Snapshot: 7A/7C Data and Representation

The seventh-grade classes began the school year by exploring the different ways data can be represented. We collected three different data sets: birth date, bed time vs. wake-up time, and favorite ice cream flavor, topping, and container. Observations and deductions were made on the first two data sets. Students made astute observations and deduced information about the classes based on the data. They made predictions about how adding the data from 7B might change or re-enforce our observations and deductions. We invited 7B to share their data with us too. We discussed the value of representing data in visual formats and how it can help us find patterns that may not be evident in the raw data form.

For the favorite ice cream flavor, topping, and container data, groups of students were asked to represent the data collected in a graphic manner. Students had to grapple with deciding which data to include, how to sort or organize the data so it was easier to consume, and which tool or strategy would best communicate the information. The diversity of representation was impressive.  A small sampling is located below. Please stop by the upper hallway in the Athena building to take in the rest of the posters. We discussed how the same data set can be distilled in so many different ways. I hoped to illustrate that graphs and data sets can be helpful, but we must be careful to ask questions like: Which data was used? Which data was left out? What is the point of view that is being shared or promoted?

We will practice our observation skills and make sense of patterns and representations throughout the year as we make our way into algebra and algebraic thinking. 

7B Room Design Project

The seventh grade curriculum lends itself to many real-world projects and activities. It is the last concrete and tangible mathematics the students encounter before being thrust into the abstract world of algebra. 

An end-of-the-year project I like to do with the 7s is a room design project. Students measure their bedroom, draw a scale drawing, calculate the surface area of the walls and floor, calculate the amount of paint needed, calculate the amount of flooring needed, calculate the cost of paint and flooring and sales tax, all on a budget. We tackle this project as a series of phases to be completed with many small deadlines to keep them on track. Students get into drawing their blueprints with architectural symbols, picking out paint chip colors, deciding on the finish of the paint, and negotiating how to spend their budget.  It is a practical and real world application of many of the concepts and skills learned in the seventh grade curriculum.

Last year, I had a student independently tape all of his drawing together into a net of his room.  It was brilliant! So this year, I added it to the project and the students liked seeing how their 2D net could be transformed into a 3D representation of their bedroom. I felt like I could imagine standing in their rooms from their scale models. I learned a few things from the construction process that I would change for the future, but it was a great addition to the project. The science teacher and I discussed the possibility of having the students 3D print their rooms next year. I love the idea of cross-curricular integration.  We just need to make the time to plan and execute it next year!

Snapshot: 8A Food Deserts

Berkeley, CA

As a final project, I like to find a way to incorporate a social justice lesson into the eighth grade curriculum. Last year, the class spent the final weeks of the year tackling the question, "Is minimum wage a livable wage?" They explored by calculating living expenses for a year (rent, food, transportation, entertainment, etc) and then compared it to what you would earn if you were working a minimum wage job. They had a a guest speaker from the Human Resources department come and talk about the taxes and deductions that are taken from a pay check. In the end, we had a good debate/conversation about whether or not you can live off of minimum wage.

This year, the class took on the idea of food deserts. This is a project I have been tossing around for about a year. The essential question was, "What is a food desert? Who is impacted by food deserts?" We researched and defined a food desert. They looked at research about the impact of food deserts. For four classes, a group of students were charged with locating grocery stores on a set of maps from AAA of the Bay Area, Lake Tahoe, and Portland, OR. They had to cut out 1-mile radius circles to represent the reach of the grocery store. The areas that were not covered by the circles are defined as food deserts. These maps are not comprehensive because we were limited in time, but students were able to get a sense of how food deserts occur and who is impacted by these deserts. 

Our discussions centered around how they live in an region of the country were access to fresh fruits, vegetables, dairy, and whole grains is easy. They recognized the high density of markets and grocery stores is high in the Bay Area and that affluent areas had great overlap of circles. Some students were able to recognize living in Northern California is not representative of the issue of food deserts. If we had more time and I had planned ahead, we would have done a second round of maps that represent cities where food deserts are a significant issues, such as New Orleans, Atlanta, and Detroit, and compared maps with the Bay Area. I would extend this to look at grocery stores per capita and other ratios that might have helped us understand the issue further.

