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Math Investigation
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The Investigation 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 - Triangular Numbers Instructions (Word Format) (87.0K)

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 Triangular Numbers Investigator




Math Investigator 1.2


TRIANGULAR NUMBERS on the Math Investigator prints up to 100 triangular numbers between two given triangular numbers.

One student was looking at a list of triangular numbers and noticed that the sequence of units digits began repeating in reverse order after the 9th triangular number.

Triangular numbers    1    3    6    10    15    21    28    36    45    55    66    78 . . .

Units digits    1    3    6    0    5    1    8    6    5    5    6    8 . . .

Starting Points for Investigations

  1. If the list of triangular numbers is extended, will the units digits continue in reverse order? Look for patterns.
  2. The sequence of units digits eventually contains two consecutive zeros. Are there other pairs of zeros if the sequence is extended? Will the sequence of units digits ever contain 3 or more consecutive zeros? Look for patterns and form a conjecture.
  3. Use your patterns and write a set of directions for determining the units digit in any given triangular number. What is the units digit in the 5147th triangular number?
  4. The sketch shown below represents the first 60 triangular numbers in intervals of 20. Use this diagram to find the 40th and 60th triangular numbers? Use the visual patterns to describe extensions of this sketch for predicting the 80th, 100th, and 120th triangular numbers. Check your predictions using the Mathematics Investigaor.
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::Graph::/sites/dl/free/0072532947/78558/1sect2.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Graph (53.0K)</a>Graph  





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