National Academies Press: OpenBook

Engineering in K-12 Education: Understanding the Status and Improving the Prospects (2009)

Chapter: Appendix C: Curriculum Projects - Detailed Analyses

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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 217
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 219
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 220
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 221
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 222
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 223
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 224
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 225
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 226
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 227
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 228
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 229
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 230
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 231
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 232
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 233
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 234
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 235
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 236
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 237
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 238
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 239
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 240
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
Page 241
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 242
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 243
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 244
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 245
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 246
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 247
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 248
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 249
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 250
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 251
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 252
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 253
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 254
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 255
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 256
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 257
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 259
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Page 260
Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
×
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Suggested Citation:"Appendix C: Curriculum Projects - Detailed Analyses." National Academy of Engineering and National Research Council. 2009. Engineering in K-12 Education: Understanding the Status and Improving the Prospects. Washington, DC: The National Academies Press. doi: 10.17226/12635.
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Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Building Math Institution Museum of Science Science Park Boston, MA 02114 Tel: (617) 589-0230 Fax: (617) 589-4448 E-mail: eie@mos.org Web site: http://www.mos.org/eie/index.php Leaders Peter Y. Wong, National Center for Technological Literacy Barbara M. Brizuela, Tufts University Funding GE Foundation Grade Level 6-8 Espoused “…to involve math students in collecting and analyzing their own Mission data in hands-on investigations integrated with engineering design activities.” Organizing The curriculum features the following three units of instruction: Topics x Everest Trek is a sixth-grade unit presented in the context of scaling the world's tallest peak. It engages students in designing a well-insulated coat, a ladder bridge to span a crevasse, and an emergency zip-line transportation system. x Stranded! is a seventh-grade unit presented in the context of being marooned on a deserted South Pacific island. It engages students in designing a shelter, a water collection device, and a strategy for loading and unloading a canoe. x Amazon Mission is an eighth-grade unit that is presented in the context of helping indigenous people in Brazil. It engages students in designing an insulated carrier that will keep medicine cool, a water filtration system, and a strategy for tempering the spread of an influenza virus. Format The Building Math program comprises three spiral-bound books. Each book represents a unit of instruction for a given grade level that features three distinct design challenges. Every design C-1

challenge features a series of lessons that follow an eight-step engineering design process that is outlined at the beginning of each unit. The books have reproducible handouts, rubrics, and self- assessment checklists for students. Pedagogical The following pedagogical elements can be found in each unit. Elements x All the units and their design problems are framed in authentic sounding contexts that middle school students should find interesting and challenging. x Every unit begins with a series of exercises that can be used to assess or address prerequisite knowledge and skills. x Each unit also begins with a team-building activity that asks small groups of students to complete a task that cannot be achieved without benefit of cooperation. x Each design challenge includes a series of lessons (or tasks) that use an engineering design process to construct knowledge in small and sequential increments. x The lessons (or tasks) feature objectives, implementation procedures, guiding questions, possible answers, and support materials for students. x The instruction is very Socratic in nature (i.e., posing questions, addressing questions). x Most of the learning activities involve inquiry. More specifically, developing solutions to the problems posed involves making observations, taking measurements, gathering data, interpreting data, generalizing patterns, applying patterns to the solution, building and testing models, and reflecting on the quality of the solutions as well as the learning process. x Each unit includes a very detailed and comprehensive rubric for facilitating student assessment. Maturity The GE Foundation funded the project for three years. The materials underwent two years of pilot testing and refinement during that period of time. The final units are currently available through Walch Publishing. Stranded and Everest Trek bear a 2006 copyright and Amazon Mission shows a 2007 copyright. Diffusion The series was pilot tested with hundreds of students in ten & Impact Massachusetts schools over the course of two years. This process produced positive testimony from pilot-site teachers. For example, Joseph McMullin at the Mystic Valley Regional Charter School in Malden, Mass., was quoted as stating: "In addition to relating math concepts to the physical world, my students improved their communication, graphing, critical thinking, and problem solving skills. Students especially enjoyed designing their own test." C-2

An analysis of teacher testimony, samples of student work, direct observations, and videotape data supported the underlying premise of the curriculum. More specifically, the study of mathematics can be enriched with contextual units of instruction that employ hands- on learning activities that require students to apply a variety of math concepts and skills while following an engineering design process to solve problems. The collection and analysis of their data during engineering design activities helped math students develop and demonstrate algebraic thinking skills. C-3

Initiative Building Math Title Amazon Mission Broad Goals During Design Challenge 1: Malaria Meltdown, students will: x Calculate and interpret the slope of a line. x Graph a compound inequality. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze a line graph that relates two variables. x Distinguish between independent and dependent variables. x Determine when it’s appropriate to use a line graph to represent data. x List combinations of up to five layers of two different kinds of materials. x Draw a three-dimensional object and its net. x Find the surface area of a three-dimensional object. x Apply the engineering design process to solve a problem. During Design Challenge 2: Mercury Rising, students will: x Calculate the surface area of a sphere using a formula. x Solve a multistep problem. x Convert measurement units (within the same system). x Use proportional reasoning. x Write a compound inequity statement. x Graph and analyze the relationship between two variables. x Design and conduct a controlled experiment. x Apply the engineering design process to solve problems. During Design Challenge 3: Outbreak, students will: x Identify and extend exponential patterns. x Generalize and represent a pattern using symbols. x Graph simulation data and describe trends. x Calculate compound probabilities. x Use a computer model. x Apply the engineering design process to solve a problem. Salient Math Science Technology Concepts x making line graphs x climate zones x shabono & Skills x heuristics (rules of x tropical x model thumb) x subtropical x prototype x independent x temperature variables x cold C-4

x dependent x polar variables x rate of heat x X-axis transfer is based x Y-axis on differences in x scale temperature x scaling axes x controlled x proportional experiment reasoning x extinct x exponential x endangered patterns x indigenous x linear patterns x virus x rounding up x mercury x rounding down x malaria x interpreting line x rain forest graphs x ratios x converting units x equivalent fractions x cross-multiply x recursive equations x Cartesian plane x calculate the slope of a line x graph a compound inequality x sphere Engineering The materials introduced the following ideas about the nature of engineering. x Engineers play a part in the design and construction of things like houses, roads, cars, televisions, and phones. x Engineering is “the application of math and science to practical ends, such as design or manufacturing.” x All engineers use the engineering design process to help them solve problems in an organized way. x The engineering design process includes defining the problem, conducting research, brainstorming ideas, choosing the best solution, building a model, testing and evaluating a prototype, communicate the design to others, and redesigning the solution. x The engineering design process “is meant to be a set of guidelines” for solving technical problems. x Engineers may not always follow all the steps in the design process in the same order every time. x Engineers communicate their designs to others to solicit C-5

