# Math

### Robot to the Middle

Robots have long been used to help students with geometry. In 1971, Seymour Papert and Cynthia Solomon wrote a paper called “Twenty Things to do with a Computer” in which they talk about using a robot they call a turtle to draw geometric shapes.

Turtle Robot

Last year at the MakingMath Expo we had two versions of this, drawing bots and a program where you could draw with a virtual turtle robot.

Drawing Bots (foreground) and Virtual Turtles (background)

This year we are going to use the bots to raise the question, “How can you figure out the exact middle of various shapes?” Students will start with a rectangle and move through other shapes like parallelograms, triangles, and circles. At each shape they will have to justify how they know they are right about where the middle of the shape is before they are given a robot. Once they have the bot they will drive it with a remote control to the exact middle then stop. In the classroom, however, they would have to program their bot to go from the origin and stop in the center on its own with minimal information about each shape. Here’s what the entry document might look like. At the expo there will be a leader board with a prize going to the closest at the end of the day.

Hope to see you there!

– Jim Town MakingMath Specialist

### #Scratch-ing the 6th grade Math Itch

Our first project highlight for the 2nd annual Making Math Expo is “Using Scratch for 6th grade Math,” where 6th graders will teach attendees how to use the computer program Scratch while sharing their final projects from their work with the program. As attendees learn Scratch firsthand, creating their own coded projects, students will share how they linked blocks to build a “code,” building both programming and mathematical proficiency.

As programmers, participants must strategize about the choice of coding blocks in order to make their code more efficient, and as mathematicians, they develop a conceptual understanding of positive and negative numbers as they move objects around the xy-grid, using academic vocabulary to describe their location in the grid.

Want to scratch your coding itch and do some math in the process? Come play with this and more at the Making Math Expo on March 12! Registration is free but limited slots are available, so sign up today!

-Celine Liu, Mathematics Specialist at ACOE

### Social Justice + Math = Education

*Education is not preparation for life; education is life itself. –*John Dewey

*People are aware that they cannot continue in the same old way but are immobilized because they cannot imagine an alternative.* -Grace Lee Boggs

Over the course of the year, our Social Justice Math study group has been hard at work, trying to figure out what it means to be a math educator with a social justice lens.

There are many approaches to this question, from looking at math literacy as a civil rights issue, to understanding how culturally relevant pedagogy impacts student achievement, to integrating economic and social justice issues into our classrooms, among others.

Regardless of where we land on the question of what social justice math *is*, it has become more clear with each conversation that math education through the experiential lens of working-class communities of color is an *essential principle of education *if our goal is to grow a self-determined, powerful human force to continue to evolve the way we live as humans in today’s society.

Grace Lee Boggs was an “evolutionary” who worked for a lifetime in Detroit to address the systemic injustices that the city’s residents have experienced through the years. She posited that “the community itself with its needs and problems must become the curriculum of the schools,” where learning is not just about skills and information, but the ideas, principles, and struggles needed to transform their community.

Want to know what this might look like? Check out Max Ray’s talk on how math teachers are the key to ending racism. Or see how Rico Gutstein and a group of 9th graders analyzed a Chicago redistricting proposal that could have resulted in upheaval and increased racial tensions for the students and families living in the neighborhood. Or listen to Saraswati Noel share about Seattle World School’s campaign to lock down a permanent school site after bouncing from location to location for years.

How would it look in your classroom? How different would your school be if the community was an active asset and participant rather than an occasional resource? How are you educating for social justice in your math class?

For more information on the Social Justice Math study group, see our site at socialjusticemath.acoe.org or contact Celine Liu, Math Specialist at cliu (at) acoe.org.

### March Math Making Madness

Join us for a month of #makingMath! A whole month of free activities brought to you by the Alameda County Office of Education Core Learning Math and Technology team to promote Making in the Math Classroom.

In our Make and Take series, educators will work on a specific, standards-aligned project to take back to their classroom. They will leave with a better understanding of how making can be embedded into the classroom, and construct a whole new meaning from the phrase: “use appropriate tools strategically.”

Thursday March 3rd is the **Make and Take: Gravity Car** workshop, participants will make a “gravity car” using simple tools, recycled materials, and just plain tinkering. They will struggle with the question: “What math can my students learn by making a gravity car?”

Participants will:

- Experience making a gravity car using various materials and mathematics
- Plan a MakingMath gravity cars lesson/project to take back to their classroom

Thursday March 10th is the **Make and Take: PVC Flute** workshop, participants will make a flute using simple tools, PVC pipe, and math. They will struggle with the question: “What Math Can Your Students Learn by Making an Instrument?”.

Participants will:

- Build a PVC flute using mathematics and simple tools
- Explore ways math can be applied to designing and building musical instruments
- Plan a MakingMath instruments lesson/project to take back to the classroom
- Leave with a better understanding of how making can be embedded into the classroom

Finally, on Saturday March 12, come get inspired at our **Making Math Expo** where educators from around the Bay Area will we showing off their #makingMath projects at Lighthouse Community Charter School in Oakland. This is a day dedicated to the fun and exciting world of Problem Solving, where students, teachers, and parents will have various opportunities to apply their math and problem-solving skills. Come experience an assortment of non-traditional problems that will work your thinking muscles, and understand why the Mathematical Practices must be an integral part of every math classroom. All participants will leave with strategies and tools to improve student problem-solving abilities.

