Mathematical
Practice Standards: Reason
abstractly and quantitatively. Construct
viable arguments and critique the reasoning of others.
Aaron needs to rip (cut length wise) a 2 x 10 into 3 equal
strips. He does not like working
with the ugly number that is the width of the 2 x 10, which is 9 ¼”. Fractions are not his friends and he
doesn’t want to divide a fraction by 3 (or any number). He claims he can pick a number that is
easy to divide by three (15, for example) and measure that distance diagonally
across the board. Then mark the
board at 5 inch increments (5, 10, and 15”) and his marks will divide the board
into equal widths.
Does this method work or is this a shortcut that Aaron has
fabricated that is a result of his wishful thinking?
Provide an argument supporting why this works or why it
doesn’t’ work. Use diagrams and
words combined with your detailed mathematics to support your argument.
Hint for answer: Use what you know about congruent triangles. In this problem, you created 3 of them.
