Category Archives: technology tools

What’s in a Name? Having Fun with Data

by Sarah Lonberg-Lew

My name is Sarah. (If you don’t believe me, check the byline.) On my first day of high school, I met four other girls named Sarah. It has often been my experience to not be the only Sarah in a group, especially a group of people close to my age. I’ve had to add descriptors to my name to be able to be uniquely identified. I’ve been “short Sarah,” “Sarah short hair,” “Sarah L,” and on more than one occasion I’ve been “math Sarah.” If you also have a common name, you can probably relate.

Just how common is my first name? There is a fantastic internet tool that can answer that question for me with a wealth of interesting data. It is WolframAlpha, the computational search engine. If you are looking for quantitative information of any kind on the internet, this is a great place to look. One exciting thing this site can do is provide current and historical data about the popularity of a name. For example, here are some things I learned about my own name:

  • About 1 out of every 303 people in the United States is named Sarah.
  • There are about 909,700 Sarahs living in the United States right now. That means I may not be one-in-a-million, but I’m close!
  • The most common age of a Sarah in the United States is 30.

WolframAlpha also showed me data that helped shed some light on why I so often have to qualify my name in large groups. This graph shows the popularity of my name over time:

When I was born, my parents didn’t know that my name was getting more popular. Looking at this graph, I wonder if a lot of other parents might have been similarly unaware. Can you guess about when I was born?

The same site also provided a graph showing the age distribution of people with my name in the United States:

What do you notice about the two graphs? What do you wonder?

There are many mathematical avenues to explore within the name results at this website. Beyond looking up your own name or your students’ names, you can also compare multiple names. For example, here’s a graph that compares the popularity of my name with the name Donna (the name of the esteemed director of the Adult Numeracy Center):

What do you notice about this graph? What do you wonder about? One thing I wonder about is whether the Ritchie Valens 1958 hit song “Oh Donna” had anything to do with the name’s popularity. What do you think?

The trends in naming babies can reflect what is going on in the world as well as what is popular in music, literature, movies, or TV shows. Here’s a striking example – this graph shows the historical popularity of the name Barack:

One interesting thing to note on these graphs is that the scale on the y-axis is not always the same. The peaks for the graphs of Sarah and Donna are at over 1.5% of babies born in a given year. The peak for Barack is at about 0.0035% of babies born that year.

A few notes about exploring names with WolframAlpha
  • It’s important when looking at data to know where it comes from. WolframAlpha gets these numbers from the Social Security Administration.
  • If you have an uncommon name, WolframAlpha may not recognize that you are looking for name data. You can fix this by adding the word “name” to your search.
  • WolframAlpha may make assumptions about your search term that affect the results. The site lists the assumptions it made in a blue box at the top of the results. You can modify those assumptions if you need to.
How you can use this resource with your students
  • Have them look up their own names or compare their name to a classmate’s. Are they surprised by what they find? Or does it confirm their lived experience?
  • Do you have students who are thinking about baby names? They may want to look up the names they are thinking about to see how common or unique certain names are.
  • Challenge students to draw connections between the different ways that information is presented in the search results. For example, WolframAlpha told me that the most common age of a Sarah in the US is 30. Where can I find evidence for that in the graphs?
  • Click on the “more” button at the top right of the history graph to see even more graphs. What does each graph show? Why are the shapes similar or different? What is the y-axis measuring on each graph?
  • Ask your students what they see in their search results. They may surprise you!

There’s so much math you can explore with this engaging and personally relevant data. Clicking on links in the results may also bring you to interesting (although possibly not useful) information. For example, I discovered that the combined weight of all the Sarahs living in the U.S. is about 63,682 metric tons! What will you discover about your name? Go have fun!


Sarah Lonberg-Lew has been teaching and tutoring math in one form or another since college. She has worked with students ranging in age from 7 to 70, but currently focuses on adult basic education and high school equivalency. Sarah’s work with the SABES Mathematics and Adult Numeracy Curriculum & Instruction PD Center at TERC includes developing and facilitating trainings and assisting programs with curriculum development. She is the treasurer for the Adult Numeracy Network.

