The first chapter of B3D sets out dimensions very clearly for a mathematically dormant person (namley myself.) However, it seems to have made more sense after reading part of Flatland and getting into that "mindset." The example of the amoeba allows one to think of an example of flatland in real life. Also looking at the picture of the maze we understand how important and illuminating it can be to have an "exterior" vantage point. Just like someone from spaceland has the ability to overview the inhabitants of flatland. The chapter then continues to exemplify how useful dimmensions can be and how they are used in society (such as formulating data.) Here it might be an idea to ask or include an exercise.
Find three sets of numbers that are related and graph them using one, two and three dimensions. This will practice the reader and introduce the reader to the possible proggression from three to four dimensions.
Now the progressions are analysed and the connections are realized between the dimensions. Perhaps an exercise could now be introduced which made the reader draw the progression from pointland to fourdimesionalland. Once the reader has managed to draw the hypercube, he or she could be asked to draw it using colors so that all the different cubes are identified. And in so doing the reader could be asked to form a table which denoted the different numbers of points, edges etc. like we did in class - then make some assumptions and theories about the amount of sides squares woud have in different dimensions.
After having drawn a hypercube I began to wonder about the question in the book, "How can we see what a hypercube will look like?" because after having made a model of one I think I know what it would look like. Maybe I am completley wrong and it is not possible for us in spaceland to visualise the next dimension, but it has left me confused.