Snapshot: 6 Subtracting Integers

Sixth graders were tasked with figuring out how to subtract integers. Each group of students were given a type of subtraction problem and they were required to figure out how to teach the rest of the class how to solve that. They were required to find at least two ways to solve the type of subtraction problems. The posters were shared and displayed in class. It was great to see the creative ways the students were able to apply what they already know about integers to make sense of subtracting integers. 

Snapshot: 6 Coordinate Plane Designs

The sixth grade is exploring integers. They are looking at the multiple uses of integers and applications of integers. One application we have used extensively are integers on a coordinate plane.  Students have plotted points, read points from a coordinate plane, identified the origin, and identified trends for each of the four quadrants. 

As an extension exercise, the students had to design their own coordinate plane design. They will get feedback from a peer who will complete them for homework. 

Check out the variety of designs!

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. 

Event: Evening with Dr. Jo Boaler, Standford Professor

The Mindset Revolution: How to Help Children Learn and Love Math

In this presentation Dr. Boaler will share the latest brain science that sheds important new light on the best ways to learn math. She will also engage the audience through videos of students learning math in different ways and share a wealth of resources to help students on their mathematics journeys.

December 7th, 2016 6:30 - 8:00 PM
Jordan Middle School, Palo Alto
750 N California Ave, Palo Alto, CA 94303

Free child care is available.

PLEASE RSVP: http://goo.gl/forms/kb00AQ44fD

Event: Julia Robinson Mathematics Festival in San Mateo on Nov. 21, 2015

Registration has just opened for the November 21, 2015 Julia Robinson Math Festival in San Mateo. Two years ago, I took a group of BPC students to this event and we had a terrific time exploring math in a collaborative environment. I highly recommend this event if you have the time to check it out!

Register here. 

Video: The Great Math Mystery (NOVA)

Thanks to EB2018 for sharing this video with me. We discussed the Fibonacci sequence when we were studying arithmetic sequences. Through that discussion, EB recalled this program he saw and shared it with me. The sixth graders have watched the first 6:30 minutes related to math and nature. I highly recommend the video as it ask the question, "Is math part of the natural world, or is math a construct of our mind?"

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. 

Video: TED-Ed How Folding Paper Can Get You to the Moon

This is a great illustration of how exponential growth is different than multiplication. How realistic is this example? 

Snapshot: 7A Four 4's Challenge

The seventh grade kicked off the school year with the Four 4's challenge. They had to use four 4's to make equations for each number between 0 and 50. They could use the operations add, subtract, multiply, divide, parentheses, exponent, and square roots. They were introduced the concept of factorials (4! = 4 x 3 x 2 x 1 = 24). We found patterns to find families of answers and exercised our understanding of order of operations to find solutions. The even numbers were easier to find and we are now left with the challenge of finding solutions for 31, 33, 37, 39, and 41.  

Can you figure out the missing numbers? 

Snapshot: 6 Order of Operations

Sixth grade grappled with why it is necessary to have a single answer when solving an expression. We discussed how mathematics is a form of communication and that if every "sentence" had different meanings, it would be very hard to communicate clearly and effectively. Hence, the importance of the order of operations. This foundation is helping us develop the "grammar rules" of how to create sentences and share our mathematical thoughts. 

Snapshot: 8A Slope Battleship

To solidify and extend our understanding of slopes of lines and to get practice graphing linear equations, we played Slope Battleship.  Teams of two battled with each other to sink the other team's submarine, destroyer, and battleship. Each team gave the other team an equation for a line and they would report back if it was a hit or miss. Some games got very animated!

Snapshot: 7A Variables & Expressions

The seventh graders are grappling with making the leap from concrete numbers to abstract algebraic symbols. This transition is developmental and is nurtured by regular exposure to patterns and looking for connections to the concrete examples. This week, 7A was working out the concept of like algebraic terms. How is x different than an x squared? What does 2x mean? How do we do operations on like and unlike terms?  These the foundation the algebra that is to come.

Snapshot: 6 Millet by the Million

The sixth grade took time to explore the meaning of place value and the relative size of large numbers. They worked as a collective to count out a million millet seeds to visual the number one million. We started by individually counting out 10 millet. Each student then counted out 100 millet. Many were surprised by how small one hundred appeared in their Dixie cups.

