Question

Jenna’s method: Mia’s method: 5(30 + 4) 5(30 + 4) (5)(30) + (5)(4) 5(34) = 170 150 + 20 = 170 Explain why both Jenna and Mia arrived at the same answer and the advantage of one method over the other.

Answer 1

Every single equation equals 170:
MIA
5(30+4) = 5(34) = 5 x 34 = 170
(5)(30) + (5)(4) = 5 x 30 + 5 x 4 = 150 + 20 = 170
5(34) = 5 x 34 = 170

JENNA
150 + 20 = 170

Jenna's method is the equation in its simplest form.  Addition that is easily understood.  While Mia's method is just as valid as Jenna's, some people may have trouble remembering the steps of multiplication within parentheses as well as being able to look at large multiplication problem such as 5x34 and automatically knowing the answer, or being able to get the answer, as fast as simple addition. 

Answer 2

Both methods multiplied 5 and 34, but Jenna’s method used the distributive property to simplify the multiplication so she could do the math mentally. Mia’s method would require more complex multiplication.