### Hour of Code

As we are ramping up for ACOE’s Math and Technology Team’s first Hour of Code hosted in our very own Meaning Maker Studio, I wanted to share the resources we are using in case you can’t make it.

**Lightbot**

**Ages:** 5-9 (and up)

**HOC Website:** lightbot.com/hoc.html

**What is it?** You are responsible for telling a little robot what they need to do in order to blink a light on top of all the blue squares. As with most engaging games, the challenges start of simple so you can learn about the game and then increase in rigor. What starts out as a coding game for five year olds quickly escalates into an interesting challenge, even for adults.

**How is this coding?** Coding, according to thefreedictionary.com is “a system of symbols and rules used to represent instructions to a computer; a computer program.” Which is exactly what you are doing to help the lightbots meet their objectives.

**Can I use this after the hour of code?** Yes, but the app costs 2.99 for iOS and Android.

**Scratch**

**Ages:** 9-12 (and up)

**HOC Website:** scratch.mit.edu/hoc

**What is it?** Scratch is a block based language that has a simple, but powerful interface. Besides being easy to use, they have great resources for people teaching themselves and teachers looking to use this in their classes. The Scratch online teacher community has a plethora of resources, lessons, and active participants who can answer your questions quickly and intelligently.

**Can I use this after the hour of code? **Yes! Scratch is free and has both a browser based version that work on most modern laptops (including Chromebooks) and an offline version that work better on older computers (including really old ones that can only run Puppy Linux) or places with spotty internet.

**CS Unplugged**

**Ages:** 8-14 (and up)

**Website:** csunplugged.org/activities/

**What is it?** Activities were created to get students thinking about computer science even if their school couldn’t afford computers (or their teacher could never book time in the lab, the lab was always down, etc) or the students had access, but felt reticent to sit down at a computer and hammer out some code.

**How is this coding? **The two activities are a Magic Trick and Binary Cards. For the Magic Trick, students turn one card upside down in an array of two sided cards. Using a parity bit at the end of each row and column, the magician can tell the student exactly which card was turned over. This is a form of error detecting commonly used when transmitting data. Another common method of error detecting similar to this that most people have heard of are check sums. The activity helps them understand the idea using physical cards so they understand it in a different way than if they had learned it on the computer. The binary cards are dots representing the first few powers of two. Students represent base ten numbers using the cards (ie 12 would be an 8 dot card plus a 4 dot card) then translate that into a binary number (ie 12=01100). Binary numbers are how computers transmit and store information, this activity help students understand that binary is just a different way to represent numbers (and letters).

**Raspberry Pi + Scratch = Scratch IRL**

**Ages:** 12-18 (and up)

**Website:** raspberrypi.org/hour-of-code/

**What is it? **Raspberry Pi is a small, inexpensive computer that was designed to help students learn to code. Scratch is described above. With the Raspberry Pi, students can integrate objects in the real world (etc buttons, LEDs, etc) into their Scratch projects. This helps bring the abstract world of coding into the real physical world and opens up exciting possibilities like playing a buzzer noise when someone opens your door or blinking a light when you get a high score on a game. If you don’t have a Raspberry Pi, but still want to play with Scratch IRL, there are several options that work with regular computers such as Lego WeDo, Picoboards, and Makey Makey.

**Can I use this after the hour of code? **Yes! Scratch is free and has both a browser based version that work on most modern laptops (including Chromebooks) and an offline version that work better on older computers (including really old ones that can only run Puppy Linux) or places with spotty internet. Also, Raspberry Pi’s are available for $40 and the new Pi Zero is only $5.

### Algebra 1 with Robots

In August, a group of dedicated teachers came together to build a series of project based Algebra 1 with Robots units to support the Algebra 1 with Robotics and Computing class that is approved by UCOP for mathematics (‘c’) credit. Approved course outline.

After two months of work, it is finally ready to be unveiled.

Each project starts with an entry document that generates a need to know for the math topics the students will be learning. Most of the projects utilize robots so students have a physical way to interact with abstract concepts and learn the ideas in a different way than in a traditional classroom.

These projects are a work in progress. As the teachers here in Alameda County test them out over the course of this year, we will be updating them. If you find ways to make them better, or would like to contribute your own project, please contact Jim Town (jtown(a)acoe.org). This is an open source project, it can only get better with your help!

Though this course was written for the Barobo Linkbots in Python or Ch, many (if not all) of the projects can be adapted to work with other classroom robots (Finchbots, Lego NXT, etc). We would be happy to help you translate any of the projects and incorporate adjustments you made so that more teachers and students can benefit from this course. Please contact Jim Town (jtown(a)acoe.org) for assistance.

– Jim Town

### What Do the SBAC Scores Mean?

The SBAC scores have been released to districts, and are about to be released to the public. But what do the scores mean, and how have they been organized?

