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by Rachel D.L.



Chapter 1

Measurement: Distance and Weight

Picture yourself standing in an endless line of people. The line stretches from Chicago, IL to Madison, WI. Your Challenge: 

You’re homeless.

You have 356 dollars in your pocket, a black backpack, 36 cents.


At the beginning of the line, in Chicago, the endpoint that you left: a shoreline stitched by sandcastles. A house made of two side-by-side boxes of red brick. Cracked concrete. A tan garage door caving with crater’s the shape of your brother’s basketballs. Your sister. Your mother. A human shaped hole in the shape of your father.


At the end of the line, in Wisconsin, is movement toward the right: rolling hills.

Kames and kettles. A landscape divided by railroads, red lines, and glaciation. The line you make between beginning and end, left and right, swerves, omits, and stumbles toward an unknown destination.


The road you stand on, in suburban Chicago, is cold and dark. The lamplights push your shadow down on the sidewalk, a shortened ghost. But focus on the numbers now. Focus on the rhythm of your feet against the concrete. Hear that: One. Two. Three men waiting for you in the darkness.  The roll of money in your hand feels soft and spent.


Divide this sum into half. Then divide this half into fifths. Put one 4/5th of the 1/2 in your shoes. Hand 4 dollars of the remaining 1/5 to the conductor for a train ticket.


a) How much money is in your shoes?

b) How much money is left of the one fifth of the one half in your hand?

c) If it costs 7 dollars a day to eat, how many days of food will 356.56 pay for?


Bonus question:


If 1/3 of runaways will be prostituted within 48 hours of leaving home, and this is your fifth hour alone on the streets, how many hours left before your survival is an anomaly?

IL to WI.jpg


Welcome to the Language of Homelessness, Chapter 1, Measurement and Weight. First things first. You’re gonna need to do a little math here. If you have a calculator on hand, feel free to use it. No problem in this textbook requires the use of a calculator. No problem in this textbook prohibits the use of a calculator either. This text isn’t about denying you access.


If you have the resources, use them. If the pixels in the screen of your calculator have exploded and you can’t see anything but black goo, I’m very sorry. If you don’t have a calculator and you thought you could solve that problem by using the calculator app on your family home’s only computer but then your brother decides the computer room is his basketball court and throws a basketball and destroys your only computer, I’m very sorry that you no longer have the tools.

That’s not my problem. 


The problems in this text you will have to solve yourself with whatever resources you have. Answers to odd numbers questions are in the Back of the Book (BOB). Feel free to check your answers here. 


In this chapter, we will discuss measurement in terms of distance, weight, mass, and scale.


Distance is a measure of difference between a beginning point and an end point. Take two walls and narrow them closer and closer around your lungs. The distance in this case is the difference between the two walls.

Weight is a measure of an object’s pull to the surface by gravity. The weight of an object changes when the pull of gravity  changes. Is the weight of X on the moon, the same as the weight of X on earth? Can X exist in a vacuum?


Mass, on the other hand, does not change in relation to location. Forty pounds of books, clothes, food, water remains forty pounds of books, clothes, food, water in any planet or place. Mass can accumulate. Or it can erode.


The scale, for the purposes of this text, is used to decrease the value of an object, distance, or other thing so that the object, distance, or other thing fits neatly on a page. In some textbooks, scales will be drawn to scale. If a scale is drawn to scale that means the reader can pick up a ruler and translate the distance on the ruler accurately to a distance in real life.


In other textbooks, such as this text, the scale is not drawn to scale. If you thought you had all the manual tools you needed to tackle this text, picked up a ruler and measured from point A to B, you would be overestimating the distance you needed to travel by a long shot. You’d land on the edge of lake Michigan or in a suburban gas station, and by the time you had an opportunity to get to a safe shelter, it would be far past midnight. And you’d be a teenage girl. And because you’d be a teenage girl, standing alone at a gas station past midnight, the difference between the present and the future would become very narrow. And the future might end any moment, come speeding like a wall up to your body and you would worry, truly, that this might be the very endpoint.


In this case, a calculator would be very handy.

1) Below is a map of suburban Chicago: The scale is 1 unit = 4.93 miles. It’s your first night homeless and your friend Abby agrees to take you in if you can get to her house by yourself. Abby’s house is in Des Plaines. You live in Glencoe. You travel 0.263 units to the Glencoe train station then get on the train and travel 2.19 units to Evanston. You get off the train in Evanston and then get on the Pace Bus, route 250, and travel 2.19 units to the Des Plaines train station. Here, Abby picks you up and drives you to her house.

a) How many miles is it from 0919 Vinecone Lane to the Glencoe train station?

b) How many miles is it from the Glencoe train station to the Evanston, Davis St. train station?

c) How many miles is it from the Evanston, Davis St. train station to the Des Plaines train station?

d) How many miles in total do you travel to get to the Des Plaines train station that night?