feedback and ways to improve the design. x Engineers often go back to an earlier step in the design process during the “redesign” process. x The solution to a problem might go through several cycles of the design process before it is ready for “real-world use.” x A full-scale working prototype may be constructed once the design has gone through several cycles of the design process. x Constraints are “limiting factors” that engineers need to consider during the design process. x Criteria are the specifications that need to be met for the solution to be successful. Prominent The unit starts with a team-building activity and a review of Activities prerequisite math skills. 1. Read and analyze a poem (The Law of the Wolves) and discuss how it relates to working in teams. 2. Review basic mathematics skills that will be utilized during the unit (e.g., make a line graph, find the slope of two points, calculate surface area). 3. Review basic math skills related to converting units of measure. 4. Compose and use heuristics or rules of thumb. Introducing the Engineering Design Process engages students in the following activities to develop a basic understanding of the nature of engineering. 1. Read background information about the Yanomami people (i.e., their way of life, the threats to their existence). 2. Discuss the questions: What is an engineer? What does an engineer do? 3. Put cards describing the basic steps of the engineering design process into a logical sequence. 4. Match a series of events related to making and testing sails for a boat race with the basic steps in the design process. Design Challenge 1: Malaria Meltdown engages students in the following activities to design a container for transporting medicine that has to be kept cool in a tropical climate. 1. Read a scenario that contains the problem to be solved, the criteria that needs to be met, and the material constraints. 2. Analyze a graph containing data (temperature over time) that depicts the performance of the current container for transporting the medicine. 3. Gather, graph, and interpret data regarding the rate of heat conduction for specific materials (corrugated cardboard, foam board, bubble wrap, aluminum foil). C-6

4. Gather, graph, interpret, and present data regarding the rate of heat conduction for combinations of multiple materials. 5. Utilize research findings and material costs to develop a dimensioned sketch for a potential medicine-carrier design. 6. Select the best design from those developed by the members of the team through discussion and consensus. 7. Sketch a three-dimension representation of the selected design that includes dimensions and labels the materials used. 8. Sketch a “net” (a.k.a., development) of the selected design (a drawing that illustrates what a three-dimensions object would look like if it were spread out in the form of a two-dimensional layout). 9. Calculate the area of the materials needed to construct the selected design and use the results to determine the cost of making the final product. 10. Build a prototype for the selected design. 11. Use pieces of scrap to test the heat transfer rate of the materials used to make the container. 12. Test the ability of the container to protect a fragile object (an egg) by dropping the container to the floor from a height of one meter. 13. Determine the cost of making the actual container (a scaled-up version). 14. Present the final design to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the design, the disadvantages of the design, the cost and profit potential of the design). 15. Reflect on the design and describe how it might be improved through redesign. 16. Conduct a self-assessment of the contributions made by each member of the team. 17. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 2: Mercury Rising engages students in the following activities to design a water filtration device that removes mercury from river water. 1. Read a scenario that contains the problem to be solved, the criteria that needs to be met, and the material constraints. 2. Calculate the surface area of spheres with different diameters. 3. Determine the most cost-effective package of spheres to achieve a desire amount of total surface area. 4. Convert the units of measurement for minimum flow rate from 540 liters per day to the number of seconds need to filter 250 milliliters. C-7

5. Convert the units of measurement for maximum flow rate from one liter per minute into the number of seconds need to filter 250 milliliters. 6. Gather, graph, and interpret data for the amount of time required for 250 milliliters of water to pass through different diameter holes. 7. Conduct a controlled experiment to gather, graph, and interpret data regarding another factor that could affect the amount of time required for 250 milliliters of water to pass through a filter. 8. Sketch a potential design for a water filter that shows where water will enter, be filtered, and subsequently exit. Use the research results to define how large the exit opening needs to be. 9. Select the best design from those developed by the members of the team through discussion and consensus. 10. Develop a drawing for the selected design that shows dimensions, identifies the materials used, and describes the role that each material plays in the filtering process. 11. Build a model filter based on the selected design. 12. Test the amount of time it takes for 250 milliliters of water to pass through the filter. 13. Present the final design to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the design, the disadvantages of the design, what materials would be used to make a real filter). 14. Reflect on the design and describe how it might be improved through redesign. 15. Conduct a self-assessment of the contributions made by each member of the team. 16. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 3: Outbreak engages students in the following activities to design a virus intervention plan to contain the spread of the flu. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Conduct a simulation to illustrate exponential rate at which a virus can spread and infect a population. 3. Calculate the rate at which a virus would spread if a doctor were able to treat one member of the population per day. 4. Determine the rate at which a virus would spread if every member of the population wore a filtration mask that reduced the risk of infection by 50 percent. C-8

5. Use the results to graph the rate at which people become infected if there is no treatment, if there is one doctor, and if everyone wears a mask. 6. Calculate the chance of infection based on different combinations of interventions (e.g., the use of air filtration masks and antiviral hand gel, the use of antiviral hand gel and vaccinations). 7. Develop intervention plans that will reduce the rate of infection to less than 25 percent during a 30-day window of time. 8. Discuss the advantages and disadvantages associated with each team member’s intervention plan. 9. Identify the best intervention plan by determining what the individual plans have in common, identifying the best parts of the individual plans, and combining the best parts into one design. 10. Test the final intervention plan using a computer simulation model (an applet). 11. Use the results of the computer simulations to redesign the intervention plan and make it as cost effective as possible. 12. Present the refined intervention plan to the class (e.g., how it performed in relation to the design constraints and criteria, the advantages of the plan, the disadvantages of the plan, how would it be different if more money were available, how would it work with a larger population). 13. Reflect on the design and describe how it might be improved through redesign. 14. Conduct a self-assessment of the contributions made by each member of the team. 15. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). C-9

Initiative Building Math Title Everest Trek Broad Goals During Design Challenge 1, Geared Up, students will: x Interpret a line graph. x Locate and represent the range of acceptable values on a graph to meet a design criterion. x Extrapolate data based on trends. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze graphs that relate two variables. x Determine when it’s appropriate to use a line graph or a scatter plot to represent data. x Apply the engineering design process to solve a problem. During Design Challenge 2, Crevasse Crisis, students will: x Use proportional reasoning to determine dimensions for a scale model. x Use physical and math models. x Conduct two controlled experiments. x Collect experimental data in a table. x Produce and analyze graphs that relate two variables. x Compare rates of change (linear versus non-linear relationships). x Distinguish between independent and dependent variables. x Apply the engineering design process to solve a problem. During Design Challenge 3, Sliding Down, students will: x Conduct a controlled experiment. x Measure angles using a protractor. x Compare and discuss appropriate measures of central tendency (mean, median, mode). x Apply the distance-time-speed formula. x Produce and analyze a graph that relates two variables. x Locate and represent the range of acceptable values on a graph to meet a design criteria [criterion]. x Distinguish between independent and dependent variables. x Apply the engineering design process to solve a problem. Salient Math Science Technology Concepts x making line graphs x icefall x insulator & Skills x equal intervals x controlled x thermometer experiment C-10