This activity turned out better than I had hoped and I was pleased with how we were able to use math to explore this topic. I look forward to refining and extending this project for future classes. 

Oakland, CA

El Cerrito and Richmond, CA

San Franciso, CA

Lake Tahoe, CA

Portland, OR

Snapshot: 7B Playing Card Proportions Project

 In seventh grade, the students applied their knowledge of ratios, proportions, and scale to a project where they had to produce a scaled version of a regular playing card. The purpose of the project was to have the students apply their understanding of proportions to a real task and for students to develop an appreciation for the feature on tablets and phones where they can just pinch to enlarge and/or shrink a map or image. These are seemingly simple features that require a great deal of mathematics to make functional and accurate. 

I like this project because there are many ways for students to customize their experiences and provide differentiation. They could add difficulty in the value of the card, the suit, the scale factor, and whether or not they did the whole or just part of the card. Artistic ability is not required to succeed on this assignment, but it is an opportunity for those who have an interest in artistic expression to share their interest. It brings a little color and fun to the walls of the classroom!

6C - Discussion "Is 0.9999.... = to One?"

Video credit: ViHart

We have entered the world of rational numbers in 6th grade. We are working on building our fluency with different representations of fractions: moving between fractions, decimals, and percents. A perennial question that emerges, "Is 0.99999 (repeating) the same as 1?"

This year, I asked the class to tell me what they thought before any explanation was given. There was a clear majority who felt like 0.9999... was not equal to one. There was heated debate and we had to work on how to speak to each other so we could understand the other's point of view. We recognized that repeating the same response is not going to help someone see another point of view.  The challenge is finding another way to explain it help someone see from a different perspective. 

We capped off the discussion by watching the ViHart video (above). There is a lot of information to take in and unpack, but there are some very convincing arguments.  For homework, the class was asked to reflect on where they stand on the questions now. Many students found reasons to change their thinking and a few are steadfast in their belief that 0.9999.... is not equal to one.

8A: Barbie Bungee Jump - Explore More

As introduced in the post, Snapshot: 8A Barbie Bungee Jump, the eighth grade applied their knowledge of linear functions to a Barbie bungee jump challenge. The intent of the project was to provide a real world application of linear functions to ground student understanding.  Students were divided into groups of two or three to do some introductory experimentation with a Barbie, up to three rubber bands, and a meter stick.  Here are all the bungee jump groups with their test Barbie and company name.

Groups plotted their data two ways: by hand and using the an online regression tool. Using their math skills they drew a line of best fit and did their best to estimate the slope of the line. Once they had their calculations figured out, they plotted their data on regression tool and it gave them a linear equation. They had to figure out what the slope and y-intercepts represented in this scenario and use these data points to decide how many rubber bands to add to their bungee rope.

We had to wait patiently for a dry day to perform our bungee jumps. Jump day was thrilling. They students made their initial jumps and then modified their numbers one last time.  Here are some photos from jump day.

We experimented with filming and photography of the event.  There were a couple of GoPros and lots of iPhone footage. Our favorites were the slow-motion jumps taken from the ground.For our final jump, we had all Barbies jump simultaneously.  It was a great way to make a direct comparison of all the bungee cords.

 Student reflection and feedback gave me insights into how to improve upon this activity. Fun was had by all and we made math come to life! 

Thank you to all the people who shared their Barbies for us to use and to B. Hansen for the great video clips. 

Snapshot: 8A Equations of Lines

Much of the fall was spent working with various forms of a line. The class saw different representations of lines: tables, graphs, equations, and word problems. In this activity, the class was split into groups and they had to match a table with an equation, a graph, and a story problem. They are working to understand the relationship between these representations and know when each type is useful. There was lots of great discussion and testing of understanding as the activity progressed. 

Next, we are getting ready to solve systems of linear equations!