2.2+Thinking+in+Different+Ways+0809

March 18, 2009 SO Equations can be used to model real things. How can I tell if two expressions have the same value? Notes: A good way to check and see if your expressions are equivalent is to make a table or to substitute the variable with a number..

B. Jeri wrote the expression s+s+s+s+4** **to represent the number of border tiles. Draw a picture that illustrates how Jeri might have been thinking about the border of the pool. C. Sal wrote the expression 2s+2(s+2) to represent the number of border tiles. Draw a picture that illustrates how Sal might have been thinking about the border of the pool. D. Jackie wrote the expression 4(s+2)-4 to represent the number of border tiles. Draw a picture that illustrates how Stella might have been thinking about the border of the pool. E.** **Explain why each expression in parts A-D is equivalent to Takashi's expression.** A - 4(s+1) is equivalent to Takashi's expression because 4xs is equivalent to 4s and +4x1 is equivalent to +4 in Takashi's expression. B - s+s+s+s+4 is equivalent to Takashi's expression because 4s is the same as s+s+s+s, +4 is equivalent to adding on the 4 corners. C - 2s+2(s+2) is equivalent to Takashi's expression because 2s+2 is equivalent to 4s, and 2x2 is equivalent to 4. D - 4(s+2)-4 is equivalent to Takashi's expression because 4xs is equivalent to 4s, and 4x2-4 is equivalent to 4.
 * A. Stella wrote the expression 4(s+1) to represent the number of border tiles. Draw a picture that illustrates how Stella might have been thinking about the border of the pool.

1. Evaluate each of the five expressions given in the problem for s=10. Can you conclude from your results that all the expressions are equivalent? Takashi 4s+4 - 4(10)+4 - 40+4 = 44** Stella 4(s+1) - 4(10+1) - 4(11) = 44 Jeri s+s+s+s+4 - 10+10+10+10+4 - 40+4= 44 Sal 2s+2(s+2) - 2(10)+2(10+2) - 2(10)=2x12 - 20+24= 44 Jackie 4(s+2)-4 - 4(10=2)-4 - 4x12-4 - 48-4= 44 Yes I can conclude that all of the expressions are equivalent because for each expression, when I substituted s for 10 the answer was always 44, so that tells me that each of the expressions are equivalent.
 * Follow Up

Yes the expressions are equivalent, and because I knew they were equivalent after question 1 I only needed to make 1 graph and 1 table because equivalent expressions will make equivalent tables and graphs.
 * 2. Make a table and a graph for each of the five expressions. Do the tables and the graphs indicate that the expressions are equivalent? Explain.**
 * Side Length (s) || Number Of Tiles ||
 * 0 || 4 ||
 * 1 || 8 ||
 * 2 || 12 ||
 * 3 || 16 ||
 * 4 || 20 ||
 * 5 || 24 ||