## Reflection: Letters & Postcards, Day 1 of 2 - Section 1: Individual Time

This assignment may be better suited for the introductory problem for linear programming.  Asking students to simply identify points by examination – after spending the previous few days working with a system of inequalities – seems out of order.  That said, this problem certainly wasn't too easy for them.

Many students struggled to find potential solutions.  The most common points first identified were pairs making 14, such as (8, 6) or (12, 2).  After seeing a number of points falling in line, many students mistakenly assumed that any point on the line x + y = 14 was a feasible solution.  It seemed that as they recognized the graphical pattern, they simply forgot about the rest of the conditions.  In this case, I would point to one of the incorrect solutions and innocently ask, "Can you explain to me why this option is viable?"  As the students began to explain, they would quickly recognize that it violated one of the other conditions.

Once students began to also identify pairs making 18, such as (15, 3) and (12, 6), they didn’t recognize the solutions in between.  For example, after seeing that along with 3 letters Alice could send either 15 postcards or 12 postcards, they failed to see that she could also choose to send 13 or 14 postcards along with the 3 letters.  Again, they were seeing the graphical pattern, but not attending to the meaning in context. In this case, I would say something like, "Oh, I see.  In this case she writes to 14 friends and in this case she writes to 18.  Good.  Would it be okay if she wrote to 15 friends?  How about 16?"  With guidance like this, they were able to find the rest of the solutions (See the sample of Student Work).

A small handful of students opted to immediately set up a system of inequalities.  One of these graphed the lines correctly, but needed help identifying the feasible region.  Several others mixed up their axes and plotted the solutions inconsistently.

I thought it would be easier than this!

# Letters & Postcards, Day 1 of 2

Unit 1: Modeling with Algebra
Lesson 4 of 15

## Big Idea: Linear systems are useful mathematical models for situations with a several of constraints. Time is money!

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45 minutes

### Jacob Nazeck

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