At Taipei American School, we just completed a math review year where we wrote a new Mathematics philosophy and adopted a new textbook. As I am working through the Algebra unit, I am constantly aware of a specific phrase in our philosophy statement:
Introduce concepts through a logical progression from concrete to abstract (e.g. tactile and kinesthetic experiences, pictorial representations, simulations, simple and abstract algorithms, theorems)
Due to the fact that we have adopted a new textbook this year, I am in the process of creating a new algebra unit for my sixth grade students. At TAS, we use the Understanding by Design model of planning our units and are constantly aware of our standards and benchmarks for each unit. All lessons are strictly linked to the benchmarks, and only those are formally assessed.
One of my professional goals this year is to incorporate more technology into my daily lessons … and in saying this, I am constantly referring to the NETS standards for students and teachers, as well as the standards and benchmarks for the unit. I have worked hard on developing daily lessons utilizing a SmartBoard. I have attempted to make several of them interactive so that I can invite the students to come up to the front of the class and model various concepts, thus in keeping aligned with our philosophy as well.
Below, you will find a unit outline, as well as 1) a few snapshots of lessons that I have created and/or taught during this unit, and 2) some fantastic web links involving interactive activities. Help yourself!
Project Title: Introduction to Algebra
Unit Description: Students develop their understanding of how letters are used to represent numbers in mathematics—an important foundation for algebraic thinking. Students use tables, words, numbers, patterns, and algebraic expressions/ equations to describe algebraic rules. They write and evaluate expressions and write and solve equations. By developing these algebraic skills at the middle school level, students will be able to make a smooth transition to the Pre Algebra course.
Standards Met:  
Math Standards 
NETS Standards  

1b. Creativity and Innovation – Students demonstrate critical thinking, construct knowledge, and develop innovative products and processes using technology. Students create original works as a means of personal expression.2b. Communication and Collaboration – Students use digital media and environments to communicate and work collaboratively, to support individual learning and contribute to the learning of others.Students communicate information and ideas effectively to multiple audiences using a variety of media and formats.5a. Digital Citizenship – Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior. Students advocate and practice safe, legal, and responsible use of information and technology.6b. Technology Operations and Concepts – Students demonstrate a sound understanding of technology concepts, systems and operations. Students select and use applications effectively and productively. 
Enduring Understanding:The students will:

Essential Questions:1. Is math a language? Can it be translated?2. Are there multiple ways to represent mathematical ideas?3. Do patterns exist in algebra?4. Can an algebraic expression be solved?5. How can you maintain the balance of an algebraic equation? 
FINAL ASSESSMENT  
GRASPS Task:Goal: Each student will create a 6th grade appropriate instructional video “teaching” one concept from our algebra unit.Role: Students will play the role of a teacher.Audience: Grade 6 studentsSituation: Students will choose a topic/concept from out unit that they feel comfortable explaining to their peers. They will choose gradelevel appropriate vocabulary and sample problems to explain/teach.Product: Every student will have produced an instructional video using various forms of multimedia. These videos will be used to teach other students and will be made available to all MS math students at TAS through our media server.  Six Facets of Understanding:Explain: Explain stepbystep instructions on how to solve a mathematical problem, based on one concept or skill.Interpret: Students are encouraged to use visual methods to teach their concept. Additionally, they must show each step of the solving process.Apply: Students will apply what they have learned during the unit to choose their own problems to teach to their peers. They will apply various media tools to strengthen the lesson and enhance the learning outcomes. (i.e. graphics, sound files, inking)Have perspective: Due to the fact that each student is producing a multimedia file, they are able to watch it and make adjustments several times (if necessary) before submitting it. Additionally, the projects will be reviewed by the class and feedback will be provided. Several projects will be chosen to upload to our school media server to serve as a resource to other students.Empathize: Students who started the unit with a difficulty in understanding a certain topic, but then achieves a good grasp of the concept by the end of the unit, may be more likely to want to “teach” this concept to others.Have selfknowledge: The ability to explain how to do something to an audience requires a much higher level of thought and selfknowledge. 
Instructional Videos
BrainPop Video: http://www.brainpop.com/math/algebra/equationswithvariables/
(This video served as my introduction to the Algebra unit – can only be accessed with a login code)
SmartBoard Lessons (I have included a few screenshots of the lessons I have created below)
Online Interactive Activities
Pan Balance Shapes: using shapes to balance out a scale
Algebra Equations: using Algebra Tiles to balance a scale, stepbystep, by creating “zero pairs”
Pan Balance Numbers: using a balance to create balance with numbers
Algebra Four: balancing equations and competing in a 2person game of “Connect Four”
Equation Solver: stating the steps the computer must use to solve the equation; includes additive and multiplicative inverses
As you saw from unit plan above, the students will create an instructional video based on one concept they learned throughout the unit as the culminating project/assessment. I leave the directions very vague, allowing them to choose their own software and programs to create their masterpiece.
Here is an example of an instructional video created by one of my students during the algebra unit:
You can read more about these instructional videos in my blog post titled “Technology to New Heights – Creating MathCasts in Grade 6”.
As a onetoone school, all technology tools and software are taught within our classes as we see fit. And in fact, it’s often the students teaching each other. It just goes to show that students figure out how to use technology on their own without ever having a techspecific class. But as always, there are “issues” that arise. At TAS, we have several technicians on hand at all times, some that work specifically on the hardware side of things and others who are able to come into our classrooms for support. We have the financial support of the board and the admin to properly equip our school with enough bandwidth so that the learning never stops. Additionally, the school has provided it’s faculty with hours of professional development. Due to the overwhelming support for technology at our school, the onetoone laptop program has been a success!