| 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 - Fraction Patterns Instructions (Word Format)
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Laboratory Investigation 5.3Fraction Patterns
This tower of bars represents fractions with denominators 2 through 12. Each geometric pattern corresponds to a pattern of fractions. The edge of a piece of paper or straight edge can be used to line up equalities and inequalities.
 <![CDATA[<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0072532947/78543/LI_5_3.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"> (41.0K)</a>]]>- Investigate the tower for patterns, there are many. For each geometric pattern, write the corresponding number pattern.
- One student noticed that the difference between the 1/2 bar and the 1/3 bar is one-half of 1/3 (see dark line). That is, 1/2 - 1/3 = 1/2 x 1/3. Does 1/3 - 1/4 = 1/3 x 1/4 ? Does 1/4 - 1/5 = 1/4 x 1/5 ?
- If the line at the end of the 1/2 bar (top of tower) is continued down, it divides one of the thirds in half. This shows that 1/2 = 1/3 + 1/2 x 1/3. Do the bars show that 2/4 = 2/5 + 1/2 x 1/5 ? or that 3/6 = 3/7 + 1/2 x 1/7 ?
- What other patterns can you find?
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