Show the students collections of objects on an overhead projector. Mask the collections initially with a book then uncover them briefly. Encourage strategies like looking for instantly recognisable patterns and using these as a sample with which to estimate the whole collection. You might also develop sampling by using a frame, like a cut out plastic lid, to isolate part of the collection. For example, 10 objects are inside the frame, that is about one-sixth of the collection, so there are about 60 objects in total in the collection.

Activity

The students at the Advanced Additive thinking stage and onwards should apply multiplicative strategies. Fill clear plastic jars with beads, buttons, or similar objects and get the students to estimate the total number. Encourage strategies like taking a cross section and multiplying that by how many times the cross section will fit into the collection.