x cross-multiplying x temperature x materials for x heuristics (rules of x hypothermia clothing (wool, thumb) x compression fleece, nylon) x data extrapolation x tension x layering materials based on trends x strength x prototype x complete data x modulus of x model tables elasticity x beams (e.g., T- x application for line x tensile strength beam, I-beam, graphs versus x ultimate tensile square channel) scatter plots strength x bridge x identifying x altitude x ladder bridge variables x density of air x zip-line x independent x altitude sickness variables x gravity x dependent x acclimatize variables x altitude sickness x X-axis x insulator x Y-axis x proportional reasoning x scale x non-linear patterns x linear patterns x measuring angles with a protractor x interpreting line graphs x ratios x measures of central tendency (mean, median, mode x Cartesian plane x calculate the slope of a line x calculating speed x centimeters Engineering The materials introduced the following ideas about the nature of engineering. x Engineers play a part in the design and construction of things like houses, roads, cars, televisions, and phones. x Engineering is “the application of math and science to practical ends, such as design or manufacturing.” x All engineers use the engineering design process to help them solve problems in an organized way. C-11

x The engineering design process includes defining the problem, conducting research, brainstorming ideas, choosing the best solution, building a model, testing and evaluating a prototype, communicate the design to others, and redesigning the solution. x The engineering design process “is meant to be a set of guidelines” for solving technical problems. x Engineers may not always follow all the steps in the design process in the same order every time. x Engineers communicate their designs to others to solicit feedback and ways to improve the design. x Engineers often go back to an earlier step in the design process during the “redesign” process. x The solution to a problem might go through several cycles of the design process before it is ready for “real-world use.” x A full-scale working prototype may be constructed once the design has gone through several cycles of the design process. x “Engineers use a lot of math in their work.” x “Using statistics and probability, engineers can test their hypotheses by analyzing data” from samples. x “Engineers use data analysis, such as filtering and coding information, to describe, summarize, and compare the data with their initial hypotheses.” x “Engineers use modeling and simulations to predict the behavior and performance of their designs before they are actually built.” x Constraints are “limiting factors” that engineers need to consider during the design process. x Criteria are the specifications that need to be met for the solution to be successful. Prominent The unit starts with a team-building activity and a review of Activities prerequisite math skills. 1. Use a simple device made out of a rubber band and segments string to stack cups in a limited amount of time without touching them directly and discuss how it relates to working in teams. 2. Review basic mathematics skills that will be utilized during the unit (e.g., interpreting a line graph, making a line graph, measuring length in centimeters, adding and multiplying decimals). 3. Compose and use heuristics or rules of thumb. Introducing the Engineering Design Process engages students in the following activities to develop a basic understanding of the nature of engineering. 1. Read background information about climbing Mount Everest C-12

(i.e., the challenges associated with climbing, the gear that is used, the importance of teamwork). 2. Study a simple map of the southern route up Mount Everest and relate the height and distances to more familiar things. 3. Discuss the questions: What is an engineer? What does an engineer do? 4. Put cards describing the basic steps of the engineering design process into a logical sequence. 5. Match a series of events related to making and testing sails for a boat race with the steps in the design process. Design Challenge 1: Gearing Up engages students in the following activities to design a coat that protect team members from the harsh weather conditions on Mount Everest. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Interpret a line graph illustrating heat loss under simple cotton clothing and relate the pattern to the design problem. 3. Determine a range of values for meeting the design criteria, explain the relationship between time and temperature, and describe the rate of change in the data. 4. Conduct a controlled experiment to determine the insulation qualities of different clothing materials (e.g., denim, fleece, nylon, wool). 5. Develop a line graph illustrating the relationship between the independent variable (time) and the dependent variables (temperature) for the four materials. 6. Conduct a controlled experiment to determine the potential benefit of layering a given materials. 7. Develop a bar graph illustrating the relationship between the independent variable (number of layers) and the dependent variables (temperature after 30 seconds). 8. Review the criteria and constraints associated with the design problem (i.e., minimum insulation performance, maximum material thickness, keeping the cost as low as possible). 9. Brainstorm potential coat designs (e.g., materials, number of layers, cost). 10. Select the best design from those developed by the members of the team through discussion and consensus. 11. Draw sketches of each team’s coat designs. 12. Assemble swatches of material to represent the design of their coats (prototypes). 13. Test the insulation quality of their designs (layers of different materials) using ice packs. 14. Reflect on the design and describe how it might be improved through redesign. C-13

15. Conduct a self-assessment of the contributions made by each member of the team. 16. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 2: Crevasse Crisis engages students in designing a bridge that can be used to cross a crevasse in the ice. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Determine the basic dimensions for building scale models. 3. Brainstorm factors that affect the strength of a bridge and how a craft stick will react to a force applied to its thickness versus it width. 4. Test their ideas about the strength of a craft stick relative to it orientation to a force (applied to its thickness versus its width). 5. Conduct controlled experiments to determine how the width of foam strips affect their strength when spanning the distance between two books while supporting the weight of a penny. 6. Develop a line graph illustrating the relationship between the independent variable (width of the foam strips) and the dependent variables (the amount of deflection under the load). 7. Conduct controlled experiments to determine how the thickness of foam strips affect their strength when spanning the distance between two books while supporting the weight of three pennies. 8. Develop a line graph illustrating the relationship between the independent variable (thickness of the foam strips) and the dependent variables (the amount of deflection under the load). 9. Build and test the strength of different shapes of beams (e.g., I- beam). 10. Individually brainstorm and sketch potential designs for bridges. 11. Select the best design from those developed by the members of the team through discussion and consensus. 12. Draw sketches of each team’s bridge designs. 13. Build models for each team’s bridge design (prototype). 14. Test the strength their bridge designs by spanning the distance between two books, suspending a cup from the middle, and adding pennies until it fails. 15. Reflect on the design and describe how it might be improved through redesign. 16. Conduct a self-assessment of the contributions made by each member of the team. 17. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be C-14

improved). Design Challenge 3: Sliding Down engages students in designing a zip-line transportation system to bring a sick teammate down the mountain. 1. Read a scenario that contains the problem to be solved, the criteria. 2. Conduct controlled experiments to determine how the speed of something (a drinking straw) traveling down a zip-line (fishing line) is affected by the angle of descent. 3. Review measures of central tendency (i.e., mean, median, mode) and select the best representation to decrease the effects of human error (using the median). 4. Calculate the average speed for the straws traveling down the line by dividing the amount of time required to travel the length of the line by the length of the line. 5. Develop a line graph illustrating the relationship between the independent variable (angle of the line) and the dependent variables (speed of the straw). 6. Brainstorm factors that can affect the stability and safety of the zip-line transportation system. 7. Review the design criteria and constraints (speed, safety, return) and draw designs for the zip-line transportation systems. 8. Select the best design from those developed by the members of the team through discussion and consensus. 9. Draw sketches of each team’s zip-line transportation systems. 10. Build models for each team’s zip-line transportation system (prototypes). 11. Test the zip-line transportation systems using toy figures. 12. Reflect on the design and describe how it might be improved through redesign. 13. Conduct a self-assessment of the contributions made by each member of the team. 14. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). C-15