Chicago Map.jpg

2) Real World Connection! Blueprinting


Rachel’s blueprint shows a bird's eye view of her mother’s (once her mother’s and father’s) house. Every 2 cm of the blueprint represents 6 ft. of the actual house. If Rachel walks down from the bathroom to the main level, and Rachel’s father is in the basement, and they are 14 cm away from each other in the blueprint, how many feet away from each other are they in real life?




3) Your friend Abby’s house in Des Plaines has 7 bedrooms and 5 people. Unfortunately, Abby also has two cats and you are allergic to cats, so you cannot sleep over. Oh no!


15 miles away, a shelter has 7 bedrooms and 16 people. You call to see if you can stay there but learn that all beds are full. Oh no! You wait for Abby to finish talking with her mom in the kitchen so that you can plan what to do next with her. In the meantime, you do some math. What is the ratio of bedrooms to people in Abby’s house vs the ratio of bedrooms to people in the shelter?

4) Algebra Connection: Blueprinting with Variables! In the map below, find X.


5) Kennedy is a high school senior planning on going to Princeton the following year. She calculates she will need to carry 5 suitcases of 50 pounds each plus two 30 pound shelving units to college for a total of 310 pounds. Included in the suitcase are snacks, clothing, Tupperware, school supplies, and reusable water bottles. Her mom has a car and agrees to bring Kennedy and her 310 pounds up to school. Because Kennedy’s mom has a car, it costs no extra money to bring 310 pounds than it does to bring 50 pounds.

Rachel is also a high school senior and she is planning on going to college at the University of Wisconsin-Madison. Unfortunately, Rachel is Homeless. She does not have a Mom or a Car. Because she has taken out over $14,000 in loans, she regularly gets emails from her loan provider (OSLA student loans) that suggest she “learn to budget!” by not going out to eat, not buying clothes, walking instead of taking public transportation, living with her parents instead of renting an apartment, and Saving and Reusing As Much as Possible.


          a) Considering that budgeting means Saving and Reusing as Much as Possible, this would require Rachel to carry 310 pounds of material across the Chicago streets, to her friends’ houses, through an alleyway, on the subway, to strangers’ house, to a dog park, on the PACE bus, and into a shelter. What budget-friendly way can Rachel use to get her 310 pounds of material to college without a car?


          b) Unfortunately, Rachel decides to resist OSLA student loans and gets rid of 250 pounds of material. She walks five miles with 60 pounds of material divided between a backpack, a suitcase, and a box of books. As a result, the soles of her converse fall off, her spine begins to curve, and a tick bites her leg because she decided to take a shortcut through a forest preserve. What budget-friendly way can Rachel use now to get to college now?


          c) Rachel’s severe asthma makes her stop breathing when she over-exerts herself. Rachel also gets seizures and collapses in situations of extreme emotional or physical stress. Her legs begin to shake when she carries anything over 2/3rds her body weight. The 90-degree summer weather makes her dizzy and pass out. Again, OSLA student loans recommends budgeting by Saving and Reusing as Much as Possible and walking instead of using public transportation. If Rachel saves everything she owns, walks everywhere, has no Mom, no Car, and collapses with seizures in situations of extreme emotional and physical stress, will Rachel be able to afford college if she follows OSLA’s budgeting recommendations?

Dream Rachel has while napping in the forest preserve:


6) The food pantry distributes food on a point system. The amount of points each item is worth is based on weight. One point is awarded for every 0.7 pounds. Bags of carrots are worth 3 points. Bags of chips are worth 1 point. Bags of potatoes are worth 4 points and packs of dried noodles are worth 2 points.

          a) If you are allowed up to thirty points, what is the maximum number of items you can get if you must have at least one bag of carrots, one bag of chips, one bag of potatoes, and one pack of noodles?

          b) If you are looking to lighten your load but carry the highest quantity of food possible, what food is most friendly to your back: 5 bags of carrots or 5 bags of chips?

Food pantry.jpg

Time Tables for Success: If you have a calculator, no need to memorize your time tables. However, if you do not have a calculator, make sure to memorize the time tables below. 

