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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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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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Maybe some of you recall from childhood, discovering a set of 6 little cardboard cards filled with numbers that came as a prize in a Cracker Jack Box? I clearly remember the day I got this prize. I was fascinated that it always worked, playing it over and over again with anyone who would engage me. I carried the cards with me everywhere and eventually they ended up wet mush after spinning through the washing machine in the pocket of my pants. Decades later they were reintroduced into my life. It was Christmas day in London and everyone was excited about “crackers.” I didn’t understand the excitement until Jo explained that it was a little game between two people where the winner got a prize – not food. Guess what prize I won? The 6 cards were back in my life!

Here they are presented to you as a low floor/high ceiling task. The name of this task has to be Crackers, since it started with Cracker Jacks and came back to me from pulling and winning a Cracker.

Directions

• Ask a partner to pick a number between 1 and 63 and not tell you.
• Show one of the 6 cards and ask, “Is your number on this card?”
• If they say yes record the first number in the upper left hand corner of the card. If they answer “no”, record nothing.
• Show the second card. Ask, “Is your number on this card?”
• If they say yes record the first number in the upper left hand box of the card. If no, record nothing.
• Continue until you have shown all 6 cards.
• The number your partner chose is the sum of the numbers you recorded.
• The goal is for students to record and find the sum of the numbers without pencil and paper, however not being there yet should not keep them from playing or make them feel lesser. They just aren’t there yet!

Task

• What do you notice & wonder?
• Create a convincing argument showing why this works. Can you make a visual proof?
• Make a presentation showing how this puzzle might have been created.
• If you were going to continue this pattern, what would the 7th card look like? What would be the greatest number your partner could choose if you had 7 cards? Would the puzzle still work?

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It seems that taxis have been a part of my life for years. When I was a teacher and academic in London I would see the iconic Black cabs zipping around the streets of London, and I would occasionally travel in them. It was years later when these Black cabs became important again, as some of the first evidence on the plasticity of brains – even adult brains – came from studying the brains of drivers of Black cabs in London (see video link below). Researchers found that after their intensive spatial training the brains of the drivers of Black cabs strengthened and grew. Years later I was teaching my freshman class when I met Tessa, who proposed this taxi activity for youcubed.

The link below is an extract from my first online course, featuring the neuroplasticity research from the drivers of London Black cabs.

https://www.youcubed.org/resources/brain-science/

Directions:

• How many different pathways exists to get the taxi from point A to point B?
• You can only move directly to the right or directly You cannot move left, up, or diagonally.

Task

• What do you notice & wonder?
• Can you find how many paths there are in different dimension grids? What about a 2×2? 3×3? 4×4? 4×6?
• Can you find a pattern for an m x n grid?
• Can you make a visual proof?

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