Draft Draft Draft Draft
Explore: consequences of increasing
The length of a line (length)
Line up blocks, double and triple length
Discuss ratios of lengths
The sides of a rectangle (area)
Lay our a rectangle with blocks, double and triple length of both sides
Discuss ratios of lengths and areas
The diameter of a circle (area)
Estimate with blocks, double and triple radius
Discuss ratios of diameter and area
The volume of a cube (volume)
Build a cube, double and triple all sides.
Discuss ratios of length of one side and volume
The volume of a rectangular solid (volume)
Build a rectangular solid, double all dimensions
Discuss ratios of length of sides and volume
Have some discussion about the general rules
Lengths are proportional to the dimension
Areas are proportional to 2 linear dimensions and have dimension (length squared)
Volumes are proportional to 3 linear dimensions and have dimenstion (length cubed)
Have students design a warehouse (shape: rectangular solid) to hold 100 cases of breadfruit flour, given the dimensions of 1 case. They must make all decisions about length, width, height.
Open a discussion about why they picked the dimensions they did (each group should be different). What might be some practical reasons for choosing certain dimensions? E.g. High enough for a person to stand up or space to be able to walk/work when stacking or removing the contents.
Have students scale up the building to hold 200 cases of flour. They
must change at least two of the dimensions.
Discuss how the dimensions changed. They should see that while the volume must have double, lengths of the two changed dimensions did not. Ask whether there are any new practical considerations as the building holds more product, e.g. Aisles for access to certain sections of the product for First in-First out.
Using the estimate of number of employees needed to peel 1000 breadfruit in a day from the estimation exercise, ask the groups to estimate how many would be needed for output of 1500 and 2000/day.
They will likely scale things up proportionally. This is a good opportunity to discuss the consequences of scaling in a business. For example, scaling up could require also hiring a supervisor or a person to bring the fruit to the peelers and move the peeled fruit and waste (seeds and peels) away.
Copyright 2014, Robert M. Boeke