Article
Illustrations by Juliette Toma (Art)
Math,

Daring to Discover

By Alessandra Potenza and Jessica McKenna-Ratjen
From the March 2021 Issue

Learning Objective: Students will determine the unknown value to solve multistep word problems about important women in STEM (science, technology, engineering, and math).

Lexile: 800L; 610L
Focus Area: Algebraic Thinking,
Standards
  • MATHEMATICAL PRACTICES: MP2, MP4, MP7 CCSS: 3.OA.D.8 TEKS: 3.5A

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Lexile® measure

  • 800L
  • 610L
Gong

An instrument that makes an echoing sound when struck
Visionary

Having a strong imagination and ability to plan for the future
unknown value

A number in an equation that is not known until the equation is solved, often represented by a letter.
Signal

An object, such as a light, or a sound that gives information from a distance
advocating

Supporting or calling for an idea or plan
Inspired

Having a strong idea of what to do or create, or a powerful desire to create or do something
Botanist

A scientist who studies plants
occupations

Jobs or professions
perceive

To see, become aware of, or understand

Illustrations by Juliette Toma (Art)

A hundred years ago, states approved the 19th Amendment to the United States Constitution. It guaranteed American women the right to vote. Women had been advocating for this right for decades. At the time, women were not considered equal citizens. Most occupations weren’t open to women. Even today, women—especially women of color—are still fighting for equality. 

These barriers didn’t stop women from doing amazing things, including making advances in science, technology, engineering, and math (STEM). Meet three women who worked in STEM 100 years ago. 

States approved the 19th Amendment to the United States Constitution 100 years ago. The amendment gave American women the right to vote. Women had been advocating for this right for decades. Women were not considered equal to men at the time. Most occupations weren’t open to women. Women are still fighting for equality today, especially women of color.

These barriers didn’t stop women from doing amazing things. Women made advances in science, technology, engineering, and math (STEM). Meet three women who worked in STEM 100 years ago.

Christine Ladd-Franklin (1847-1930)

Illustrations by Juliette Toma

Christine Ladd-Franklin

Visionary Researcher

Christine Ladd-Franklin studied math at Johns Hopkins University. But in 1882, she was denied her degree because she was a woman. Ladd-Franklin didn’t quit. She studied with researchers in Germany and became a psychologist, someone who studies the science of the mind and behavior. Her work helped reveal how people perceive colors.  

Visionary Researcher

Christine Ladd-Franklin studied math at Johns Hopkins University. But the college refused to give her the degree she earned in 1882. They refused because she was a woman. Ladd-Franklin didn’t quit. She studied with researchers in Germany. She became a psychologist. A psychologist is someone who studies the way humans think and act. Her work helped show how people perceive colors.

Miriam Benjamin (1861-1947)

Illustrations by Juliette Toma

Miriam Benjamin

Inspired Inventor

Miriam Benjamin was one of the first Black women in the U.S. to get a patent. A patent is a legal document that gives inventors ownership over their inventions. In 1888, she patented the “Gong and Signal Chair.” The chair had a button you could press to ring a bell and display a red signal to tell others that you needed help. Similar technology is used today on airplanes in the flight attendant call button.

Inspired Inventor

Miriam Benjamin was one of the first Black women in the U.S. to get a patent. A patent is a legal document. The document gives inventors ownership over their inventions. Benjamin patented the “Gong and Signal Chair” in 1888. The chair had a button. A bell rang when you pressed the button. It also displayed a red signal. You pressed the button to tell others that you needed help. Similar technology is used today on airplanes. It’s part of the button you press to call a flight attendant.

Agnes Chase (1889-1963)

Illustrations by Juliette Toma

Agnes Chase

Bold Botanist

Agnes Chase loved studying plants. But in the early 1900s, people rarely funded female scientists’ research. So Chase raised the money herself. She traveled to South America to search for new species of grasses. Chase collected 80,000 samples and wrote dozens of books and papers. She became a respected expert on grasses. 

Bold Botanist

Agnes Chase loved studying plants. But people rarely funded research done by female scientists in the early 1900s. So Chase raised the money herself. She traveled to South America. She searched for new species of grasses. Chase collected 80,000 samples. She wrote dozens of books and papers. She became a respected expert on grasses.