Route #208:

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7) Back in Des Plaines, Rachel and Abby think about how to solve the problem of finding somewhere to sleep for the night. They decide to create a map of Abby’s neighborhood and measure the risk associated with asking the neighbors for a place to stay. Across the street from Abby’s house is the Voyeur’s house. The Voyeurs have 0 cats, 0 dogs, 1 gun, and 1 man. On the right of Abby’s house is the Anaflax’s house. They have 1 cat, 1 dog, 0 guns, and 0 men. On the left side of Abby’s house is the Shotman’s house. They have 0 cats, 0 dogs, 1 gun, and 2 men. If maximum risk is measured by the highest point value, what house would propose the least amount of risk to Rachel if having a cat is worth 3 points, having a dog is worth 2 points, having a gun is worth 1 point, and having a man is worth 1 point? What house should Rachel choose to sleep in if she chooses to sleep in the house with the least amount of risk?


8) Congratulations! You chose the right house! You knock on the door of the Voyeur’s house (with Abby by your side of course) and explain that you came over for a slumber party but didn’t realize your friend had cats. The Voyeurs are very sympathetic.  They let you sleep there for the night on the condition that you consent to a tour of their antique gallery. Mr. Voyeur shows you around the house and suggests you test out his bed from India. He smiles. He smiles. If Mr. Voyeur’s smile is 2 inches long and the door is 36 inches long, how many smiles are needed to block the doorway?

Chapter Summary and Intro to Chapter 2


In this chapter you learned how to measure distance and balance weight through the use of scales.  Through this constant problem solving, you successfully made it off of the street for one night and found a bed in the Voyeur’s house. Good job! In the next chapter, we will discuss the ways in which measurements such as distance and weight depend on their societal contexts to create meaning.


We call this relationship between a variable and its societal context a dependent relationship. For example, the relationship between distance and time is a dependent relationship. This means that for every mile traveled, it takes travelers X amount of time to get there.


In this case, we would say that distance is dependent on time. A traveler cannot move from point A to point B without a certain amount of time passing (unless time travel were to exist). On the other hand, we say time is independent. This is because time can exist without consequence for its actions. Time can pass and distance may or may not move. Time will go on regardless of what happens to distance.


In that sense, the independent variable (let’s name the independent variable X) has significantly more power in this equation. It can run around doing whatever it wants and the only one that will feel the consequences of its actions are the dependent variable (let’s call the dependent variable Y).


For example, Doctor X can diagnose diagnose diagnose and then walk out of the room and diagnose diagnose someone else and walk out of the room again and diagnose someone else and walk out of the room and go on and keep diagnosing even as the Patient Y dies or the Patient Y gets institutionalized or the Patient Y gets sent back home. (Certain structures like doctors’ offices and prisons provide exceptional structures for independent variables to function free of consequence.) 

Another example of independency and dependency might be the parent-child relationship. For example, Baby Y is dependent on Mama X to provide housing, to pay for medical expenses, and to provide food. Mama X is not dependent on Baby Y to pay for housing, to provide food, to—Hmm. Well.

healthy dependency.jpg

What happens if Mama X is in fact dependent on Baby Y to pay the bills, or is dependent on Baby Y for her happiness, or for her sexual pleasure, or for letting out her anger? What happens when Mama X thought she was very independent but then Baby Y comes to school with a bruise on her face and the teachers get worried and call DCFS and policemen come to Mama X’s house?

Abusive Dependency.jpg

While certain privileges like doctors’ offices and prisons provide exceptional structures to function independent of consequences, no variable is truly independent of the law. This is because the relationship between independency and dependency is not as simple as a two-variable equation. When more variables are added, equations become multivariable equations that consist of not just one, but many kinds of relationships.

In the following chapters, we will explore the relationship between independent and dependent variables. We will look at what happens when we add other variables like race, class, ethnicity, gender, ability, class, and religion. 

We will look at how these other variables intersect with and effect a variable’s ability to function independent of consequence. And finally, we will look at how a child’s dependency on an abusive dependent relationship might lead the child to seek independence


As we continue, the problems in this text will get harder as we add more variables. Again, feel free to use your calculator. This text isn’t about denying you access. If your calculator can not only perform simple computations but also graph multivariable equations, you’re even more equipped to tackle the remaining chapters.




The first sentence of this textbook “Picture yourself standing in an endless line of people” comes from the first page (page 13) of the first chapter in Pre-Algebra: A Transition to Algebra cited below.


Rath, James N., and William Leschensky. "Chapter 1: The Language of Algebra." Pre-Algebra: A Transition to Algebra, Glencoe Division of Macmilliam/McGraw-Hill Publishing Company, 1992, pp.13-51. 

Rachel D.L. photo.jpg

Rachel D.L. is a survivor, math lover, and undergraduate at the University of Wisconsin-Madison. She is the recipient of the Sociologist for Women in Society’s 2017 undergraduate social action award for her writing and public speaking on the topic of childhood sexual abuse. She writes about disability justice on the blog of Rooted in Rights and has had creative nonfiction and poetry published in AnomalyThe JournalColorado Review, and Columbia College Chicago Young Author’s Blog.


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