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. 

Event: Love Math! A Math Festival For Girls

The Proof School in San Francisco is holding a Math Festival for Girls called" Love Math!" It should be a great event. Here is the description from their website.

A math festival especially for girls builds community.

Come experience hands-on, collaborative activities that inspire a love for math, all for girls in grades 4 through 8 and their families.
Our math festival for girls aims to create a community by encouraging cooperative problem-solving. With mathematical art to make, fun-filled logic puzzles to solve, and ice cream combinatorics to discover, this event will be unlike most (or any!) math you've ever seen.
You'll also be able to bring home the fun. We'll have some of our favorite books, puzzles, and more for you to take home.

Special thanks to Art of Problem Solving and Beast Academy for their support!   

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Love Math! 

A FESTIVAL FOR GIRLS

Saturday, December 3  |  10am-12pm

555 Post Street, San Francisco 94102

To sign up, go to:

Love Math! A Math Festival For Girls

T-Stat in Disguise

A sampling of the many disguises that T-Stat has embodied over the last couple of weeks.

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!

Introduction

I wanted to introduce you to our newest friend in A203. This is T-Stat. Currently, he/she resides on our whiteboard. In an attempt to embrace the quirks of the classroom, I have given T-Stat space and character.  Students are invited to add personality and flare to T-Stat. We will post any interesting iterations of our friend T-Stat for all to enjoy!

Snapshot: 7B Rational Numbers

Today, we reviewed our understanding the categories of real numbers. We discussed inclusion and exclusion of different types of numbers at different points in the framework. We used an analogy about which numbers have access to different categories. For example, natural numbers have the all-access pass and fit into all categories of rational numbers. We expanded our conversation to irrational numbers, imaginary numbers and complex numbers. There was lots of curiosity and questions, but many students ended up "with their brain full!" 

7B: Math Challenge 2 - Cyclic Number

Math challenges are designed to push the students on multiple fronts. They need to decipher the problem; they must identify the tools required to solve the problem; they must use the tools correctly; determine if their solution is reasonable; and then figure out how to communicate their thinking on paper and then translate it for an audience. Whew!

I choose math challenges for different purposes each week. Sometimes it will push their problem-solving skills or it might be difficult to document or both! This was a tough math challenge, but I wanted to see what 7B would do when up against something that was hard and that they might not have all the pieces to figure out. Here is the original problem:

The symbols and representation were a hurdle for most students. Those who were able to translate the information in the problem then struggled to figure out how to glean information from the statements. It was great to have students share what they were able to find out and what they could rule out to be true. Everyone who came up to share added more information to the pool of knowledge. I was really impressed with how students were able to give credit to peers and their efforts, especially those who did not solve the problem, but advanced our understanding of the problem. 

The students who were able to complete the problem shared their strategies and key pieces of information that helped them solve the problem. To quote the students, "My mind is blown!" It was satisfying to see the students who solved the problem be able to answer questions about their work and defend their choices. I was particularly impressed with EB2018's ability to find different ways to answer essentially the same question, multiple times. 

We are starting a new tradition with our math challenges this year. After the sharing phase, students are going to reflect on their process, describe what they learned during sharing, and synthesize their experience in a journal entry. I was pleased with our first go around with the reflections. I believe that this is the next step to developing their skills as problem-solvers and communicators. Here are samples of what was written.

Please ask you child to tell you more about this problem and its solution!  

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!

Curriculum Night 2016

Thank you to all the parents/guardians who came to Curriculum Night 2016 on Thursday evening. It was a pleasure to meet you and share a little about myself and my philosophy on teaching mathematics. This marks the beginning of our year-long partnership in your child's education. 

For those who could not make it, here are copies of the handout for each class. 

6C Grade Math Curriculum Night Handout
7B Grade Math & Geometry Curriculum Night Handout
8A Grade Algebra 1 Curriculum Night Handout

Snapshot: 6C Off and Running

It was our first day of math class for 6C. We started off tentative and not sure what to expect. We broke the ice with a few sentence finishers. The class responded to the following prompts: 

• Math is important because...
• Math is ...
• Our class should be ___________ everyday.

Below are a sampling of the diverse answers for each prompt! I am excited to get to know this group and I am eager to see where our math adventure takes us this year!

Snapshot: 8A Opening day

We are back! It was the first day of the 2016-2017 school year and my only class was with 8A. We opened the QLab and there was lots of energy and enthusiasm for the newly renovated space.  We opened class with an introduction for the new students to the group. Then we jumped into an activity called 31-derful. We just got a start on the challenge and will continue when we return from our trip to Catalina. Stay tuned for more information on this fun challenge.

New Space!

We are in a new space this year! It is a whirlwind, but we are opening the school year in a newly renovated educational space. Black Pine Circle raised the funds and built a new Science educational space for K-8 use. We are excited for the new Maker Space and wet lab. This opened up the opportunity to renovate the 6th St. building and make all the spaces more functional. 

I am excited to be in a new space with lots of opportunities for collaboration and flexible groupings. Cheers to a new year and all of the possibilities that await us!

Welcome 2016!

Welcome to the blog space for Ms. Seto's middle school math classes at Black Pine Circle School! This is the second year for this blog and we are going to pick up where we left off last year. 

