Mathematics Coaches’ Training
November 13, 2009
Presented by
Carla Clayton-Lewis
Mathematics Instructional Specialist
Capacity Development and School Reform Accountability
PDCA Inst ruct ional Cycle
PLAN
• Data Disaggregation
• Calendar Development
DO
• Direct Instructional
Focus
ACT
• Tutorials
• Enrichment
CHECK
• Assessment
• Maintenance
• Monitoring

 Silence cell phones
 Participate and share
 Listen with an open mind
 Ask questions
 Work toward solutions
 Use time effectively

 Hands-On Equations is a visual and kinesthetic system developed by Dr. Henry Borenson for introducing students in grades 3 to 8 to essential algebraic concepts.
 It is a system designed to enhance student self-esteem and interest in mathematics.

HandsOn Equations (cont’d )

In a few lessons students learn to solve equations such as
4x + 3 = 3x + 9 and 2(2x + 1) = x + 8. Later lessons teach additional concepts.
 The students physically set up the equation using the game pieces and a flat laminated balance and then proceed to carry out "legal moves" to solve the equation.

The legal moves are the physical counterpart of the abstract mathematical principles which are used to solve these equations.

What are the benefits of using
Hands-On Equations?
 No algebraic prerequisites are required
 It is a game-like approach that fascinates students
 The gestures or "legal moves" used to solve the equations reinforce the concepts at a deep kinesthetic level
 The program can be used as early as the 3rd grade with gifted students, 4th grade with average students and 5th grade with
LD students

Benefits of using HandsOn Equations (cont’d)
 Students attain a high level of success with the program
 The program provides students with a strong foundation for later algebraic studies
 The concepts and skills presented are essential for success in an
Algebra 1 class

Hands-On Equations Sample
Equations: Three Levels
 Level I: Lessons #1 - #7: Red Booklet.
Students use the red cubes and blue pawns to setup and solve :
4x + 3 = 3x + 9 and 2( 2x + 1) = 3x + 10
 Level II: Lessons #8 - #16: Blue Booklet.
Students use the red cubes, blue pawns, and white pawns to setup and solve:
2x = * + 6 and 2x - * + 2 = * + 10
 Level III: Lessons #17 - #26: Green Booklet.
Students use the red cubes, blue pawns, white pawns, and green cubes to setup and solve:
2* + 3 = -6 + x and x – 2 (* + 2) = 5

You will be given a set of questions to answer without any directions on how to answer the questions.
Your task is to:
Answer the questions without the use of manipulatives.

A Step by Step visual guide to
Hands-On
Equations

Mathematics Capacity Development Team
Michelle White, Mathematics Manager
Michelle.white@palmbeach.k12.fl.us
Shabana Ahmad-Farook farook@palmbeach.k12.fl.us
Altoria Henley altoria.henley@palmbeach.k12.fl.us
Bobbie Brooks brooksb@palmbeach.k12.fl.us
Sharon Martinez martinezs@palmbeach.k12.fl.us
Dale Carothers carothers@palmbeach.k12.fl.us
Kim Pirtle pirtlk@palmbeach.k12.fl.us
Cara Hayden haydenc@palmbeach.k12.fl.us
Carol Sheffield sheffic@palmbeach.k12.fl.us
Carla Clayton-Lewis claytoc@palmbeach.k12.fl.us
Noel Elvir
Noel.Elvir@palmbeach.k12.fl.us
Stephen Smith
Stephen.Smith@palmbeach.k12.fl.us
Allison Castellano
CastellA@palmbeach.k12.fl.us
Thank you for all that you do for our students!