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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 - Sums and Differences of Squares Instructions (Word Format) (26.0K)



Calculator Investigation 3.4


Sums and Differences of Squares

One student noticed that 12 divides 102 - 22. Further investigation revealed that 23 divides 202 - 32 and that 57 divides 502 - 72.

Starting Points for Investigations

  1. Will this pattern hold for other two-digit numbers?

  2. Will the pattern hold if, instead of taking the difference of the squares, we take their sum? For example, does 12 divide 102 + 22? Are there other two-digit numbers for which we can use the sum of the squares?

  3. Will the pattern of using differences hold for three-digit numbers? (For example, does 134 divide 1002 - 342?

  4. To gain further insight in this investigation, use the distributive property to expand (10 + 3) x (10 - 3). What does this result suggest?





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