# A Mathematical Approach to Designing Insulators

Kathryn E. Pedings-Behling (SC Governor's School for Science and Mathematics, USA)
DOI: 10.4018/978-1-5225-2334-5.ch012
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## Abstract

How do we keep hot drinks hot and cold drinks cold? Companies such as Tervis, YETI, and Thermos spend their time researching and designing products around that very question. In this lesson, students will discover, through mathematical modeling, which materials provide the best insulation and be tasked with designing their own insulator. This lesson has been designed at two different levels for students from grade three through high school with an optional extension activity for more advanced students. Students will use technology to explore the rate of change of the temperature of hot water over two minutes using different insulation materials. After this exploration, students will use the data they have collected to determine the best materials for designing their own insulator. This insulator will then be judged based on the ability to keep a hot drink hot and on the aesthetic value.
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## Content Information

This activity aligns with many national standards across several different subject areas. Most notably, this activity puts to use several standards from the Common Core State Standards for Mathematics (CCSSM). Certain questions in this activity are written at two different levels with an optional extension for students beyond the Algebra 2 level. The questions specifically written for grades 3-5 align with CCSSM standards related to differences and numerical comparisons such as 3.NBT.A.2, 4.NBT.A.2 and 4.NBT.B.4. The questions specifically written for grades 6-12 draw from standards about ratios and rate of change including 6.RP.A.3, 7.RP.A.3, 8.F.B.4, and HSA.CED.A.1. Finally, the optional extension activity relates to standards involving modeling exponential functions found in HSA.CED.A.2 and HSF.LE.A.1 (Common Core Standards Initiative, 2010).

Although this activity takes a mathematically-forward approach to designing insulators, standards from the other STEAM fields are integral to the well-roundedness of the learning experience. From the Next Generation Science Standards, the activity specifically aligns with standards relating to thermal energy transfer and engineering including 3-5-ETS1, MS-PS3-3, MS-ETS1, HS-PS3-3, and HS-ETS1 (NGSS Lead States, 2013). This activity also heavily relies on technology and draws from the International Society for Technology in Education (ISTE) standards 1.c, 4.b, and 4.c (ISTE, 2007). Finally, the arts component of this activity aligns with the creating anchor standards 1, 2, and 3 from the National Core Arts Standards (2014).

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