Using data to generate conversations about strategies

Recently, as a part of my evaluation, I gave students in a 5th grade class the following two problems to solve:

1. OfficeMax sells pencils in large boxes.  Mrs. Bailey bought some pencils for the students at school.  There were 150 pencils in each box.  She bought 8 boxes.  How many pencils did Mrs. Bailey buy?
2. 86 x 23 = ____

Students were able to solve the problem in any way they wanted during this pre-assessment.  In past years, I felt like I had involved students in discussing their strategies and analyzing both their own work and the work of others.  Because I am not a classroom teacher this year, I was more explicit in presenting the data to students and in this process we noticed some interesting patterns about strategies.  Here is a chart of the accuracy and strategies students used to solve the problems above:

For the first problem:  OfficeMax sells pencils in large boxes.  Mrs. Bailey bought some pencils for the students at school.  There were 150 pencils in each box.  She bought 8 boxes.  How many pencils did Mrs. Bailey buy?

Strategies                                                       Accuracy

Repeated Addition	10/11 students answered correctly	91%
Standard/Traditional Algorithm	6/9 students answer correctly	67%
Doubling/Halving	1/1 students answered correctly	100%

For the second problem: 86 x 23 =

Strategies                                                       Accuracy

Repeated Addition	0/1 students answered correctly	0%
Standard/Traditional Algorithm	6/15 students answered correctly	40%
Partial Products with Boxes	4/4 students answered correctly	100%
Partial Products	0/1 students answered correctly	0%

Students were engaged in the conversation and shared great thinking!  For example, students explained why someone might use repeated addition in the first problem but not in the second problem since the numbers became too large to easily keep track of the addition. 

We WANT for students to have multiple strategies for solving problems and to know WHEN and WHY to use them.  It might make more sense to use repeated addition when solving 175 x 3 because the numbers are reasonable for addition.  Students should recognize, however, that when solving 175 x 83 that repeated addition is not a reasonable strategy to use.  This activity also led to a great conversation about efficiency.  Which algorithms are most efficient?  In what situations?  I'm sure the students in your classrooms have great ideas to share!