Initiative Building Math Title Stranded Broad Goals During Where Are We, students will: x Interpret a scale on a map. x Use proportional reasoning to calculate actual distance and drawn distance on a map according to a scale. x Use the relationship speed = distance/time to find one quantity given the other two quantities. x Solve a multistep problem. x Use a ruler. During Design Challenge 1, A Storm Is Approaching!, students will: x Identify similar three-dimensional objects. x Identify corresponding dimensions of similar objects. x Use a ruler to measure three-dimensional objects. x Calculate surface area and volume of rectangular prisms. x Analyze a table of values for patterns. x Generalize patterns using symbols. x Use a scale to calculate the amount of materials available for building a scale model. x Apply the engineering design process to solve a problem. During Design Challenge 2, We Need Water!, students will: x Find the area of an irregular two-dimensional shape using strategies for finding the areas of triangles, rectangles, and parallelograms. x Use a ruler to measure three-dimensional objects (cylinders and rectangular prisms). x Calculate the surface area and volume of three-dimensional objects. x Analyze a table of values for patterns. x Make and test conjectures about the relationship between surface area and volume, and dimensions and volume. x Produce and analyze line graphs that represent the relationship between two variables. x Apply the engineering design process to solve a problem. During Design Challenge 3, Balancing Act!, students will: x Investigate how the weight and distance of objects on a horizontal platform with a center fulcrum relate physically and mathematically to keep the platform balanced. C-16

x Generalize and represent a pattern using symbols. x Apply the engineering design process to solve a problem. Salient Math Science Technology Concepts x scale x balance x shelter & Skills x heuristics (rules of x fulcrum x model thumb) x prototype x scale (on a map) x rainwater collector x proportional x canoe reasoning x use a formula to calculate an unknown quantity based on two known quantities x linear measurement (centimeters) x three-dimensions x detect patterns in data x ratio x nets (or developments) x calculate surface area (square, rectangles, trapezoids, triangles parallelograms) x square centimeters x calculate area for an irregular shape x calculate volume for cylinders and square boxes x radius x circumference x relationship between surface area and volume x relationship between dimensions and volume C-17

x plotting a double- line graph x interpreting a double-line graph x cubic centimeters x milliliters x relationship of weight and distance in the context of balance x physical and mathematical representations of balance. Engineering The materials introduced the following ideas about the nature of engineering. x Engineers play a part in the design and construction of things like houses, roads, cars, televisions, and phones. x Engineering is “the application of math and science to practical ends, such as design or manufacturing.” x All engineers use the engineering design process to help them solve problems in an organized way. x The engineering design process includes defining the problem, conducting research, brainstorming ideas, choosing the best solution, building a model, testing and evaluating a prototype, communicate the design to others, and redesigning the solution. x The engineering design process “is meant to be a set of guidelines” for solving technical problems. x Engineers may not always follow all the steps in the design process in the same order every time. x Engineers communicate their designs to others to solicit feedback and ways to improve the design. x Engineers often go back to an earlier step in the design process during the “redesign” process. x The solution to a problem might go through several cycles of the design process before it is ready for “real-world use.” x A full-scale working prototype may be constructed once the design has gone through several cycles of the design process. x Constraints are “limiting factors” that engineers need to consider during the design process. x Criteria are the specifications that need to be met for the solution to be successful. Prominent The unit starts with a team-building activity and a review of C-18

Activities prerequisite math skills. 1. Address a problem related to retrieving a limited number of survival items from a stranded shipwreck yacht before it sinks. 2. Discuss how solving the problem relates to working in teams. 3. Review basic mathematics skills that will be utilized during the unit (e.g., interpret a scale on a map; solve for speed, distance or time given two know quantities, measure in centimeters, calculate surface area). 4. Compose and use heuristics or rules of thumb. Where Are We engages students in using given pieces of information along with a map featuring a scale to determine the location of a deserted island. Introducing the Engineering Design Process engages students in the following activities to develop a basic understanding of the nature of engineering. 1. Read background information about being stranded on a deserted island. 2. Discuss the questions: What is an engineer? What does an engineer do? 3. Put cards describing the basic steps of the engineering design process into a logical sequence. 4. Match a series of events related to making and testing sails for a boat race with the steps in the design process. Design Challenge 1: A Storm is Approaching engages students in the following activities to design a shelter for protection from the wind and rain. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Investigate the concept of scale relative to one-dimensional, two-dimensional, and three-dimensional objects (e.g., width, depth, height, area, volume). 3. Identify the scale that will be used to make a model shelter and determine the dimensions of the materials that will be used to make the model. 4. Explore potential configurations for a simple shelter and discuss their advantages and disadvantages based on the available materials. 5. Individually brainstorm and sketch potential designs for a simple shelter. 6. Select the best shelter design from those developed by the members of the team through discussion and consensus. 7. Draw sketches of each team’s bridge designs. 8. Build models for each team’s shelter design (prototypes). C-19

9. Test the sturdiness, spaciousness, and water-resistance of their model shelters. 10. Reflect on the design and describe how it might be improved through redesign. 11. Conduct a self-assessment of the contributions made by each member of the team. 12. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). Design Challenge 2: We Need Water engages students in the following activities to design a rainwater collector. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Calculate the area of an irregular shape using multiple strategies. 3. Explore the relationship between area and volume in the context of making and testing two cylinders with the same surface area. 4. Make a line graph illustrating the relationships between cylinder radius versus volume and cylinder height versus volume. 5. Determine the optimal height and diameter for a cylinder with a given amount of surface area to achieve the greatest volume. 6. Measure square boxes and calculate their surface area and volume. 7. Determine the relationship between the height and width of boxes with the same surface area relative to their volume. 8. Individually brainstorm and sketch potential designs for a water collection system. 9. Select the best design for a water collection system from those developed by the members of the team through discussion and consensus. 10. Draw sketches of each team’s designs for a water collection system. 11. Determine if they have enough material for their designs by calculating its surface area. 12. Build models for each team’s water collection system (prototypes). 13. Test the strength, integrity, stability, and capacity of their water collection systems. 14. Reflect on the design and describe how it might be improved through redesign. 15. Conduct a self-assessment of the contributions made by each member of the team. 16. Reflect on how well the team worked together on the project C-20

(e.g., what went well, what did not work well, what can be improved). Design Challenge 3: Balancing Act engages students in the following activities to design a strategy for loading, balancing, and unloading objects in an unstable canoe. 1. Read a scenario that contains the problem to be solved, the criteria that need to be met, and the material constraints. 2. Investigate, both mathematically and physically, how the weight and distance of objects on either side of a central fulcrum affect balance. 3. Individually brainstorm a strategy for loading and balancing people and goods in a 10-meter canoe. 4. Select the best loading strategy from those developed by the members of the team through discussion and consensus. 5. Organize weights that will be placed on a scale to represent a strategy for loading and balancing people and goods in a 10- meter canoe. 6. Test strategies for loading and balancing people and goods in a 10-meter canoe by placing weights on a scale in a step-by-step manner. 7. Reflect on the design and describe how it might be improved through redesign. 8. Conduct a self-assessment of the contributions made by each member of the team. 9. Reflect on how well the team worked together on the project (e.g., what went well, what did not work well, what can be improved). C-21

