The example of two travelers meeting somewhere along the road has been a stereotypical joke about algebra as long as algebra has existed. Here in this detailed presentation, this old trope gets a careful and approachable treatment. Learners are guided through strategies for converting word problems to one-variable linear equations, and then led through working two examples. Special emphasis is put on the reasonableness of units and solutions, making this lesson a great fit for a curriculum with an engineering focus.

Concepts

word problems, linear equations writing, linear equations applications, solving for 1 variable

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Additional Tags

math

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Instructional Ideas

• Provide a link to the presentation on the class website for pre-class viewing in a flipped classroom model or for on-demand remediation during homework in a traditional setting
• Work with a shop class to develop a working model to go with the second example, then test the solution
• Young algebrists can re-create the scenario in the first example using distances in their own lives: relative's homes, vacation destinations, potential college or military locations

Classroom Considerations

• Viewing the PowerPoint lesson requires the ability to access a *.pptx file
• Accessing the online interactive applets requires Internet access and an updated Java player
• Learners unfamiliar with the distance, rate, and time relationship might need extra help developing the formula in the first example
• The key realization that the two travelers must travel the same time in the first example might require explicit explanation

Pros

• Detailed notes with common mistakes identified
• Attack strategies written out and then demonstrated
• Linked applet with pre-filled information for quick use and manipulation
• Problems use real-life examples and quantities
• Highlight on reasonableness of solutions and units

Cons

• Coefficients and constants defined as only rational numbers
• Bottom sentence of slide 3 should read "...and a ratio is a rate that compares different kinds of units."
• Shaky treatment of significant figures on slides 4 and 16
• Examples numbered 3 and 5 instead of 1 and 2
• No independent practice or homework problems provided

Common Core

HSA-CED.A.1 HSA-CED.A.4 MP1 MP2