Mathematical+Reflections,+p33+0809




Wednesday, March 18th, 2009 Z.K.  Big Idea: Equations can be used to model real things.

Essential Question: How can I tell if two expressions have the same value? ** Mathematical Reflection ** // Investigation Two //
 * 1. **** What do we mean when we say that the expressions 4n + 4 and 4(n+1) are //equivalent//? Make a diagram, a table, and a graph to illustrate that the expressions are equivalent. **

These two equations are equivalent because you get the same results. The relationship shown in both the table and graph is linear.
 * ** X ** || ** 4n + 4 ** || ** 4(n+1) ** ||
 * 0 || 4 || 4 ||
 * 1 || 8 || 8 ||
 * 2 || 12 || 12 ||
 * 3 || 16 || 16 ||
 * 4 || 20 || 20 ||
 * 2a. Write 5x + 8x in factored form. **

5x + 8x in factored form becomes x(5+8) or (5+8)x 5(x+7) in expanded form becomes 5x + 35 The factored form is a product of two numbers, while the expanded form in the sum of two numbers. These two equations are equivalent because the results are the same. Since the results are the same the two equations are equvialent.
 * 2b. Write 5(x+7) in expanded form. **
 * 2c. How can you tell whether an expression is in expanded form or factored form? **
 * 3a. Use drawings, graphs, tables, or some other method to show that 5(2x) is equivalent to 2x(5) **
 * ** X ** || ** 5(2x) ** || ** 2x(5) ** ||
 * 0 || 0 || 0 ||
 * 1 || 10 || 10 ||
 * 2 || 20 || 20 ||
 * 3 || 30 || 30 ||
 * 4 || 40 || 40 ||
 * 3b. Use drawings, graphs, tables, or some other method to show that 5 + 2x is equivalent to 2x + 5. **
 * ** X ** || ** 5 + 2x ** || ** 2x + 5 ** ||
 * 0 || 5 || 5 ||
 * 1 || 7 || 7 ||
 * 2 || 9 || 9 ||
 * 3 || 11 || 11 ||
 * 4 || 13 || 13 ||


 * 3c.** [[image:MR_2(1.jpg]]
 * 3d.** You have a common factor in expanded form so in the case of factored form you can have the factors multiplied by each term.


 * Summary:**

In this investigation I learned how to tell how equivalent expressions are equivalent.