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We will use the context of snail/mollusk shells to discover how nature, math, science and storytelling overlap in real and beautiful ways. We have lowered the floor of this task so that students in grades 3-5 can meaningfully interact with these topics in the first part of the task. Alternatively, the ceiling of this task could exit through cellular automata, permutations, Sierpinski’s Triangle, computer coding and more!

This lesson on shell patterns is inspired by material from the book, “The Big Bang of Numbers: How to Build the Universe Using Only Math,” authored by Manil Suri.

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Throughout their exploration, students will interact with key concepts such as the trivial knot, knot deformation, and the 3-colorability rule. This hands-on approach encourages students to engage with the material actively, providing opportunities to enhance their ability for abstract thinking. Never heard of Knot Theory? That’s okay! Our friend Steve Strogatz made a podcast about Knot Theory so you can learn more!

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https://www.amnh.org/learn-teach/curriculum-collections/giants-of-the-sea

Students can also listen to live and recorded whale sounds captured with an underwater microphone at this website:

https://www.mbari.org/project/soundscape-listening-room/

We are featuring the task on our page because of the interactivity of the data and the way the data is presented with video. If you would like to go directly to the worksheet created by the American Museum of Natural History and MBARI you can find it here:

https://docs.google.com/document/d/1jV0cokg5EQDF0pm1-9O8V0euGOCl6FzNQlfQfuAf-_w/edit

We hope that you enjoy this wonderful task and the videos and information about whales as much as we did at youcubed.

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This activity provides students an opportunity to go through the data cycle process focusing on a statistical investigative question based on something students would like to learn about themselves. In our day-to-day experiences we are surrounded by variability and this activity provides students an opportunity to formulate a question that can be answered with data, as they collect, consider, and analyze the data and then interpret and communicate their findings. We are thankful for Giorgia Lupi and Stefanie Posavec who shared their Dear Data journey with the world. You can find out more about their year of Dear Data postcards at:

http://www.dear-data.com/theproject

Data Talk

The purpose of this data talk is to introduce students to unique data visuals created by students who completed a Dear Data lesson. We have included a few options in the handout so you can pick one or more that will work for your students. You might choose to make your own data visual to use for this introduction.

Share a Dear Data visual and ask students, “What do you notice? What do you wonder?” As students share their ideas record a summary of their statements for class discussion. Make sure students notice the key components of the data talks like the meaning of colors, images and icons and the different ways the author of the Dear Data visual chose to communicate their findings. You might want to print the 8 Dear Data visuals and give each small group a different one to read and interpret. The groups can then share their findings with the class.

Introduction to the data cycle

Share the data cycle visual from the handout with students and explain the importance of each of the four phases. Students will engage in these four phases as they develop their own statistical investigative question and move through the cycle. Introduce the term variability by referring to the variability in the data shared in the Data Talk. For example, Kira’s data shows variability in the way she interacted with her dog Daisy throughout the day. Kira chose to study the different ways she typically interacts with Daisy on a given day.

Ask students to work in groups to determine the ways Kira moved through the process. What was her SIQ? What data did she collect and over what time period? How did she organize her data in the data visual to communicate her story and answer her SIQ? What details did she include that are important to you understanding the data and being able to read and comprehend the results? What conclusions and statements did Kira make after her data collection?

1. Formulate statistical investigative questions
2. Collect/consider data
3. Analyze data
4. Interpret and communicate data

Formulate your statistical investigative question

Ask students to work in pairs or small groups to develop their own statistical investigative question. Students should be encouraged to think about something they wonder about in their daily lives that is something they would like to know more about. For example, we have seen students study their phone usage throughout the day, how much water they drink and when, who they interact with on a given day and what do those interactions consist of and what are their emotions throughout the day. In previous student work we have seen students express how shocked they are at the data and how much they are going to focus on changing. For example, one student realized he did not eat enough throughout the day and realized he should eat and make better food choices when he does. At the end of his data cycle he reflected about how better eating might make his school performance better.

Students are working in groups during this process, so they have thought partners to discuss their ideas. Depending on the age and familiarity with the data process, some students may need support in determining a question and phrasing a question so it is a SIQ. For example, students may say their question is, “How many calories did I eat today?” This question can be answered with a number. Adjusting/editing to make it an SIQ is, “how many calories do I typically eat in a day?”. This level of question recognizes variability.

Collect and consider data

Once students have determined the SIQ they should plan how they will collect and organize the data. This is a very important step and students often do not experience this type of activity and planning enough.Students will inevitably be faced with the need to deal with uncertainty in their data collection with questions like what criterion will I use to decide what “counts” in my data? How will I structure my records so they are easy to read and easy to use in the next step?

