2. To Middle, High and beyond Teachers C/O 6.EE, 7.EE, & 8.FA Postage Stamp Problem HCPSS, MD 21043 From Fostering Algebraic Thinking by Mark Driscoll

3. The post office has stamps in the denominations of 5¢ and 7¢. What amount of postage can you buy? Explain your reasoning.

4. While working on this problem, think about the methods people in your small group tried, the questions they asked, the process for coming to a deeper understanding, and the different ways of thinking about the problem.

5. In what ways is this problem “algebraic”? How does it elicit algebraic thinking? You may have noticed yourself working from output to input.

6. What rules did group members come up with to help them generate postage values of 5¢ and 7¢ stamps? What computational shortcuts did group members use as they worked on the problem?

7. Another way 012345678 0 1 2 3 4 5 6 7 8 Number of 5¢ stamps Number of 7¢ stamps

8. From: Rich Discourse 012345678 00.05.10.15.20.25.30.35.40 1.07.12.17.22.27.32.37.42.47 2.14.19.24.29.34.39.44.49.54 3.21.26.31.36.41.46.51.56.61 4.28.33.38.43.48.53.58.63.68 5.35.40.45.50.55.60.65.70.75 6.42.47.52.57.62.67.72.77.82 7.49.54.59.64.69.74.79.84.89 8.56.61.66.71.76.81.86.91.96 Number of 5¢ stamps Number of 7¢ stamps

9. From: Rich Discourse Could you have stamps that total in amount of $1.00? $1.51? Would that make sense?

10. Are there any postage amounts that are impossible to get with 5¢ and 7¢ stamps? If so, what are they and why are they impossible? Try to extend your thinking to n¢ and m¢ stamps.

11. Thank You