Men of Magic Vocabulary: Connecting Words in Action
In this learning material, students engage in activities related to men of magic vocabulary, connecting words, and reading comprehension. The content includes exercises, photo analysis, and exploring the lives of famous magicians like Houdini and David Blaine. By using connecting words like "first, next, then," readers can follow the order of events and enhance their understanding of the text.
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Magic Fractions nRich cannot find url
Magic Fractions Choose three, different, non-zero integers that sum to zero. e.g. 3, 5, 8 Form all the possible ordered pairs you can with these numbers (you should get six) 3,53, 85,35, 8 8,3 8,5 Turn all of these into fractions using the first number as the numerator and the second as the denominator. 3 5 , 3 8 , 5 3 , 5 8 , 8 3 , 8 5 Sum all of these fractions. Find the product of all of these fractions. Can you prove any findings you make?
Magic Fractions Example: The pairs are: 3,5 3,-8 5,3 5,-8 -8,3 -8,5 3 5 -8 The fractions are: 3 5 3 5 3 5 8 3 5 8+ 8 8 8 8 5 3+ 8 8 8 3 5+ 8+5 3 5 3 Sum them: Multiply them: 3+ 3 8 5 5= 3 3 8 5 3 5= 1 Why does this happen?
Magic Fractions Let the numbers be: ? ? ? The pairs are: ?,??,??,? ?,? ?,? ?,? The fractions are: ? ? ? ? ? ?+? ? ?+? ? ? ?+? ? ? ?+? ? ? ? ? ?+? ?+? ?+? Sum them: ? ? ? ?+? Reordering: ?+ ?+ ?
? ?+? ?+? ? ? ?+? ?+? ? ? ?+? Reordering: ?+ ?+ ? ?+? ? Simplifying: Remembering that? + ? + ? = 0, we know that ? + ? = ?, ? + ? = ?, ? + ? = ? + + ? ? ? ? ? ? So, we get: Simplifying: 1 + 1 + 1 = 3 + +
Magic Fractions ? ? ? ? ? ? 1 1 1 = 1 ? ? ? ? ? ? ? ? ? ? ? Multiply them: ? ? ? ? Reordering: Simplifying: ? ? ? Did the numbers we chose need all the restrictions that were imposed on them?
