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the Sainte - Laguë method or the method of ma jor fractions. It is used in Germany, Norway, Sweden, and New Zealand, to name a few. Recreating the results of another country ’ s re cent election can help give our students a great er understanding of how the world wrestles with different approaches to apportionment. 5. In addition to the decennial census, the Census Bureau computes official annual estimates of state populations every July 1. The page titled “ Hypothetical Apportionments ” has the July 1, 2021, estimates as well as the official 2020 Census populations. There are several different questions that are worthy of consideration based on these numbers: A. Do the 2021 estimated values give a different apportionment? B. Would the method of Webster give a different apportionment? C. How many more people did Virginia need to gain another seat? D. If ten more seats were added, which states would get them? E. What is the maximum number of repre sentatives allowed by the Constitution based on the 2020 Census? F. The populations of the District of Co lumbia and Puerto Rico are included. How many seats would they have got ten had they been states in 2020 or 2021? G. The Greater Idaho Project encourages parts of eastern Oregon and northern California to join Idaho. What effect would this have on the apportionment? Experiments like these help us better understand how our government operates, and they also re mind us that not all aspects of its structure are stat ic but, change over time. As people who like to calculate, we should be experimenting with differ ent governments in silico . It is fitting to close with a quote from Thomas Jefferson from a letter he Conclusion

Experiments

We now understand the history of apportionment for the House of Representatives to the states, but Congress only does this once every ten years. Knowing how this process works allows us to ap ply the current method (or others) to any number of hypothetical situations that can help us to better understand our country, its history, and where people live, provided we have the computational skills to answer various “ What if …” questions. Some suggested classroom activities are shown below. 1. Examine the effect of increasing or decreasing the number of representatives or changing the divisor on the title page “1790 Census. ” 2. The 1790 Census page shows the free and en slaved populations of each state. The Three Fifths Compromise was negotiated between states that wanted to count only the free popu lation and the states that wanted to count the entire population. Had either of these perspe cives been enacted, how would it change the apportionment and the maximum number of representatives? 3. Each reapportionment determines the number of electoral votes each state receives for the next two to three presidential election cycles. Could some presidential winners have been different based on the apportionment? A. 1796 and 1800: Hamilton ’ s vs Jeffer son ’ s? Three - Fifths, free only, or entire population? B. 1876: Nine states received extra repre sentatives after Hamilton ’ s method was applied. 4. Proportional representation occurs in other countries that award parliamentary seats to par ties based on their proportion of the vote. Jef ferson ’ s method is commonly known as the d ’ Hondt method, and it is used in Belgium, the Netherlands, Spain, and Israel, among many others. Typically, a minimum percentage of votes acts as a threshold for a party to qualify for seats. Webster ’ s method is often known as

Virginia Mathematics Teacher vol. 48, no. 1

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