Black and Red Tile Model for Integers The Investigation below poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find. Click on the Read Me file below to open the investigation in a Word file: Read Me - Integer Differences Instructions (Word Format) (61.0K) The Math Investigator is a data collection software program that may be used to collect data for the investigation. You may type answers onto the Word file or copy and paste in data from the Investigator. Click here to launch the Integer Differences InvestigatorMath Investigator 5.1INTEGER DIFFERENCES on the Math Investigator computes the differences of consecutive pairs of integers at adjacent vertices (corners) of a k-sided polygon, and repeats the process as many times as desired. Select any four integers and place then at the vertices (corners) of a square. Then between each pair of integers write the difference of the larger minus the smaller and form an inner square whose vertices have these differences. Continue this process of taking differences and forming inner squares. Will this process result in an inner square of all zeros? (Observations in the 1930's concerning this investigation are attributed to the Italian mathematician E. Ducci.) Starting Points for Investigations
| ||||||
|