Description of the challenge:

Some sweets in a jar/container. Students have to figure out how many (in order to claim the sweets ;)

What people have tried before (1) , (2) and (3) , (4) as real life examples :) Students would not have access to the internet though!

Aims:

Through this challenge I want the students to;

a) review all formulae for 2D and 3D shapes
b) review/learn how to combine them 
c) puzzle out their application to this challenge
d) review/learn how to break a 2D/3D shape down into components
e) review/learn how to combine 2D/3D shapes with limited available measurements
f) review/learn % error or % uncertainty and estimation vs 'guessing'
g) plan their attack! AND document results
h) develop positive disposition towards employing thinking models and using thinking skills!

Possible limitations to introduce:

Start with a simple cylindrical container (fairly simple algorithm specific to those shapes) and move on to other shapes (make algorithm more generalised) THEN move on to more complex compound shapes (makes the algorithm more generalised to cope with all possibillities).

   

 Students are NOT allowed to touch or move the container - measurements are made on separate accessible parts (students may not combine them as in the challenge).

Students must arrive within 5% of actual number.

Students steps/procedure must be used by another student to complete the challenge.

Steps expected from students (eventually)	Knowledge and understandings and processes students are expected to use (from prior knowledge)	knowledge and understandings needing to be taught	Skills or processes needing to be taught	Thinking skills needing to be used or taught	Where will they likely get stuck
look at the container	:)
write down all the 2D shapes	2D shape recognition; circles, semicircles, rectangles, squares, etc.			identification of parameters and values (shapes - circles, squares etc)
write down all the 3D shapes	3D shape recognition; spheres, cuboids, cones, hemispheres,	cones, partial cones recognition		defining & identifying a shape based on its parameters	HERE
find/recall the formulae for each shape	recall	new conical sections formulae
make measurements & calculations			multiple measurements to get a more accurate average
find volume of one sweet	if it's a regular 3D shape then easy (measure & use formula)    finding the average	- average volume of a small irregular shape (science curriculum link) by displacement of water (use 5 or 10 objects and divide)
find empty space (between sweets)	students may try guessing	?? are there different ways (random & not) for items to fit into container?	modelling using available materials or on paper?		HERE!

 

The resulting algorithm for this task should be quite involved.

I'm not sure yet whether it will be better to start from the hardest option and then break it down or start with an easier option and introduce limitations?

What do I expect to happen?

At first I think students will want to 'get the answer' by

 

a) measuring the outer dimensions of the container and finding the volume using the formula for the volume of a cylinder
b) measuring the volume of the sweet (regular sphere) by measuring the diameter (badly!) and using the formula for the voume of a sphere
c) dividing a by b

 

Students will likely ignore the spaces between sweets and won't give a thought to whether the packing is random or not (makes about a 10% difference in the answer). If they don't ignore it, they will probably 'guesstimate' the left out volume rather than developing a strategy to measure it. The 5% tolerance limit for the final answer will likely take care of this (if not I will reduce the allowed error).

I expect students to employ the ENV thinking model and associated skills (see list here) (and  here).