My hope for this space is to share and post glimpses into what is happening in the classroom and to share our mathematical adventures with the world. A long-term goal is that the students will be sharing in their own words what is going on in the classroom, but for now, this will be from my perspective (facilitator/teacher).

For students: this is a portal to access materials and resources for class, a place for class notes and shared documents, and a place to share our reflections with a greater community. 

For parents: this is a window into the math classroom and an opportunity for you to access to what happens in your child's day. It can be a tool to connect and create conversations with your child. 

For others: this is a place to share our learning and to reflect on our mathematical journey. 

It is an ambitious project, but I hope that we can live up to the expectations and make our learning visible.  

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? 

Where did the Year Go?

Here we are on June 22, 2016 and I am reflecting on the 2015-2016 school year. I realize that I was able to achieve some of what I set out to do and that on other fronts, I did not quite reach the goal line. Here are some of the thoughts I have about the school year.

• I did a decent job of posting glimpses into the math curriculum until February. The snapshots capture interesting moments in our math journey. I dropped the ball in March and was unable to get back to documenting and reflecting about our work. I would like to continue this practice next year and strive to do better and make it further into the year.
• It was challenging to track and manage three different curriculums and have time to reflect on the work. Reflection is a vital aspect of the learning process and I strive to create more space and time for reflection and to actively work at not getting swept up in the break-neck speed of life. I hope to do that more for myself and my students. 
• I am proud of all that we achieved together in each of my classes.  In reading the students' self-reflections about their year in mathematics, there was much to celebrate and acknowledge. It was satisfying to hear students reflect back many of the values and practices that I value as a teacher and a learner. It was gratifying to see the growth in all of the students and especially when they were able to recognize their growth edges and accomplishments. 
• I had students write a progress report for me as their final assignment in 6th grade. I enjoyed reading them and was reminded of how it feels to be assessed on something that is very personal. Much of their feedback was similar and it was reassuring to get similar feedback from students who find math easy to the students who struggle with mathematics. The comments that stung highlighted the areas that I know I need to address.

It is hard to capture all the ideas, thoughts, questions, and feelings that run through my head at this time of year. It boils down to this: I love what I do. I love that it is challenging and that I will never get it all right. It is the journey and striving towards "better" that keeps me coming back.  I will take the summer to recharge and to fill my tank. I look forward to next fall and having the privilege of trying to do it all over again. 

7A: Tessellated Ceilings of Iranian Mosques

Celling of Hazrate-Masomeh’s mosque in Qom, Iran, all images courtesy of Mehrdad Rasoulifard (@m1rasoulifard) via Colossal

Tessellated Ceilings of Iranian Mosques

Related to our discussion of tessellations, this article came across my feed. The beauty and artistry of these mosques are stunning. Enjoy.

7 Math and Art Connection: M.C. Escher Tessellations

Today, we began exploring how to translate a figure in geometry. We have already looked at line symmetry, rotational symmetry, and reflections. In the course of our discussion, I casually mentioned M.C. Escher's tessellations. I was startled to discover that most of the class had no idea of who M.C.Escher was. I promised the class that I would post a few links so they could explore his work further. 

Resources
M.C. Escher (official site)
Artsy.net: Maurits Cornelius Escher
The Mathematical Art of M.C. Escher
Tessellations.org - Escher Gallery 

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 Playing Card Proportions

The seventh grade is in the midst of reviewing their understanding of ratios and proportions. They worked with unit rates, did unit conversions in customary and metric units, solved proportions, found percent of change, and applied percents to mark ups and discounts. As we transition into our geometry unit, the class was asked to apply their skills with proportions to make a scale drawing of a playing card. 

Detailed calculations done to scale the playing card.

I like this project because it give the students a sense of how much mathematics is embedded in apps and tools that allow them to proportionally scale images on their devices: click and dragging the corner of an image; pinching or expanding an image on a touch screen; or when a mapping application zooms in or zooms out.


The project allowed for student choice and differentiation. There was a large range of difficulty depending on the card they choose (easy = ace, medium = number cards with increasing difficulty as numbers approached 10, difficult = face card) or the scale factor (easy = 2x, medium = 3.5x, difficult = 1.75x). The project required careful measurement and an understanding of proportional change. 

The students did an outstanding job on the assignment. The scale factor range was 0.5x to 8x. Please stop by the first floor of the sixth street building to check them out in person. 

Video: 9.999...reasons 0.9999...=1 by ViHart

As we explore the world of fractions, decimals, and percents, the sixth graders have stumbled into the annual debate about whether 0.9999...repeating is equal to one. I enjoy hearing their reasons for both sides and how passionate they get about their point of view.  To wrap up the debate, I share this definitive video about why 0.999.... is equal to one. It is the work of one of my favorite YouTube stars, ViHart.  If you have not had the pleasure of experiencing ViHart, enjoy. I recommend just letting the experience wash over you first, then go back for a closer look on the second time round. Or third....

Does she convince you? 

Population Growth

In 6C, we ended up on a tangent discussing population and population growth. I shared this video with the class because I thought it was a nice illustration of why the population on the planet earth has grown so much. It unearthed questions about history, and where are we headed. They asked that I share this with them, so here it is!