Salient Building Math was developed through a collaborative effort Observations between the Museum of Science, Boston, and Tufts University with funding from the GE Foundation’s "Math Excellence" initiative. The project was launch in response to the “national concern that high schools are not graduating enough students with the necessary math skills to study mathematics, engineering, science, or technology in college.” The authors sought to put a dent in this problem by increasing both mathematics and engineering content at the middle school level in the interest of establishing a stronger foundation for the study of mathematics at the secondary and post-secondary levels. This initiated a three- year effort to provide professional development for middle school teachers in the area of mathematics and engineering and to develop an innovative approach to teaching mathematics by integrating it with engineering. The basic design of the curriculum uses contextual learning to engage students in applying a variety of math concepts and skills while following an engineering design process to solve problems. The curriculum comprises three units of instruction, one for each grade in most middle school settings (i.e., sixth, seventh, eighth). Each unit is framed in a fictional context that uses a remote setting featuring a unique culture to pose three design challenges. To meet the challenges students must work in teams to employ algebraic reasoning, investigate linear and non-linear relationships, identify and generalize patterns, and work with variables. The problem-solving process requires students to collect and analyze data. They also use physical and mathematical models to uncover quantitative patterns and explore natural phenomena. During the course of the program, students also use both kinds of models to represent, test, and convey their design ideas. Engineering The materials define engineering as “the application of math and science to practical ends, such as design or manufacturing.” This definition is consistent with the nature of the activities that students are asked to perform. For the most part, engineering is portrayed as a process that is used to solve problems. Little if any attention is given to the different fields of engineering that can be associated with the problems that students are asked to solve. The most deliberate treatment of engineering can be found in the introduction of each unit. For the most part, engineering is equated with a process for solving problems. C-22

Design All three units use an engineering design process that features eight basic steps. The model utilizes the following themes to orchestrate the design process. 1. Define the problem 5. Build a model or prototype 2. Conduct research 6. Test the prototype 3. Brainstorm ideas 7. Communicate the design 4. Chose the best solution 8. Redesign the prototype Although the materials clearly stress engineering design is not a linear process, the learning experiences that are based on the engineering design process are structured in a very linear way. Furthermore, the design process is very repetitive across the units and their challenges. However, it is important to note that the units are designed to be implemented across three years of instruction. The richest portions of the design process are the steps that involve conducting research and testing the final design. The other steps follow a simple formula and even use the same wording. One of the final steps in the design process asks students to reflect on their solutions and consider ways to make them better under the auspices of redesign. Analysis The lessons and learning activities engage students in doing a variety of analyses. The richest and most prominent forms of analysis in the materials involve interpreting data and uncovering quantitative patterns and relationships. The materials also ask students to conduct analyses in the contexts of solving engineering problems. More specifically, students perform analyses in conjunction with testing, evaluating, and reflecting upon their designs. Constraints The materials define constraints as “limiting factors” that engineers need to consider during the design process. Most of the constraints are presented in the form of limitations regarding the materials that can be used to solve the problem. Another factor that tempers the designs is financial considerations. In most cases, students are simply asked to solve the problem at the lowest cost possible while still achieving performance expectations. In other cases, students are given a finite amount of funds to work with. Modeling The materials define a model as “an object that has been built to represent another, usually larger, object.” Most of the design challenges require students to use simple materials to construct physical models that can be used to represent and/or test their C-23

design ideas. The materials also engage students in using models that go beyond this definition. Several design challenges involve mathematical models that range from simple formulas to relatively complex paradigms. For example, students are presented a simple formula for balancing loads on either side of a fulcrum in Balancing Act. This model is used to make decisions about the location of items in a fictitious canoe that are subsequently tested on a simple balance. Students also use mathematical modeling in Outbreak to work with compound probabilities that inform the development of a strategy for containing the spread of a flu virus. The intervention plan is then tested using a computer model (the applet). Both models and modeling play integral roles in the learning activities. However, the concepts of models and modeling are given little formal attention in the instruction beyond the definition that is presented in the glossary of terms. Optimization The concept of optimization is not targeted directly in the goals, objectives, or glossary of important terms. However, the concept is embedded in all the design challenges by virtue of the fact that the challenges require balancing the performance of a design with its cost. More specifically, the problems are posed in such a way that the pursuit of performance is mitigated by the need to minimize the cost of materials. Conversely, the quest for economy is tempered by the need to achieve performance goals. The concept of optimization is also addressed through mathematics. This is especially prominent in Outbreak, the third challenge in the Amazon Mission. It asks students to design an intervention plan to contain the spread of a flu virus. More specifically, given limited resources, their task is to reduce the rate of infection to less than 25 percent within a 30 days. This is accomplished by configuring the most advantageous combination of doctor’s care, vaccinations, air filtration masks, and antiviral hand gel. Systems The word systems appears in several design challenges that require configuring parts that must work together in a purposeful way. For example, in Stranded students must design, model, and test a rainwater collection system using materials that represent pieces of wreckage from their crashed airplane. Similarly, Everest Trek challenges student to configure a zip-line transportation system. Amazon Mission asks students to design a filtration system that will remove mercury from the water supply at a given rate. C-24

It can be argued all the solutions to the design challenges are essentially systems. Most problems that have to be solved involve bringing together parts that need work together in interdependent ways to perform a task that the individual parts alone cannot perform. Furthermore, most of the systems can be designed, analyzed, and discussed in terms of their inputs, processes, and outputs. However, the concept of systems and systems thinking is not addressed in a direct and overt manner. Science Most of the emphasis in all units is on mathematics. However, consistent with the nature of engineering, the units also involve the application of science. For example, several units require students to conduct “controlled experiments” with independent and dependent variables. For example, in Everest Trek students have to determine how the thickness of foam strips affects their strength (a.k.a., deflection) while spanning the distance between two books under the load of three pennies. Another challenge in the same unit requires students to determine the effect that the angle of a fishing line has on the speed of a straw traveling down the line in the context of developing a zip-line transportation system. The challenges also address science concepts. For example, both Amazon Mission and Everest Trek involve thinking about climate and temperature. The Crevasse Crisis problem in Everest Trek has students exploring the concepts of compression, tension, modulus of elasticity, tensile strength, and more. Stranded targets the concept of balance relative to weight and distance on either side of a fulcrum. There are instances were the treatment of key science concepts is flawed or incomplete. For example, Amazon Mission challenges students to design an insulated container/carrier that will protect medicine from the imposing topical heat. The problem statement and subsequent investigations include numerous references to “keeping heat out.” The frequency and use of this phrase suggests a linear interpretation of heat transfer that is akin to popular misconceptions in contrast to a more dynamic representation of heat transfer. Furthermore, very little attention is given to the actual science of heat transfer (i.e., conduction, convection, radiation). The investigations that inform the selection and configuration of materials to “keep the heat out” emphasize minimizing conduction. The lack of attention given to convection and radiation is problematic given the nature of the materials students were asked C-25

