These materials on irrational numbers are designed for use in workshops for pre- and in-service teacher training, especially for teachers in junior high schools. The general aims are: to improve teachers' mathematical knowledge of topics, to enrich teachers' mathematical background, to allow opportunity to discuss relevant didactics, and to create a reasonable image of mathematics and mathematical activity as a human endeavor. The worksheets (in booklet form) generally have a brief biographical-chronological introduction to set the historical scene, an historical source, and leading questions on the source materials and on mathematical and didactical consequences thereof. Each worksheet is accompanied by answer sheets (also in booklet form), containing solutions and further sources and information. Six worksheets are contained in the set: the Pythagoreans, Euclid and the Elements, irrationals in the 16th and 17th centuries, Rafael Bombelli, Nicholas Saunderson, and Dedekind and the definition of the irrationals. Comments on how to use the worksheets are briefly presented. (MNS)