Thought a good title might be "Shi?ts" and might make you "notice and wonder". Students walked into my class on a Monday morning to this pile of shirts on my desk.
I immediately asked them to write down what they noticed and what they wondered. I did this with two classes for the record.
Here are their noticings:
And here are their wonderings:
After we got through all the noticings and wonderings we focused in on this question.
How many shirts are in that pile?
Asked students to  Guess too low, guess too high, best guess.
Students were randomly put in groups of three. I let them know I would give them a sample of 10 shirts.
Here are some samples of groups work on vertical surfaces.
Group 1
Group figured out the volume of all the shirts and then the volume of their ten shirts as a sphere and as a cone. Got 771 shirts using sphere and 258 shirts using the cone.
Group 2
Group figured out the volume of all the shirts and then the volume of their ten shirts as a cone. Got 304 shirts.
Group 3
Group figured out the volume of all the shirts and then the volume of one folded shirt (rectangular box). Got 146 shirts.
Day 2
At the start of class I modelled a solution to find out the number of shirts. It looked like this. Two solutions one for each class.
And the reveal.
The rest of the second day was spent figuring out how many shirts each student could fold per second. Class decided to include time to get shirt from pile, lay it out, fold it and pile it on their chair.
Students kept a table of values of time and number of shirts folded. We did it for 0, 20, 40, 60, 80, 100 and 120 seconds. Students plotted data, did line of best fit, and calculated slope to find their rate.
Here are some photos of one students data, scatterplot, equation, and graph.
Here are the final rates for both classes:
NAME


A

0.042

C

0.080

M

0.080

H

0.077

E

0.051

C

0.090

W

0.007

E

0.040

D

0.090

Z

0.117

W

0.083

K

0.046

M

0.067

L

0.081

A

0.046

E

0.041

E

0.082

F

0.092

L

0.033

K

0.039

D

0.047

NAME

RATE in Shirts per Second

S

0.063

R

0.044

T

0.080

L

0.036

R

0.047

J

0.084

A

0.068

L

0.046

A

0.053

S

0.044

A

0.067

H

0.058

0.067
 
L

0.038

B

0.046

O

0.054

E

0.027

M

0.032

T

0.046

And a photo of the madness.
Day 3
Today's question to focus on."How long would it take the class to fold all 282 shirts?" Asked students to  guess too low, guess too high, give best guess. Students were asked to devise and write out a strategy individually on how they might figure it out. Students were then put into random groups and asked to share their strategies. Once they talked it over they were to execute the group strategy on vertical white boards. Many groups wanted the data from the day before  I provided that. Some groups asked how many students were in the class  I provided that (23 for one class and 24 for the other). Some groups asked about attendance  how many students were in class on average. I told them to make their best guess based on a usual day. Groups were given the entire period to work on this.
Here are some samples of group work on vertical surfaces:
Day 4
Today's question to focus on, "What area could we cover with all those shirts?" Asked students to  guess too low, guess too high, give a best guess. Students were asked to devise and write out a strategy individually on how they might figure it out. Students were then put into the same groups as yesterday and asked to share their strategies. Once they talked it over they were to execute the group strategy on vertical white boards. I gave groups about 30 minutes to get through this problem.
A few photos of students doing some measuring.
And some of the groups solutions on vertical surfaces.
Time to do answer "How much area could we cover?" we went out in the hallway and got to work.
After some measurements with both classes, here is what we got.
I hustled students back into the class with all the shirts. We tossed them back into the pile and set up the room for folding. I posted the predicted times from the group work on day 3.
And then it was time to fold.
Actual time to fold them all for each class.
Final Reflection:
This was great. Based on the number of selfies that were taken during the area layout of all the shirts I would say this was a success. I bet you all have questions?