to test and subsequently use in their designs. For example, the inclusion of aluminum foil introduces some complexity to activities that are designed to be simple. Although aluminum foil is not a good insulator from a conduction point of view, it can be a very effective material in reflecting radiant heat. Thus, in combination with other materials, it can play an important role in an insulation system, especially one that is configured to keep something cool in a tropical context. The investigations do not account for this valid application of the material. However, observations made during pilot testing indicate that there was a lot of confusion surrounding the use of the material. Anecdotes from classrooms suggest students had an intuitive sense that foil could contribute something to the solution to the problem. Furthermore, it was an attractive material because it was portrayed as inexpensive. More importantly, pilot testing indicated that the students’ experience of conflicting test results was associated with the use of foil that could not be accounted for in the absence of a richer treatment of the science involved. The curriculum authors attributed some of the students’ inclinations to use aluminum foil in their designs to its use in other applications (e.g., food packaging). In reality, the fact that reflective materials are often used when keeping something hot or cold is an issue. For example, it is likely students have seen it used in construction projects. Modern homes are often enclosed with rigid foam insulation with a foil facing to reflect radiant heat away from the house during the summer months. Thus the desire to transfer this kind of observation to the making of an insulated container is understandable. A more in depth treatment of the science associated with heat transfer was needed to legitimize the inclusion of aluminum foil and to inform it use. Mathematics Math concepts and skills dominate the objectives and learning activities. The study of mathematics is clearly the primary focus of all three units. Each unit requires students to use a variety of math concepts and skills in conjunction with designing viable solutions to problems. The emphasis on using algebraic reasoning, investigating linear and non-linear relationships, identifying patterns, and working with variables is very consistent with how mathematics is used in engineering. More importantly, it is not simply introduced to ensure the inclusion of math. The mathematics that students are asked to perform has a direct bearing on the solution to the problem. In some cases, doing the math clearly makes solving the problem easier. The subtle need to optimize solutions in light of economic constraint gives additional C-26

credence to the mathematics. The problems are designed in such a way that attempts to circumvent the mathematics with trial and effort are not likely to render the desired results. Despite all the attention given to mathematics, the only unit that calls attention to the fact that engineering uses mathematics as an essential tool in the engineering design process is Everest Trek. It points out engineers use mathematics to test hypotheses and to predict the behavior and performance of their designs prior to making them. Technology Very little attention is given to the nature of technology in the three units. For example, students are asked to design a shelter in the unit titled Stranded. The brainstorming process is informed by a series of simple drawing of basic structures constructed out of natural materials (e.g., teepee, hut, lean-to). No attention is given to what makes a simple shelter stable and structurally sound. Similarly, little attention is given to technology used to construct clothing, insulated containers, and simple bridges. Treatment of The materials are correlated with selected standards from the Standards National Council of Teachers of Mathematics. More specifically, they outline standards related to number and operations, algebra, measurement, geometry, and data analysis. Attention is also given to problem solving, communication, representation, and connections. One can connect the standards cited with the objectives and learning activities with relative ease. However, it is important to note that most of the unit objectives and the learning activities address the application of mathematics concepts and skills in contrast to their initial construction. The materials also claim alignment with the national Standards for Technological Literacy (ITEA 2000); the Massachusetts Mathematics Curriculum Framework; and Massachusetts Science and Technology/Engineering Curriculum Framework (MA DOE 2006). These alignments tend to be more vicarious than those articulated for the math content. It is easy to envision how students would encounter many of the idea expressed in the technology standards by virtue of the learning activities. However, most of the objectives for each unit are dedicated to the study of math content. For the most part, the study of technology and engineering is used as a vehicle for achieving the math objectives. The fact that students have multiple experiences going through the design cycle in different contexts is likely to result in some insights about the nature of technology that are consistent with those outlined in the cited standards. C-27

Pedagogy The units are very deliberate in their use of contextual learning to make the study of mathematics more interesting, practical, and engaging. Students do not manipulate numbers for the sake of math alone. The numbers, patterns, and relationship that students encounter during the course of their learning experiences are grounded in the context of the unit and have a direct bearing on the solution to the problem. The mathematics is genuinely needed to solve the problems posed. The use of contextual learning strategies in the units make them very compatible with the popular practice of implementing interdisciplinary units at the middle school level. By virtue of their design, the units include content related to geography, anthropology, environmental science, physical science, and biological science. The potential of these units to provide a basis for interdisciplinary instruction in a middle school setting is not addressed in a direct manner. However, the materials are rich enough in their treatment of mathematics, social science, and natural science to inspire implementation in ways that involve teachers and content from different subjects. The materials are also very consistent in their use of the engineering design process to orchestrate the learning experiences. The use of the engineering design process is consistent with the notion that students construct their own understanding of concepts by using prior knowledge, posing questions, seeking answers, testing ideas, revising ideas based on experience, and reflecting on the nature of knowledge and the learning process. Implementation According to the authors, the Building Math units are designed to be used in place of analogous units in an existing algebra program. They can also be used as supplementary or enrichment lessons in the core math curriculum. Lastly, they are written in such a manner that they can be used for summer programs. Each challenge requires approximately one week, or five to seven 50- minute class periods, to complete. Each book in the series includes reproducible student handouts and teacher support materials (for each grade level). A set of materials includes a poster outlining the design process and DVD. The DVD features video vignettes that can be used for professional development activities and a Java applet that provides a computer model for one of the learning activities. The three books that comprise the program are available through C-28

Walch Publishing for about $114. They can also be purchased individually for approximately $40 each. The consumable materials needed to implement the investigations and design activities are commonly available and relatively inexpensive if they had to be purchased. Most of the non-consumables are also relatively inexpensive and easy to obtain. C-29

City Technology Institution Stuff That Works City College of New York 140 Street & Convent Avenue, Room T233 New York, New York 10031 Tel: (212) 650-8389 (phone) Fax: (212) 650-8013 (fax) E-mail: citytechnology@ccny.cuny.edu Web site: http://citytechnology.ccny.cuny.edu/ Leaders Gary Benenson James Neujahr Funding National Science Foundation Grade Level Elementary (K-6) Espoused “…to engage elementary children with the core ideas and Mission processes of technology (or engineering, if you prefer).” Organizing x Designed Environments: Places, Practices, Plans Topics x Mapping x Mechanisms & Other Systems x Packaging & Other Structures x Signs, Symbols & Codes Format The curriculum materials are presented in the form of five soft cover books that are between 150 and 190 pages in length. Each book includes the following elements: x Information about the curriculum (e.g., purpose, history, goals, organization) x Simple and concrete things that the teacher can do to become familiar with the technology in question. x An encyclopedia-like section that uses simple language and everyday examples to explain the technical concepts that will be addressed in the curriculum. x Lesson plans and handouts that guide and support the implementation of the curriculum and instruction. x Case studies that describe what the curriculum looks like in C-30

action (e.g., sample of student work, teacher observations, student comments, project leader commentaries). x A list of resources that can complement and support the curriculum implementation process. x Lists that show how the curriculum aligns with national standards for technology, science, mathematics, and English language arts instruction. Pedagogical x Lessons plans feature elements like prerequisite knowledge, Elements vocabulary, key concepts, strategies for pre-assessment and set inductions, and group work. x The instruction is very Socratic in nature (i.e., posing questions, addressing questions). x Most of the learning activities involve inquiry (e.g., analyzing common objects, making observations, taking measurements, gathering and analyzing data, drawing conclusions). Maturity Started in 1979 Diffusion x Field-tested in 19 states throughout the country & Impact x Forty-nine teachers have been trained to provide professional development in 16 states across the country C-31

