How to Use this Resource
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From Issue 53: Doing Our Jobs and Caring for Our Children
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Is It in Proportion?
Eric Appleton
Proportion (noun): The size of something compared to something else
Example: A large proportion of essential workers are employed in health care.
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When you look at the word proportion, you might notice that it includes the word “portion.” A portion is part or a share of a whole.
Example: At the end of the shift, each worker took her portion of tips.
Related words: share, percentage, ratio
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When we read, write, and talk about statistics (the study of numbers in the world), the idea of proportion is often an important part of the conversation.
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Based on the information we have, a proportion tells us what size or share we might expect
in a different situation.
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For example, if oranges cost $1.50 for one pound, we would expect two pounds of oranges to cost $3.00.
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Paying $3.00 dollars for two pounds of oranges is proportionate to paying $1.50 for one pound of oranges.
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If we had to pay $4.00 for 2 pounds of oranges, that would be disproportionate; we would think it was unfair.
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Here’s another example. Let’s say Ndeye works 10 hours and earns $150.
Her co-worker, Moise, has the same job.
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He works 15 hours and earns $300. Is the pay Ndeye and Moise received in proportion? You could also ask, “Is this fair?” What do you think?
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Let’s practice thinking about proportions and populations of people. In 2020, the U.S. Census counted all people living in the United States. The population data in the Census is often used in proportions.
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Approximately what proportion of people in the U.S. do you think identify as “white alone”?
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A. 20%
D. 60%
B. 40%
C. 50%
Approximately what proportion of people in the U.S. do you think are Black?
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A. 15%
D. 45%
B. 25%
C. 35%
Approximately what proportion of people in the U.S. do you think are female?
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A. 49%
D. 52%
B. 50%
C. 51%
Race and Ethnicity of
Frontline Workers in New York City
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Let’s compare different populations of people.
About 8 million people live in New York City.
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On the right, you can see the approximate percentages of New York City’s population by race and ethnicity.
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Now look at the chart below. What do you notice?
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In her piece, Adriana Herrera López writes, “In New York City where I live, people of color do more than their fair share of the essential work.
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They are disproportionately represented.”
Female Frontline Workers in New York City
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According to 2019 Census estimates, 52.3% of the population of New York City is female.
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Based on this information and the chart on the right, write three true sentences about women as frontline workers in New York City. Use terms like underrepresented and overrepresented.
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Sources: United States Census Bureau. American Community Survey 2014-2018 5-Year Estimates; https://comptroller.nyc.gov/reports/newyork-citys-frontline-workers/
Now look at the bar graph below. What do you notice when you compare the table of data with the bar graph showing the same data?
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The bar graph gives a visual representation of the data. How is that helpful (or not)? Why is it important to look at both percent differences and differences in hard
numbers?
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Answers to questions on slides 10-12
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Eric Appleton is a math professional developer for the City University of New York (CUNY) Adult Literacy/HSE Program. Before coming to CUNY, he taught in an education program for formerly incarcerated people. Eric is a founding member of the Community of Adult Math Instructors (CAMI), which meets monthly to do math and talk about teaching. In 2018, he became resident-elect of the Adult Numeracy Network (ANN).
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