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: 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: 8A Barbie Bungee Jump

Students are always asking,"When will I ever use this?" in math class. I do my best to give them real world contexts for the skills they are learning. In the 8th grade, we began the year learning about linear functions and figuring out how to graph them. To help make these skills real, the students did an activity where they had to use linear functions to figure out how many rubber bands a Barbie required to get the most thrilling bungee jump off QLab 201's balcony (16 feet).  Thrilling was defined as getting as close to the ground without actually touching the ground.  Here is a compilation of shots from our jump day. 

Thank you to Blake Hansen for the video footage and editing.


If you wish to read more about this adventure or see more photos and video, check out: 8A Barbie Bungee Jump: Explore More.

Snapshot: 6C Subtracting Integers

Negative number - Positive Number

The students in 6C are grappling with how to subtract integers. This is a challenging lesson for sixth graders because it requires a depth of understanding of what it means to subtract and how negative numbers can impact that concept. 

Class was divided into groups to work on understanding a specific subset of integer subtraction problems. They were given manipulative ands and two different tools to help them work through what is happening in each subset of problems. They were asked to summarize their work on a poster and then required to "teach" the rest of the class how to think about their type of problem. Everyone had to be versed in their type of problem and able to communicate their understanding of the material. 

I like this activity because it requires the students to make sense of something they have not been taught formally. They have to struggle to put together information they already know and apply it in a new way. I like to challenge their thinking and make sure they are able to see when conclusions they make are logical and when they make sense only because they want it to make sense. I enjoy hearing students work to explain their thinking to their peers. Listening to students find ways to make sense of the material in different ways because the way they are explaining it is not making sense to their classmate. I love it when students challenge each other's thinking in respectful ways. All of the dialogue and communication is priceless. More learning happened in one period than most of a normal week!

This is just the beginning of their journey with subtracting integers. They walk away from these presentations with a sense of accomplishment. The next step is to see if they can apply what they have learned when the problems are not so nicely grouped together and isolated. What happens when they encounter the problems in the "wild" or mixed up with other problems? That is the first real test of their understand. 

Positive number - Positive number

Negative number - Negative Number

Positive number - Negative number

Special Cases

Snapshot: 6C Coordinate Planes

In sixth grade, we have entered the world of integers!  We have doubled out numerical world by adding all of the negative integers to our known world of positive numbers. We discussed and explored the reason we need negative number and how we use them in our everyday lives. We reviewed how a four quadrant coordinate plane worked. The class enjoyed assignments where they had to plot points to reveal an image.  We took that one step further and the class was asked to create a coordinate plane assignment for a peer to complete. They will give each other feedback on the clarity and success of their assignment. Here are the images that the students created. 

6C : Four Digit Challenge

Students in 6th grade are working on solidifying their understanding of the order of operations in mathematics. The class explored why it might be important for a mathematical phrase or sentence to have only one solution. They came to realize that without a set of universal rules to follow, communication would be flawed. It would be impossible ensure that the information you are trying to communicate would not be misinterpreted. 

To extend their understanding, the class was given the "Four-Digit Challenge." They were asked make equations that equaled 0 to 50. The requirements were:

• the digits 1, 2, 3, and 4 were required to be in each equation
• each digit could only be used once
• they could use addition, subtraction, and multiplication (no division)
• they could use parenthesis and other grouping symbols
• they could use exponents and square roots

The class was challenged to see if as a group they were able to complete all of the equations from 0 to 50. They broke into groups and set to work. 

I wish you could have been in the room to hear all of the wonderful mathematical thinking that was happening. Here is a small glimpse into the type of collaboration that was happening.

Check back for more on the Four-Digit Challenge!

6C: Group Work Norms

Working in groups and collaborating are not skills that we are born with. We must learn to work together and identify skills that help us to work in collaborative settings. Before we began a group activity, we discussed our prior group work experiences. We could all identify and describe a time when a group activity or project did not go well. 

We took that conversation and turned it into a set of norms that we were all going to strive to achieve when we do group work in math class. Here is the list that was generated.

• Be inclusive (work to include others in your group)
• Everybody tries to do an equal part of the work
• Sharing ideas is helpful 
• Look at both sides what a person has to share
• Treat your group members respectfully.
• Everyone is a leader
• Balancing stepping up and stepping back
• Everyone must participate

We acknowledged that these were things we would try to do, knowing that there will be days/times when it is hard for each of us. 

7B: Number Visuals Exploration

The first assignment for 7A was looking at YouCube's Activity, "Number Visuals," from the 1st Inspirational Week of Math in 2015. The class was given the image below to look at and make as many observations as they could. 

The class found all sorts of patterns and relationships between the shapes. Here are some of their findings:

• All the prime numbers are circles.
• Every 4th figure is a group of squares.
• All multiples of three are triangles
• The first row are building blocks for the rest of the chart.
• Starting at 6; when you go down 2 and left 2, you will arrive at a variant of the number.
• You can see the factor of a composite number in the shapes that make up the number.

The group was challenged on who to describe how to move around the chart without using world like diagonal. 

