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. 

Snapshot: 6C Sugar Packet Posters

As part of our study of proportions, 6C did an activity by Dan Meyer called Sugar Packets. They watched this video and had to figure out how many packets of sugar are in a bottle of Coca Cola. 

We extended this activity to other beverages. They predicted which beverages had the most sugar and the least amount of sugar. They recognized that the sugar content could not be compared if the volumes of the beverages were different, so they made unit rates of sugar to volume so they could compare like amounts. Many students were surprised by the sugar content of some of their favorite beverages.

The last phase of this activity had the class take a point of view and promote one beverage based on its sugar content over other possible beverages. The students had the freedom to pick which point of view they wanted to promote, but they had to use the math to support their claims. 

These are a sampling of some of the more creative and unique posters that were created. I was impressed with the class' use of humor and puns to catch people's attention. There were a few new ideas that made us think. I have never had anyone compare the sugar content of different milks. The comparison of different waters was a new spin on this project. 

I really like this activity because it forces students to think about how proportions can be used to compare different items. I like adding the dimension of having a point of view and supporting it with numbers. It helps to dispell the idea that numbers to not lie and that data can not be manipulated if it is numerical. It provides an opportunity for students to look critically at how numbers and data are used to express a point of view and how they can be used to manipulate how you see something. This project is an opportunity to practice clear communication and sharing of ideas. 

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.

Snapshot: 7B Shooting Percentages

As we start off the school year in 6th and 7th grade, the students jump start their brains with an eight-day run of multiplication math facts practice. As a way to add a little fun to necessary skill practice, we let off some steam by doing target practice with our crumpled up mad minute sheets. We keep track of the number of shots made. There was a healthy level of competition on which class did better on the paper shooting. 

This is LO's analysis of the shooting scores for both 6C and 7B. She was methodical and very clear in her process of showing how to convert the fraction into a decimal by division and then converting the decimal into the percent. It is a wonderful example of how to show your thinking and process.

The students were asked to determine which class "won." They came up with several different ways to to do their data analysis. Please ask your child to tell you all the different ways the data was processed!