**Draft Draft Draft Draft **

Ex-Scaling

Use blocks.

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.

Wrap up

Copyright 2014, Robert M. Boeke