10-3
90	7.0	1.11
			-0.03	-1.00 x 10-3
120	6.8	1.08
			-0.11	-3,67 x 10-3
150	6.1	0.97
			-0.09	-3.00 x 10-3
180	5.5	0.88
			-0.08	-2.67 x 10-3
210	5.0	0.80
			-0.04	-1.33 x 10-3
240	4.8	0.76
270	4.8	0.76
			-0.04	-1.33 x 10-3
300	4.5	0.72
			-0.04	-1.33 x 10-3
330	4.3	0.68
			-0.02	-6.67 x 10-3
360	4.1	0.65
			-0.09	-3.00 x 10-3
390	3.5	0.56
			-0.04	-1.33 x 10-3
420	3.2	0.51
			-0.03 -0.08	-1.00 x 10-3
450	3.0	0.48		-2.67 x 10-3
480	2.5	0.40	-0.05	-1.67 x 10-3
510	2.2	0.35	-0.10	-3.33 x 10-3
540	1.6	0.25	-0.25	-8.33 x 10-3
570	0	0

Using DESMOS

Conclusion:

(1) What is the volume of the lollipop? 

     V = 4/3πr3

C = 9.0cm

r = C/2π

r = 9/2π

r = 1.43cm (2dp)

V = 4/3πr3

V = 4/3π(1.43)

V = 12.25cm3

(2) How many licks to the center? 300 seconds
(3) How long until it has gone? 570 seconds.
(4) What is the relationship between Time, Radius, Volume, Circumference and surface area? We are going to move onto this next week.