The beauty of this problem is its changeability. It is identified with a specific grade or course, but it can be manipulated for various ability levels. Along with its changeability, this problem is practical. As mentioned prior, students struggle to understand problems that have no real-world context. Many students want there to be purpose in solving given problems. Many SMPs are implemented when solving this problem. SMPs are used in the mathematics classroom, but they can also apply to the real-world. Making sense of problems and persevering in solving them does not apply to strictly mathematics problems. Students will face multiple obstacles in their lifetime, and they need to know how to make sense of them and solve through perseverance. Attending to precision is also an SMP that will be used outside of the mathematics classroom. Precision is look for and praised in the workforce, so developing this characteristic now will benefit student in the future.

This problem brings together many aspects both inside and outside of the mathematics classroom. Mathematics is deeply embedded in many aspects of daily life, both seen and unseen (NRC 2011, as cited in NCTM, 2018). When the multiple purposes of school mathematics are emphasized as Catalyzing Change in High School Mathematics recommends, students are prepared to “flourish as human beings”, no matter what paths they take in life or what profession they choose (Su 2017, p.483, as cited in NCTM, 2018). Students may see a volume problem, but as teachers we see a way to mold our students into flourishing human beings.

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References:

National Council of Teachers of Mathematics. (2018). Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA: Author.

National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common core state standards for mathematics. Washington, DC: Authors. Downloaded from http://bit.ly/commcoremath

Alabama Department of Education. (2016). Alabama college and career ready standards for mathematics. Montgomery, AL: Author. Downloaded fromhttp://bit.ly/alcos-math2016