Using Desmos: How Can It Fit in My Classroom?

by Connie Rivera

I was sold on the idea of using free Desmos Classroom Activities as soon as I tried one myself. Why?  Because I discovered math ideas I didn’t already know just by working through an activity

Using tech tools in class can’t be technology for technology’s sake. Our instruction must be focused on the mathematical understandings we want students to develop. Only then should we search for the activities that help students discover those ideas. Desmos is a great source for facilitating deeper understanding of math concepts. Below is a way I’ve helped students develop a concept, beginning with paper and ending with Desmos. 

Triangles and Rectangles

First, I started with this printable activity which is an exploration of the relationship between Triangles and Rectangles.  

Here are some ideas students develop from Triangles and Rectangles:

  • Parts of a fraction must take up the same amount of space, but they might not begin as the same shape.
  • If I can prove an area is half of a shape, the other parts must total half the area.
  • I can flip and rotate images in my mind to consider a fit.
  • For a triangle to be half the area of a rectangle it’s within, it must share at least one side (base) with the rectangle.

In a broader sense, these realizations are about noticing a pattern, generalizing an idea, and visualizing.

Desmos Classroom Activity: Exploring Triangle Area with Geoboards

Next, I used Exploring Triangle Area with Geoboards with my students. Here are some step-by-step thoughts.

Follow the link above and find the blue “Student Preview” button in the “Screens” section. In order to experience the activity the way your students would, use the  at the bottom of the screen to close the “Teacher Moves” and “Sample Responses” the first time through. In fact, try working through the activity yourself before continuing to read this article.

Screen 1: Find the Area #1 Here are two examples of how students used the sketch tool to work through their reasoning.

As you can see from the screenshots, other students’ responses would show up on the screen as well — a feature that allows students to see other students’ thinking whether or not they are on the computer at the same time! Knowing that there’s an audience encourages students think about their answers more carefully beforehand. Afterwards, they can consider the accuracy of their answers and edit their responses if need be.

Screen 2: Find the Area #2 The problem on Screen 2 reminds some students of the triangle that didn’t work in the initial Triangles and Rectangles activity, leaving them to find new approaches. In this activity, we can see how the ideas that were beginning to develop in Triangles and Rectangles are explored from a different perspective and extended using Desmos.

In the examples below, we can see in the image on the left that the first student drew a square that encompassed her triangle and found its area (12). Then she marked smaller rectangles and found the areas of the white spaces (1.5, 1.5, 4). Lastly she subtracted the total of the white spaces from the rectangle’s area (resulting in 5 square units). 

The second student (the same student from example 2 in Find the Area #1) was, to my surprise, able to carry her visualization process through to this more challenging problem. She complained there weren’t enough colors to show her work, but her explanation made it clear that she could see each piece rotating, flipping, and moving to a new spot to create a square unit.  She was surprised that everyone couldn’t see things she saw easily. 

It benefits students to hear different ways that other students think through a problem. Finding an efficient solution method doesn’t result in the same solution method for everyone; it gives everyone a chance to find something that works for them.

Here you could pause the class (a feature for teachers in the dashboard) and ask students to share answers to the question, “When you were stuck, what idea got you unstuck?” Some responses might be:

  • I can flip and rotate images in my mind to consider a fit.
  • I can find the area of a rectangle holding the triangle, and subtract out the area of the outside pieces that I’m able to find the area of. This leaves only the area of the triangle I didn’t know (and now know).

Screens 3 & 4: Create a Triangle and Class Gallery undefined Screen 3 gives students a chance to create new problems of their own to challenge their classmates (and practice what they are learning from a different perspective). Screen 4 is space where students try out their classmates’ challenges. As a bonus, they can also see how others in their class have attempted to solve the same problem.

Getting Started with Desmos

Are you interested in using this activity with your students? Here’s how to get started.

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You can “Create an Account” using the green button on the top right. Next, click the green “Create Class Code” button on the teacher page of this activity. Now you have opened a class. Click “view dashboard”. Your code and how to get there is the first thing to pop up. Share your code with friends to try it out and learn how the dashboard can help you monitor a class. 


Connie Rivera teaches numeracy skills to adults of various skill levels, including court involved youth and English Language Learners. She is also a math consultant, providing math strategies and support to programs implementing the College and Career Readiness Standards for Adult Education (CCRSAE) in Connecticut and Massachusetts. As a consultant for the SABES numeracy team, Connie facilitates trainings and guides teachers in curriculum development. Connie is a past President of the Adult Numeracy Network, the adult affiliate of the National Council of Teachers of Mathematics (NCTM), and is a LINCS national trainer for math and numeracy.