The purpose of this activity is for students to apply metric units of length, volume, and mass to solve a problem in context.
The background knowledge presumed for this task is outlined in the diagram below:
This activity should be used in a ‘free exploration’ way with an expectation that students will justify the solutions that they find.
The procedural approach (show more)
- The student finds a way to enclose $100 banknotes into a briefcase without considering how the number of notes might be maximised and calculates the mass of the banknotes using appropriate place value.
Students who operate procedurally will find a single viable solution. They research the measurements of a USA $100 banknote and of a business briefcase. By choosing millimetres as an appropriate unit of length they practically determine how many banknotes can be arranged in a single layer of the briefcase. This may include making paper notes and tessellating the notes. They determine the number of layers needed to make up $1,000,000 and calculate the height of that many layers. Similarly, they correctly calculate the mass of the $1,000,000 in banknotes using division.Click on the image to enlarge it. Click again to close.
The conceptual approach (show more)
- The student uses a systematic strategy to find the optimal dimensions of a briefcase so the maximum number of notes can be arranged in each layer.
Students who work conceptually will consider the conditions of the problem that can be varied and manipulate those conditions to get an optimal solution. Since the size of $100 banknotes is set only the size of the briefcase can be varied. A conceptual approach involves recognising that a tessellation is the best arrangement for one layer of banknotes and experimenting with the two ways to arrange the notes.Click on the image to enlarge it. Click again to close.