Fill It Up, Please - Part I (Option B)

Childhood's fond memories of beachy days building sandcastles get the algebraic treatment in this rate-of-change investigation and problem set. Learners model filling rectangular prisms with sand, then discuss the meaning and effect of various parameters and results. Scaffolded questions start with a simple set-up, then scaffold through equation solving, introduction of variables as measures, and synthesizing results. Tuck this great stand-alone activity away for a rainy (or sandy) day.

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CCSS: Designed
Instructional Ideas

  • Extend the problem set by having students physically model and measure the prism-filling situations with water and or sand
  • Have interested learners consider the filling of cylinders, then compare and contrast with the given filling of prism problems
  • Included answer key and instructions for group learning make this a good one- or two-day substitute lesson
Classroom Considerations

  • Space between problems is probably not sufficient for showing work on the student worksheets
  • Consider using the teaching suggestions for collaborative group work, especially for ESL learners, and modeling one or two problems as an example
  • Think about preparing remediation ahead of time for weaknesses in finding volumes of prisms 

  • Problems build in concepts and complexity without depending on exact results from prior work
  • Emphasis on interpreting and analyzing numerical results
  • Broad range of problem styles, from open-response to fill-in-the-blank to multiple choice

  • None