## Reflection: Intervention and Extension Solving Two Variable Inequalities Part 2 - Section 2: Investigation

This lesson went much more smoothly on day 2.  It was interesting to me that the place where students struggled the most was with determining points for the boundary lines.  I go back and forth about the questions I chose for students (which were strategically chosen).

On one hand, I wanted the students to see that not every point they use has to be composed of two integers.  Students are so worried when the get decimal values and they feel that they are wrong.  I wanted them to see that they could graph decimal values just like integer values.  For example, the boundary line for the inequality 2x-2y>5 has solutions such as (1,-1.5) (MP2).  Students had some difficulty coming up with solutions like this without being prompted.  I think I can blame that on the fact that the opening questions over the past two lessons were x+y<25 and x+y<10.  The coordinates for the boundary line of both of these can be determined very simply.  Students did not understand the procedure at first for "solving" for y to find the y-coordinate.

On the other hand, I think in the future I will change the investigation to include at least two inequalities of the form 2x-2y<4.  This way there is some solving that needs to take place but students can also reason more easily about the values that make the equation for the boundary line true (MP7).  For most of my examples there were very few integer values that made them true and that confused some students (see student work in closure).

Investigation Reflection
Intervention and Extension: Investigation Reflection

# Solving Two Variable Inequalities Part 2

Unit 2: Linear Functions
Lesson 19 of 19

## Big Idea: See how to use test points to determine how to determine the solution to a two-variable inequality.

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Standards:
Subject(s):
Math, Algebra, linear inequalities, inequality, test point, boundary line
40 minutes

### James Bialasik

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