**The California Department of Education (CDE)** has created a guide to the score report, which highlights the most important pieces of information. Each student will receive an overall score in English language arts/literacy, and another in mathematics. An additional score, this one for science, is also provided for certain grade levels–however, this test was administered as a CST test, and not an SBAC test. At the eleventh grade level, the Early Assessment Program (EAP) status is also shown.

On the second page of the score report, the literacy and math overall scores are broken down by “areas” (or what the SBAC blueprint refers to as “claims”). The four literacy areas are reading, writing, listening, and research/inquiry. The three math areas are problem solving and modeling/data analysis (which are really two claims combined), concepts and procedures, and communicating reasoning. The CST science test score is shown on a range from far below basic to advanced, while the EAP status is depicted on a range from standard exceeded to standard not met.

In addition to this resource, teachers and parents will find a plethora of information on **GreatSchools**‘ GreatKids State Test Guide for Parents:

- what a student should have learned in each of the literacy and math areas, at his/her specific grade level
- what a student may have struggled with if s/he did not meet or exceed the standard in that area
- what parents can do to help their children develop these skills

***This year, **ACOE’s Core Learning Team** is preparing multiple professional development seminars to prepare students for the Smarter Balanced Assessment this spring. View our offerings on Interpreting SBAC Assessment Data (math), Creating Literacy Performance Tasks (literacy), and Formative Assessment in Your Content-Area Classroom (literacy), among others. Join us for these powerful and enriching sessions!

-Maria Vlahiotis, Literacy Specialist, ACOE Core Learning

### MakingMath Expo: Learning Math and How to Learn Math

*Students, families, and teachers circulate to determine which project to start with. Photo credit Aaron Vanderwerff.*

On Saturday, March 28, Alameda County Office of Education and Core Learning partnered with Lighthouse Community Charter School to host a MakingMath Expo–an event designed to model how math can be taught using creative and engaging problems and activities. In spite of the gorgeous sunshine beckoning students, families, and teachers into the great outdoors, over a hundred participants spent several hours of their Saturday exploring an assortment of non-traditional problems–a testament to the great need and desire for just this kind of challenge in our schools.

* Budding animators make stop-motion math animations to illustrate step-by-step process in solving math problems using iPads and a multi-layer glass stage.*

Young people from the ages of 4 through 70 (at least!) experienced making in the wide variety of projects such as:

- a probability game that indigenous peoples from California played,
- creating battery-powered circuits from homemade conductive dough,
- writing computer code to generate custom-designed figures using Turtle Art, and
- many more.

This is not an exhaustive list! How else could you see these activities being integrated into the math learning you are involved in?

* Two young learners use Legos to understand fractions and number [de]composition.*

Weaving in Common Core Math Content Standards as well as the Standards for Mathematical Practice, the MakingMath projects provided opportunities for participants to learn about concepts including, but not limited to: ratio and scaling; computational thinking; fractions and proportional reasoning while developing their abilities to make sense of problems and persevere in solving them; use appropriate tools strategically; and attend to precision.

*Creating a mold to hold his double-size peanut butter cup*

*A photo mashup using fraction knowledge and a NYSci App *

*Alameda County Library’s Squishy Circuits table gets students thinking about data, measurement, and reasoning (abstract and quantitative).*

*Never too young to #makemath. Photo Credit Mirella Rangel*

As parents and teachers circulated, many of the conversations centered around how this problem- and project-based approach to learning could be replicated in their own learning spaces. In conceiving of the skills that students need to be successful in a 21st century world, creativity and problem-solving are two that come up over and over again in Core Learning’s work with educators. The projects and philosophy behind the MakingMath expo not only helped participants to solidify their content and skills, but also showed one way that learning (and teaching) math can be facilitated.

*Students teach themselves and each other how to use Turtle Art to express their creativity and geometric understanding.*

This promises to be the first of what we hope to be a legacy of MakingMath events; follow us on Twitter and check our blog periodically to find out about these and other Core Learning events. Until then…have fun #MakingMath!

### Squishy Circuits

Brought to you by the Alameda County Library:

*Squishy Circuits in action at the Newark Library*

Squishy circuits are a neat way to have students learn about some of the basic properties of electricity through tinkering and problem solving.

But where is the math?

Besides problem solving to troubleshoot their design, students have a chance to engage in some measurement and data. In each of the 2nd through 5th grade CCSS standards, students have to measure something and put it on a line graph. The difference has to do with the scale on the line graph, 2nd is to the nearest whole number, 3rd includes halves and fourths, and 4th adds eighths.

So after your students engage in problem solving to test and make their squishy circuits, they’ll measure the distance between the LED and the battery and add that to the class graph. After all groups add their data, they identify the longest distance. Then ask them to make a conjecture about the longest possible distance and build it to see if it works. All the circuits that work should be added to the class graph. If time and interest, repeat until you’ve found the maximum distance. An example student lab sheet can be found here.

Come play with this and more at the Making Math Expo on March 28th!

-Jim Town, Mathematics Specialist at ACOE