*‘Explorations’ are topics for students to investigate on their own. Though little hands-on work is included, we take advantage of the software package GeoGebra in several cases.*

In ‘Tiling transformations’ we perform operations to change one uniform tiling into another.

In ‘Shape counts in a tiling’ we find the ratio of the numbers of the different tiles present in a uniform tiling.

‘Number City rows’ concerns the station ‘Number City’ under the topic heading ‘Multiplication’.

‘Figurate numbers’ summarises and extends the results of the masterclass of the same name.

‘Dissection algebra’ is about finding area ratios without calculation, namely by dissection.

‘Shape & size’ shows how thirteen heuristic principles help derive and check formulas for the areas and volumes of standard shapes, and the positions of the centroid in them. Calculus is avoided, though students familiar with integral calculus can exercise their skills in finding alternative derivations.