Initiative City Technology Title Designed Environments: Places, Practices, Plans Broad Goals The content and activities… will help meet the following educational goals: x Introduce the fundamental theme of environments as complex systems that are designed and evaluated. x Develop a broad view of technology and its role in everyday life; x Develop an understanding of technology design. x Develop process skills in observation, data collection, categorization, problem identification, data organization, and presentation, design and evaluation. x Develop skills in communication and group work. x Develop awareness of problems in the immediate environment, and responsibility for solving them. x Foster a sense of control in relation to everyday problems. Salient Math Science Technology Concepts x counting x observation x designed & Skills x measuring environments x collecting data x maps x organizing data x mapping to scale (e.g., graphing, x floor plans tables) x control x analyzing data for x systems and patterns subsystems x scale x parts and functions x area x habitat (human- x perimeter made) Engineering The unit takes advantage of the fact that many of the things in school are the products of "casual design” that did not involve any thoughtful analysis or evaluation. Using everyday problems in their classroom, students engage in activities that involve “technological design.” These activities include the following: x Defining the problems clearly. x Gathering and analyzing information about the problems. x Describing the characteristic of good solutions. x Identifying the limitations (constraints). x Generating ideas for solutions. C-32

x Presenting possible solutions to others. x Selecting and trying the best solutions. x Determining how well they work. x Redesigning the solutions as needed. Prominent 1. Analyzing and reducing classroom interruptions. Activities 2. Solving problems related to classroom procedures (e.g., distributing materials, putting coats away, lining up). 3. Addressing rules that are broken in school. 4. Redesigning how to play the “Connect Four” game. 5. Redesigning their classroom. 6. Designing a habitat for a classroom pet based on its likes and dislikes. C-33

Initiative City Technology Title Mapping Broad Goals The content and activities… will help meet the following educational goals: x Develop fundamental themes of two-dimensional representation of three-dimensional space. x Illustrate and explore concepts of orienting, symbol use, point of view, scale, and one-to-one correspondences. x Demystify common artifacts, and by extension, technology in general. x Promote literacy as students interpret and develop graphic communications. x Develop process skills in observation, classification, ordering, inferring, collecting and organizing data, representing data, design, and evaluation. x Provide rich opportunities for group work. Salient Math Science Technology Concepts x scale x observation x maps & Skills x coordinates x comparing x graphic x spatial observations communication relationships x recording x orientation x one-to-one observations x symbols correspondence x cardinal directions x showing x sequencing x magnetic north relationships x measurement between things x using grids x schematic diagrams x using a compass Engineering Most of the emphasis is on making and using maps as documentation and communication tools. Direct linkages to engineering were not found. Prominent 1. Studying a box relative to top and side views. Activities 2. Drawing a “bird’s eye view” of a collection of objects. 3. Tracing one’s hand to note one-to-one correspondence 4. Identifying things, describing locations of things, and following directions to things in large and small groups. 5. Brainstorming what is a map. 6. Analyzing a variety of existing maps. 7. Reading maps to identify where things are located. 8. Drawing maps of their desktop and classroom. C-34

9. Making a map that defines a route to a location. 10. Developing a map of the classroom to scale. 11. Mapping the diffusion of food coloring in a Petri dish of water. 12. Mapping a gas (odor from perfume) in a classroom. C-35

Initiative City Technology Title Mechanisms & Other Systems Broad Goals The content and activities… will help meet the following educational goals: x Introduce and explore fundamental themes of systems, inputs and outputs, cause-and-effect, models. x Illustrate and explore concepts of force, distance, motion, lever, simple machine, friction, electric current, electric circuit, information, control, feedback and energy. x Demystify common artifacts, and by extension, technology in general. x Promote literacy as students formulate problems and find effective ways to communicate with others in order to achieve and document solutions. x Develop process skills in observation, classification, generalization, use of materials, modeling, and design. x Provide rich opportunities for group work. Salient Math Science Technology Concepts x distance x simple machines x mechanisms & Skills x ratio x Law of the Lever x systems (inputs, x measuring x lever & fulcrum processes, outputs) x estimating x 1st, 2nd, & 3rd class x links and joints x collecting, levers (pin and slide) recording, and x wheel and axle x compound levers analyzing data x wedge (a.k.a. linkages) x pulley x fixed pivot x inclined plane x floating pivot x screw x circuit x motion x switch (translation, x control rotation, x modeling reciprocating oscillating) x effort and load x mechanical advantage x current x observing x conductors and insulators C-36

Engineering The key engineering concept that is embedded in this unit is modeling. The students make and manipulate a variety of mechanical and electrical models and use their experiences with these models to make inferences about how things work. Prominent 1. Identifying the simple machines in everyday objects. Activities 2. Describing the subsystems within larger systems. 3. Dissecting a ballpoint pen for cause and effect relationships. 4. Making models of mechanisms. 5. Identifying conductors and insulators. 6. Making and testing different circuits (i.e., with and without switches, two switches one bulb). 7. Designing, making, and using electric board games. 8. Designing a water-level alarm. C-37

Initiative City Technology Title Packaging & Other Structures Broad Goals The content and activities… will help meet the following educational goals: x Develop fundamental themes of systems, material properties, spatial relationship, and trade-offs. x Motivate and illustrate concepts of forces, structure, load and failure; compression, tension, and shear; repair, redesign, and re-use. x Demystify common artifacts, and by extension, technology in general. x Develop process skills in observation, classification, generalization, prediction, control variables, design, and evaluation. x Provide rich opportunities for group work. x Develop environmental awareness. Salient Math Science Technology Concepts x counting x equilibrium x packaging & Skills x measuring x tension x structures x collecting data x compression x struts x organizing data x shear x ties x graphing data x viscosity x failure x making inferences x fair testing x fasteners from data x center of mass x beams x spatial reasoning x force x lamination x load x column Engineering Conducting tests that involve controlling variables, taking measures, and analyzing data to… x analyze existing designs (e.g., bags, pump dispensers, corrugated cardboard). x determine how shape, configuration, materials, and fastening techniques effect the strength and performance of a structure (a shelving unit that is made of corrugated cardboard). Prominent 1. Categorizing packages. Activities 2. Classifying different kinds of bags. 3. Testing the strength of bags. 4. Protecting fragile objects. 5. Evaluating pump dispensers. 6. Determining how strength is affected by the C-38

a. shape of a column b. shape of a beam (shelf) c. type of materials used (cardboard) d. direction of corrugations e. type of glue used f. type of support provided C-39