In one Dear Data project we recently saw a student wondered what her pet hamster did all day. She collected data by putting a video camera on him for 24 hours. She certainly leaned a lot about her hamster as well as how to retrieve, organize and record data from video footage. She also had to define which of her hamsters activities she would “count” and/or what time interval to use when analyzing her video.

We ask students to not work in isolation during this time and encourage them to share ideas and questions they have with thought partners. Opening questions and ideas up for whole class discussion is a wonderful way to build a mathematics learning community and support students in seeing mathematics as a collaborative subject where creativity and ideas are valued.

Analyze data

After students have collected their data they begin to look for patterns and meaning. Organizing data into a form where they can see patterns and find meaning is something that they will build on with practice. During the process you may want to pause and have class discussions about ways students are organizing their data. If there are students who have found ways to organize their data ask them to share how what they are doing and the organizational decisions they have made.

Interpret and communicate data

After students have their data analyzed the creative fun can begin. Students may appreciate time to work in groups in discuss how they are thinking of illustrating their data. Encourage students to think about which pattern(s) from their data they wish to highlight, and how they can do so visually, through icons, color, connections, and more! Make sure that each student’s data visual includes a key for how to read it!

Share

We recommend students display their data visuals and the whole class does a carousel where they move around the room reading the data visuals. We prefer to ask students to read the Dear Data visuals on their own or in groups so they can work together to understand what data story the visual is sharing. Students may leave comments and questions on notes or there can be a whole class discussion. We have received great feedback from students who have gone through the data cycle and created a Dear Data story. This is a powerful activity and one we know your students will enjoy.

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Introduction

Start by explaining to students that each of them is going to represent one data point in the creation of a live data visualization. Let them know they will be given a data card that tells them information about one Marvel movie.

Explain to students some of the details of the dataset they will work with. The data set contains all of the Marvel movies released in the past 10 years. Marvel has made many, many movies! This data set consists of 34 movies, all released between 2011 and 2021. We have excluded those that were rated R, and those that were animated. Each data card contains data on the following variables for each movie:

• Title
• Genre(s)
• Release Year
• Average Audience Rating (an average rating on a scale of 1 to 10)
• Runtime (in minutes)

Share with students from where this data was sourced. Some students may be curious about how the movies are rated. These ratings were recorded from the Internet Movie Database (IMDb) which allows registered users to cast their rating for each move. Each users rating is out of 10, then IMDb displays the average of all ratings.

Dataset sources

https://www.kaggle.com/promptcloud/all-marvel-cinematic-universe-movies-on-imdb

and updated using https://www.imdb.com/list/ls000024621/

Once you have explained to students the details of the dataset and the included variables, ask them to brainstorm different ways to use this information to organize the movies in various ways. Create a list on the board of what students come up with.

Teacher note

If your students are not familiar, it can be helpful to remind students about bar charts, histograms, and scatter plots. A bar graph is used to represent categorical data (e.g. genre, type). Each bar represents a different variable, and the height is based on the frequency of that variable. Histograms are used to represent numerical data (e.g. numerical measures, ratings) in a single variable. Across the horizontal axis all the values the variable takes on are represented through “bins” or ranges of values. The height of each bar represents the frequency of that data measure. Histograms become especially interesting when working with continuous variables like decimals. For example, in the histogram below, where would you count a data point that measured 13.71428571?

Finally, scatter plots are used to graph bivariate data— or data in two variables. The x and y-axis each represent numerical measures. For example, we can plot the height of a plant (y) over time (x).

Before you implement this activity with students, you’ll want to prepare a very large x-y-axis (unlabeled) either outside or in a large indoor space. We have provided wording and values for the labels based on which type of visual you are challenging the class to create. You will need to print and cut the pages with data cards. There are 34 data cards on pages 5 through 9. Each student should have their own data card.

The handout includes six challenges you can pose to your class (2 bar graphs, 2 histograms, and 2 scatter plots). Upon the completion of each graph you might consider taking a picture of the Live Data Visual so that students can reference at least one of the graphs in a final reflection.

Included with each graph description are suggested axis labels. You can write the axis labels on paper or wipe off boards. Ask students to place the wipe off boards or paper labels out on the axis/axes. Each graph has a note on some interesting conversations/challenges students may face when creating the Live Data Visual. Note that for the bar graph and histograms, students whose data point lie in the same “bar” will want to organize themselves so that they create a rectangular bar shape (rather than standing alone to represent a point). To show that several data points/students are together creating a rectangular bar, students in that category/bin can line up and extend their arms in front of themselves to create the sides of the bar for the picture you will take of the completed Live Data Visual. Download the handout for the six challenge graphs.

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