Math Talk

What STEM career would you most want to have, and why?

Math Talk

What STEM career would you most want to have, and why?

Multistep Word Problems

What to Do

A multistep word problem has more than one unknown value. You need multiple equations or operations to solve it.

Example

The 19th Amendment (women’s right to vote) was approved in 1920. The Voting Rights Act passed 45 years later. It helped ensure that votes—particularly those of Black women and other women of color—would count. How long ago did the Voting Rights Act pass? 

Read the problem twice. Determine what’s being asked and what’s unknown.

  • The number of years since the Voting Rights Act passed
  • The year the Voting Rights Act passed

Solve for the first unknown.

  • The 19th Amendment was approved in 1920.
  • The Voting Rights Act passed 45 years later.

1920 + 45 = 1965 

So the Voting Rights Act passed in 1965.

Use your solution to solve for the next unknown. 

  • The Voting Rights Act passed in 1965.
  • The current year is 2021.

2021 – 1965 = 56 

So the Voting Rights Act passed 56 years ago.

Multistep Word Problems

What to Do

A multistep word problem has more than one unknown value. You need multiple equations or operations to solve it.

Example

The 19th Amendment (women’s right to vote) was approved in 1920. The Voting Rights Act passed 45 years later. It helped ensure that votes—particularly those of Black women and other women of color—would count. How long ago did the Voting Rights Act pass? 

Read the problem twice. Determine what’s being asked and what’s unknown.

  • The number of years since the Voting Rights Act passed
  • The year the Voting Rights Act passed

Solve for the first unknown.

  • The 19th Amendment was approved in 1920.
  • The Voting Rights Act passed 45 years later.

1920 + 45 = 1965 

So the Voting Rights Act passed in 1965.

Use your solution to solve for the next unknown. 

  • The Voting Rights Act passed in 1965.
  • The current year is 2021.

2021 – 1965 = 56 

So the Voting Rights Act passed 56 years ago.

Now You Try It

Johns Hopkins University awarded Ladd-Franklin her degree as part of its 50th anniversary celebration. Ladd-Franklin finished her coursework in 1882, 6 years after the university was founded. In what year did she receive her degree?

Johns Hopkins University awarded Ladd-Franklin her degree as part of its 50th anniversary celebration. Ladd-Franklin finished her coursework in 1882, 6 years after the university was founded. In what year did she receive her degree?

When Benjamin was 56 years old, she patented a second invention—a special shoe for giving medication. Benjamin was born in 1861. How many years after her first patent did Benjamin patent the shoe device?

When Benjamin was 56 years old, she patented a second invention—a special shoe for giving medication. Benjamin was born in 1861. How many years after her first patent did Benjamin patent the shoe device?

Chase published her first scientific paper in 1906. She published her most well-known book, The First Book of Grasses,16 years later. Her book Grasses of the West Indies was published 5 years before. What year was Grasses of the West Indies published?

Chase published her first scientific paper in 1906. She published her most well-known book, The First Book of Grasses,16 years later. Her book Grasses of the West Indies was published 5 years before. What year was Grasses of the West Indies published?

Continue Your Learning

  • Choose a woman you find important and write your own multistep word problem about her. You can pick a family member or do research about a person in books or online. Then challenge a family member, friend, or classmate to solve the problem!
  • The women from this article each had to work hard to achieve their goals. Think about a goal that you have achieved, a goal you are currently working on, or one that you plan to achieve in the future. Then create a short comic strip about your goal journey! Use this “Create a Comic Strip” template to help you plan out and draw your comic. 

Continue Your Learning

  • Choose a woman you find important and write your own multistep word problem about her. You can pick a family member or do research about a person in books or online. Then challenge a family member, friend, or classmate to solve the problem!
  • The women from this article each had to work hard to achieve their goals. Think about a goal that you have achieved, a goal you are currently working on, or one that you plan to achieve in the future. Then create a short comic strip about your goal journey! Use this “Create a Comic Strip” template to help you plan out and draw your comic. 
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