Using Technology to Teach Pre Algebra

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 -

6.2. Core Content: Mathematical expressions and equations (Operations, Algebra)
6.2.A Write a mathematical expression or equation with variables to represent information in a table or given situation.
6.2.C Evaluate mathematical expressions when the value for each variable is given.
6.2.D Apply the commutative, associative, and distributive properties, and use the order of operations to evaluate mathematical expressions.
6.2.E Solve one-step equations and verify solutions.
6.2.F Solve word problems using mathematical expressions and equations and verify solutions.

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:

  • understand that a variable represents the value of a real number.
  • become more fluent in working with various representations (i.e. words, expressions).
  • recognize that an equation is a mathematical statement in which two quantities are equal
  • comprehend that an equation is similar to a balance beam, and in order to keep balance, the proper steps to find the value for the variable must be used (i.e. inverse operations)
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 grade-level appropriate vocabulary and sample problems to explain/teach.Product: Every student will have produced an instructional video using various forms of multi-media. 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 step-by-step 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 multi-media 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 self-knowledge: The ability to explain how to do something to an audience requires a much higher level of thought and self-knowledge.

 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 log-in 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, step-by-step, by creating “zero pairs”

Pan Balance Numbers: using a balance to create balance with numbers

Algebra Four: balancing equations and competing in a 2-person 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:

YouTube Preview Image

You can read more about these instructional videos in my blog post titled “Technology to New Heights – Creating MathCasts in Grade 6”.

As a one-to-one 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 tech-specific 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 one-to-one laptop program has been a success!