As an extension, the class was charged with figuring out what the 40th figure would look like. The class shared their different ideas (see one student's work above) and they had to defend one of the choices.  

Students are learning to support their ideas and answers with solid evidence and reasoning. This will be an ongoing work in progress, all year long.

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!

News: Why We Learn Math Lessons That Date Back 500 Years?

I heard this piece on NPR and followed up by reading the accompanying article. It asks the question of why we learn the math we teach in schools? What are the origins of learning math?
 
NPR: Why We Learn Math Lessons That Date Back 500 Years?

This is a question I encounter every year, multiple time a year. This piece sheds some new light on the historical reasons for the math we teach today. I wonder, why does it remain the same? Why can't we approach math education from a different perspective? Why do we remain so rooted in this historical context? 

Snapshot: 8A Documenting the Process

 

One of the great challenges that my students face in math class is documenting their thinking on paper. Most students are resistant to taking the time to show their work in detail. It is difficult to capture all of the decisions and step that are required to show someone how they achieved their result. Every so often, students are able to capture their thinking in a clear, detailed, and concise manner. These are two exemplar samples of what we hope every student can achieve. 

The eighth grade is learning how to factor polynomials. We began the journey by learning how to multiply monomials, binomials, and polynomials. The class spent several periods looking for the clues on how to factor a trinomial in the form of a^2+bx+c. To solidify their learning, they were asked to write out the steps to teach someone how to factor this type of trinomial. Many found this task difficult because they struggled to generalize the steps. Most could tell you what to do with a specific example, but not how to do it without specifics. These two examples were the most successful at capturing what needs to happen to factor a basic trinomial in the a^2+bx+c form.  Both capture the essence of the procedure in very different ways. One is verbal and the other is expressed with tables. We shared in class to help everyone get better at documenting their thinking. 

Snapshot: 7A Expanding our Understanding of Exponents

7A had a lively discussion that helped to expand our understanding of exponents. We began with what we knew about positive whole number exponents with base 10 (blue ink). When we arrived at 10 to the zero power, the class had to figure what made sense. They proposed that the answer could be 0, 1, or 10. We then took arguments for each possible solution. It was rewarding to see their pattern recognition skills come into focus. The two clarifying explanations are in green ink. NSK noticed that the difference in the standard forms was a 9000, 900, 90, and 9 and rationalized that 10^0 had to be 1 for the pattern to continue.  EH noticed that the pattern between values was to divide by 10 so the next number in the pattern was 1. This convinced us that 10^0 power was 1. Then they tackled 10 to the power of negative 1. There was much debate about whether the negative exponent would make the number negative. Logic prevailed and we applied our patterns from before to extrapolate that negative exponents made them fractions. It was invigorating to hear the healthy debate and hypotheses being shared.  

I was excited to hear the new questions that were then generated by these new discoveries:

"Can you have two to the power of 4 to the power of 2? Can powers have power?"

"Can exponents be fractions?"

The doors have been opened to a whole new world. Check back for other musings and discoveries.

Snapshot: 6 Math Challenge - MBA

This week the sixth graders took on their second math challenge, Modern Basketball Association. There was significant progress made in finding a variety of ways to show their thinking. Above is a sampling of the many ways 6B was able to document their thinking and illustrate their reasoning. We began evaluating which strategies were clarifying and what made them so successful. 

Snapshot: 8A Applying Systems of Equations

The eighth grade is working hard to develop their algebraic tool box. They are learning the different tools used to solve systems of equations. We have practiced substitution, graphing and elimination. The class's tool of choice is elimination!  

To help us synthesize our learning, we set out to figure out which tools worked best in different scenarios. Each group was given a pair of equations to solve. They had to graph the solution, use substitution to solve the system, and use elimination to solve the system. We discussed and identified characteristics of each set of problems to help us determine which was the best tool for each scenario. Below, are the notes from our exploration. 

Our greatest challenge in this work has been keeping track negative signs, applying the distributive property, and correctly manipulating equations according to the reverse of the order of operations. 

Snapshot: 6 Math Challenges

Math Challenge 1: Rrribbitt!

An integral part of the sixth grade curriculum our the math challenges. 

The goals of the math challenges are:

• Build problem solving strategies and tools
• Practice communicating mathematical ideas in written & oral formats
• Give and receive critical feedback
• Practice working collaboratively

The math challenges are chosen because they have multiple entry points: it can be solved with numbers, solved using a drawing, or using algebra. By design, this allows us to explore problems from multiple points of views and to check our thinking and work. The class has just begun to practice how they document their thinking and how they present their work to the group.  Look forward to many more examples of our math challenge work in the coming months. 

Snapshot: 8A Collaborative Problem-Solving

It was great to welcome the 8's back from their travels to Catalina Island. We kicked off the year with a collaborative problem-solving activity called "31-underful!" Each table was given a deck of cards and required to make a 5x5 array where each column and row had a sum of 31. Each table and group had a different approach and different way to solve the challenges that emerged along the way. Each group presented their strategy and solution to the whole class. It helped to dust off our math skills and start of the year communicating their thinking.