The purpose of this activity is to engage students in reasoning with unknowns and finding plausible values for the unknowns using information provided. The information can be expressed as three equations involving three unknowns. Students might also apply numeric processes involving addition, and multiplication.

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.

Three people, Anna, Bart and Carol are gymnasts who specialise in human pyramids. They can form three different two-layer pyramids, if they take turns to be the top person. The secret to pyramid building is for the weight of the top person to be equally shared between the bottom people.

Using the information on the scales below, find the weight of each person.

### The procedural approach (show more)

- The student uses estimation and appropriate calculations, to find the value of the three unknowns by systematic trial and improvement.

### The conceptual approach (show more)

- The student uses algebraic equations, or graphs, to find three unknowns from three linear equations.