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State Apportionment Lesson Plans and Task

By Jenifer Hummer

University of Delaware

Three secondary teachers and a mathematics education researcher planned two lessons and revised them through lesson study. The teachers adapted the State Apportionment Task from the Mathematical Modeling Handbook (Sanfratello, 2012).

Listed in Teaching Materials

Version 1.0 - published on 13 Mar 2019 doi:10.25334/Q4KB2T - cite this

Licensed under CC Attribution-ShareAlike 4.0 International according to these terms


These resources include Microsoft Word and PDF versions of the following materials. There are two annotated lesson plans for a two-day lesson which is intended to guide the implementation of the adapted State Apportionment Task. The lesson plans include anticipated student responses as well as teacher support for implementing the tasks and responding to student thinking. These lesson plans were revised three times through two cycles of lesson study, so some of the anticipated student responses are actual responses that were observed by the teachers while their colleagues enacted the lessons. There are also worksheets that match the lesson plans which can be distributed to students. There are eight files in total. 


Cite this work

Researchers should cite this work as follows:




These materials were developed in partnership with three secondary teachers who are not named due to confidentiality in research. I would like to thank them for their participation. 

Also thank you to the University of Delaware for providing dissertation funding for this work. 

The task used in these lesson plans was adapted from the State Apportionment task in the Mathematical Modeling Handbook. 

Sanfratello, A. (2012). State apportionment. In H., Gould, D.R., Murray, & A., Sanfratello (Eds.), Mathematical modeling handbook (pp. 133 – 140). Bedford, MA: The Consortium for Mathematics and Its Applications.


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