10 millet

100 millet

One thousand millet was collected by each table. At this point, we realized that this method was going to take all year! So we moved to counting by weight. We weighted the 1000 millet to the nearest hundredth of a gram. We discovered that our numbers varied by almost eight-tenths of a gram! There was great discussion about how to proceed. We agreed that finding an average weight for 1000 was needed but could not decide whether or not to add in the outlier in the data or to discard it. We looked at how much of a difference including the outlier made in our average and we finally settled on discarding the data because it made our 1000 count vary by several hundred millet. From this point, the process went quickly. Each split counted out 333,330 millet. We came together as a grade and ceremonially poured our millet together and added the final 10 millet to make a million! 

It was fun to do a collaborative project with the whole grade. Now, when we talk about millions, we have a point of reference to understand and conceptualize this very large number!

8A: The Banach-Tarski Parody

My classes quickly learn that I am easily side-tracked by interesting math ideas and conversations. This VSauce video was sent to me by a student and I felt compelled to share it with the rest of the class. In the last two years, we have tackled the concept of infinite, on multiple occasions. This video does a tremendous job of simplifying this abstract and complex idea. Our brains were stretched and I loved the interesting ideas it generated in class. I hope if you are interested in learning more, you will check out the links on the YouTube page and the many books referenced at the end of the video.

Thank you to JP for sharing this video with me and the rest of the class!

Curriculum Night 2015

It was great to meet and see so many parents at Curriculum Night! It is a pleasure working with your daughter/son and I look forward to an exciting and productive year. In case you missed the evening, you can find electronic copies of my handouts below. I have included a couple of helpful articles and a list of questions that might help you guide working with your child in math. 

6th Grade Curriculum Night Handout
7th Grade Curriculum Night Handout
8th Grade Curriculum Night Handout

Suggested Reading for Parents

Advice for Parents: Helping Children with Maths by Dr. Jo Boaler

      Do your children tell you how exciting maths is or how objects that you count stay the same number even when you move them around? How patterns can be seen in flowers and pine cones? If they haven’t started school yet they might talk about maths with curiosity and wonder, but if they have begun they are more likely to tell you that maths is confusing and scary.
      Dr. Jo Boaler, professor of mathematics and author, examines the way that maths has become the most dreaded subject for many school children, plus how we can help them begin to enjoy and even excel at it.

How Can I Help my Child Think Critically in Math?

 This is a document put together by the South Brunswick School District in New Jersey that offers a list of questions to engage your child to think critically about what they are doing in math. Also included are a list of resources for math. 

Snapshot: 7A Number Visuals

The seventh grade started off the year making connections between numbers and visualization of numbers. We studied the image below to find patterns and relationships between numbers. We found patterns of factors, multiples, and prime numbers. We predicted and designed visuals for 36 and 40. What do you notice when you look at these numbers visualized? 

Image credit: https://www.youcubed.org/wim-day-2/

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. 

Math is.....

"Math is......" was the prompt. The sixth graders responded to this prompt and the answers were diverse. This is a sampling of the answers turned in. We are getting to know each other and I love seeing their voices emerging already!

Art Benjamin's The Magic of Math: Solving for x and Figuring Out Why on Sept 11, 2015

This should be a great event hosted at the new Proof School in San Francisco. You can reserve the free tickets here.

 Art Benjamin's The Magic of Math: Solving for x and Figuring Out Why

On the evening of Friday, September 11, we (the Proof School) will host Art Benjamin for a public talk and book signing. His newest book, The Magic of Math, will be available for sale at a discounted rate of $17. This event is free, but tickets are limited.

Dr. Arthur Benjamin is both a professor of mathematics and a magician. He has appeared on many television and radio programs, including The Today Show, CNN, The Colbert Report, and National Public Radio. He has been profiled in The New York Times, Los Angeles Times, USA Today, Scientific American, Discover, Omni, Esquire, Wired, People Magazine, and Reader's Digest.

Dr. Benjamin has given 3 TED Talks, one of which has been viewed over seven million times. He is a member of Proof School's Advisory Board.

Welcome 2015!

Welcome to the blog space for Ms. Seto's middle school math classes at Black Pine Circle School!

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. 

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. 

OP's Pi Day video

I am delighted to share this video made by OP2017 to celebrate Pi Day 2015.