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One thing that puzzles a lot of young algebrists is the factors in a word problem that are taken as "understood". This presentation on solving systems of linear inequalities does a great job walking the learner through how to tease those background constraints out of an inequality word problem. By giving a concrete set of attack strategies and then modeling the strategies in problems, this lesson makes a great add-on to your algebra curriculum.
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CCSS:
Adaptable
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Instructional Ideas
- Link on the class website for an effective before-class presentation in a flipped classroom model or for on-demand homework help in a traditional setting
- Poll local painting or other hourly service providers in the community to create and solve problems modeled on example 4
- Divide the class into small groups, and have each group come up with a word problem that would result in the system of inequalities in example 1
- Brainstorm as a class different situations that would result in a system of inequalities with understood constraints, such as x or y greater than 0
Classroom Considerations
- Viewing the presentation PowerPoint file requires the ability to open a *.pptx file
- Internet access and updated Java player needed to use the interactive graphing applet linked in the presentation
- Working these problems will reveal weaknesses in graphing linear equations and testing points, so consider having remediation handy
Pros
- Detailed description of problem-solving strategies
- Examples solved step-by-step
- Common misconceptions and mistakes discussed
- Both examples contain links to an interactive applet pre-loaded with problem information
- Two different types of examples demonstrate application of attack methods in a variety of problems
Cons
- Blue and gray opaque shading in the examples makes the overlap set hard to identify, especially since equations aren't graphed in each step
- The second example is numbered 4 instead of 2
- No independent practice or homework problems provided