Initiative City Technology Title Signs, Symbols & Codes Broad Goals The content and activities… will help meet the following educational goals: x Develop fundamental themes of information, representation, sign, symbol, and communication. x Promote literacy by developing a variety of techniques for sending and receiving information.; x Promote numeracy by developing awareness of symbols as media for representing quantitative information. x Demystify common artifacts, and by extension, technology in general. x Develop process skills in observation, classification, generalization, communication, and design. x Develop awareness of immediate environment. x Provide rich opportunities for group work. Salient Math Science Technology Concepts x counting x observing x symbols & Skills x collecting data x classifying x signs x organizing data x sorting x system x analyzing data x system of notion x key x pictograms x ideograms x phonograms x channels x encoding x decoding x expressive symbols x arbitrary symbols x icons Engineering Communication is the main idea in this unit. However, several activities require students to go through a design process that involves identifying problems, designing solutions, testing solutions, gathering and analyzing data regarding solutions, evaluating the effectiveness of solutions, and redesigning solutions if needed. C-40

Prominent 1. Identifying and decoding common signs and symbols. Activities 2. Designing and making signs that address a need in the classroom. 3. Designing and testing a signal that gets everyone’s attention. 4. Interpreting symbols on a map or floor plan. 5. Creating and using a graphic symbol to express secret messages to others. 6. Devising and using hand signals for communication between the teacher and the students. 7. Designing a symbol that communicates a message on an ad or package. C-41

Salient The primary audience for this curriculum is elementary school Observations teachers. A tremendous amount of attention is given to supporting and enhancing teachers’ content knowledge and pedagogical content knowledge (how to teach specific pieces of content). This attention is evident in the intellectual “appetizers” that help teachers become familiar with the technical content using concrete examples from everyday life; the encyclopedia-like explanations of the key concepts and technologies that are being addressed in the curriculum; and the implementation stories that feature photographs, samples of student work, children’s dialog, teacher comments, and the authors’ commentaries. The City Technology materials use interesting and illuminating topics to organize the curricula into manageable chunks. They appear to be based the authors’ efforts to make the curriculum practical for teachers and developmentally appropriate for students in contrast to being based on a formal conceptualization of engineering endeavors. The materials are not comprehensive or inclusive in any way. Rather, they utilize a diverse set of topics to address the nature of design and technological systems in multiple contexts. Engineering These materials do not espouse to be an engineering curriculum. Instead, they focus on building an understanding technology through everyday things. However, the emphasis on uncovering how technology works includes engineering ideas and ways of thinking that are appropriate for elementary school children. They can be found in the analysis, design, or redesign of everyday things (e.g., mechanisms, electrical circuits, plastic bags, maps, classrooms, packages). Design The curriculum addresses design from two perspectives with almost equal attention. First, it engages students in design projects that begin with a problem and culminate with a solution. These activities represent developmentally appropriate versions of engineering design. Second, it engages students in analyses of existing designs (e.g., bags, pump dispensers, maps, scissors). This form of inquiry is analogous to reverse engineering. Analysis One of the most prominent themes running through all five books is the use of quantitative analysis to inform and/or evaluate designs. Over half of the learning activities involve collecting, organizing, and analyzing data. More importantly, the data is used to define the problem, make a design decision, evaluate a design, C-42

or refine a design. Constraints The concept of constraints is addressed in Designing Environments: Places, Practices, Plans. It is described as things that limit design possibilities. In even simpler terms it is defined as, “What limits what we can do.” Students are taught it can be time, money, space, knowledge, materials, rules, and regulations. It also introduces the notion that constraints can include a lack of authority to implement a design or the need to secure permission to carry out a design. Lots of attention is given to establishing and meeting design criteria. In this context, design criteria are the things that the design must do to be considered successful or acceptable. Students are asked to identify design criteria (in conjunction with design constraints), address the criteria during the course of the design, and evaluate the final design in relation to the design criteria. Modeling Another prominent theme is the use of physical models to illuminate the subtle technologies that are embedded in everyday things like toys, tools, packaging, signs, and maps. The models include simple objects and working mock-ups that are constructed by the students. During the course of instruction the models often serve as hands-on manipulatives as well as tangible representations of student thinking. In some cases, the models serve as sources of data in ways that are analogous to how physical models are used in engineering endeavors. Optimization The materials do not address the concept of optimization directly. However, they do deal with the concept of trade-offs and redesign. In the case of trade-offs, students are taught they involve two or more things that compete with one another and require some form of compromise. Redesign is equated with the notion that one “…can always make it [the design] better.” However, it is important to note that redesign is more than simply making improvements. The curriculum and instruction also emphasizes the need to inform a redesign based on evaluation data relative to the design criteria. While these concepts sound too advanced for elementary students, it is important to note that they are being addressed in the context of things like improving classroom procedures, refining rules that are broken, and reconfiguring their classroom. Systems The concept of systems is taught directly and indirectly throughout the materials. It is most clearly addressed in Mechanisms & Other C-43

Systems. It defines systems as “A collection of interconnected parts functioning together in a way that make the whole greater than the sum of its parts.” It uses a Socratic and developmental approach to build the students’ understandings of simple systems. More specifically, children are asked to address questions like the following. x “What is the purpose of the system?” x “What does it do?” x “What are its parts?” x “How are the parts connected to one another?” x “What do you have to do to make them work?” Mechanisms & Other Systems also addresses systems from the perspective of inputs, processes, outputs, and feedback. Toward that end, students are asked to analyze, draw, and label the “ins and outs” of simple mechanisms like can openers, ice cream scoops, and staple removers. Students are also asked to address questions about the part of the system that they use to make it work (the input) and the part of the system that actually does the work (the output). Systems and systems thinking can also be found in Packaging & Other Structures. This book defines systems as, “The arrangement or interrelation of all of the parts of the whole.” Although the instruction does not address the concept of systems directly, it does engage students in analyzing and making simple systems and paying attention to the roles parts play in the context of the whole. Science The materials are clearly dedicated to the study of technology. Science concepts like mechanical advantage, equilibrium, tension, compression, viscosity, and center of mass are introduced, explained, and used to understand how common technologies work. Science skills such as observation, classification, measurement, data collection, and documentation are introduced, applied, and reinforced throughout the materials. Furthermore, the concept of conducting a “fair test” by controlling variables is addressed in a robust manner in Packaging & Other Structures. Inquiry can be found all through the curriculum. In some cases the intent of the inquiry is to uncover a basic law of nature. However, most of the inquiry is directed toward understanding a design or informing a design (or redesign). Mathematics The curriculum does not attempt to teach mathematics directly. It does however, consistently engage students in counting C-44

phenomena, taking measurements, recording and organizing data in meaningful ways (tables, charts, graphs), analyzing data to make comparisons or uncover patterns, and using data to make inferences about problems or design performance. Technology Technology is the central focus of the curriculum. Students are introduced to different forms of technology that range from simple mechanisms to symbol systems and from everyday structures to maps. The treatment of technology includes technology as human- made objects, the knowledge used to make objects, the techniques used to make objects, as well as the need or desire to make objects. Treatment of Each book in the series features a chapter on national standards Standards that includes the Standards for Technological Literacy (ITEA, 2000), Bench