Hands-On Equations Blog

University of Louisiana Uses Breakthrough Program to Help Younger Kids Excel in Algebra

2011-11-29T15:52:00.010-05:00

This news item appeared in the Market Watch section of the Digital Network edition of the Wall Street Journal.

Nov. 29, 2011, 8:25 a.m. EST

LAFAYETTE, La., Nov. 29, 2011 /PRNewswire via COMTEX/ -- In a world where t-shirts say kids are allergic to algebra and low national test scores seem to confirm, the University of Louisiana runs a unique teaching program using a strategy called Hands-On Equations to train teachers and sponsor algebra competitions where middle-school students love and excel in the subject.

Dr. Peter Sheppard, Associate Professor of Mathematics Education, Department of Curriculum and Instruction at the University of Louisiana at Lafayette, wants kids to experience algebra earlier and be excited about it. Thus, he and the University of Louisiana hold annual H.E.A.T. (Hands-on Exposure to Algebraic Topics) Competitions where over 350 kids from 20 middle schools participate.

"We use Hands-On Equations in our teaching and developed H.E.A.T. as a means for teachers to employ this creative instructional strategy in after-school math clubs since curriculum constraints often limit the time teachers can devote to this learning approach in their regular classrooms," remarked Sheppard.

Sheppard is none too soon using the innovative approach either.

According to the 2011 National Assessment of Educational Progress, which tested 4th and 8th graders in math and reading, national test scores show only 40% of 4th graders and 35% of 8th graders received proficient math scores. Louisiana and other states including California, Tennessee, Alabama and The District of Columbia often rank near the bottom.

"Even in this digital age, kids learn algebra concepts faster and in earlier grades when they use tactile items they can see and touch such as Hands-On Equations. This program uses numbered cubes and pawns as well as a representation of a balance scale to model and solve algebraic equations," said Sheppard.

Teachers using the Hands-On Equations program ( http://www.borenson.com ) are thrilled with the results.

"Middle-school students have a hard time understanding and grasping algebraic concepts," says Heather Olson of Edgar Martin Middle School in Lafayette Parish.

"Since I have been using Hands-On Equations, my students love to solve algebraic equations because the approach is like a game. Forty-three students joined our after-school math club. The students understand the representation of the balance on the board, the pawns for the unknown number, and the number cubes for whole numbers. The students are enjoying solving the algebraic equations, especially the extremely long equations," continued Olson.

The H.E.A.T. project is funded through a grant from the Louisiana Board of Regents, Louisiana Systemic Initiatives Program and the State of Louisiana STEM Goals Office.

The program provides participating teachers with professional development in algebra instruction. The students involved in H.E.A.T. learn using Hands-On Equations materials in after-school programs. Some 50 undergraduate students will assist in grading the student papers during the competition.

Dr. Henry Borenson, the creator of Hands-On Equations, will address teachers and be present at this year's H.E.A.T. Competition Awards on December 7, 2011 at the Student Union Ballroom of the University of Louisiana at Lafayette, from 9 a.m. to 1 p.m. Award ceremonies take place from 12:30 - 1 p.m.

Drs. Sheppard and Borenson are available for media interviews. Email Dr. Sheppard at psheppard@louisiana.edu or call 337-482-1514. Contact Dr. Borenson via Heather Harter at 800-993-6284, 404-925-2840 or Heather@borenson.com

About Borenson and Associates:

Borenson and Associates, Inc. provide the Making Algebra Child's play workshop for teachers with students in grades three through nine. Additionally, they present introductory webinars for parents. Even in the digital age, the hands-on approach to learning algebraic concepts is in high demand, as the company celebrates its 25th year in business. The company is based in Allentown, PA.

For information, go to http://www.Borenson.com

Contact:

Heather Harter

Heather@borenson.com

Phone: 800-993-6284

404-925-2840

SOURCE Borenson and Associates, Inc.

Hands-On Equations Introductory Webinars

2011-11-27T04:15:00.000-05:00

Demystifying the Learning of Algebra

A Hands-On Equations Learning System for use with one student ($34.95)will be raffled off at each introductory webinar!

Click here for current free webinar offerings. Invite your friends or colleagues to join you.

Overview of Complimentary Introductory Webinar

This webinar will provide an overview of Hands-On Equations. Participants will gain an idea of how equations are represented and solved and how the concepts are applied to the solution of verbal problems.

We will show how the game pieces are used to represent equations such as:

4x + 3 = 3x + 9
2(x + 4) = x + 10
5x + 2(-x) + 3 = x + 9
2x = (-x) + 12

In addition, we will provide a glimpse of Hands-On Equations can assist students in solving verbal problems such as:

Three times a number, increased by 2, is the same as the number increased by 10. Find the number.
Eight years from now, Tom will be 4 years older than twice his present age. How old is he now?

By participating in this introductory webinar, participants will understand how Hands-On Equations can be of value to them in introducing their students in grades 3 - 9 to basic algebraic concepts. Full-length webinars and full-day workshops are available to provide educators with in-depth training.

New: Verbal Problems Introductory Webinar...also free. Click on the above link for more information.

Learning the Relational Meaning of the Equal Sign

2011-01-13T16:49:00.006-05:00

"Students who exhibit the correct understanding of the equal sign show the greatest achievement in mathematics and persist in fields that require mathematics proficiency like engineering."

- Education Research Report Blogspot, citing the research of Robert and Mary Caprano

As Robert Caprano notes students need to see and experience the relational meaning of the equal sign. Young students are quite familiar with its operational meaning, whereby the equal sign is used to indicate the result of a series of operations, such as 4+3=7. This is indeed a legitimate and pervasive use of the equal sign and one can open any advanced mathematics or science textbook to practically any page to find this use being employed. Hence, the calculator use of the equal sign is not incorrect; it is simply only one use of this sign.

An understanding of the relational meaning of the equal sign, on the other hand, as Mr. Caprano notes. would enable students, to provide the answer of 7 to the problem 4+3+2= __ + 2.

In studies involving more than 2500 students conducted with the assistance of researcher Larry Barber, the results are conclusive: students as early as the 4th grade can solve equations such as 4x+3= 3x+9, thereby demonstrating that a) they understand the relational meaning of the equal sign, b) they can understand the concept of an unknown and c) they can work with equations having unknowns on both sides of the equal sign. This research can be found on www.borenson.com.

A video of an 8-year old solving 4x+5=2x+13 can be found by going to YouTube and searching for Algebra Hands-On Equations.

What is particularly interesting about this approach is that students pick up the relational meaning of the equal sign in only a few lessons. The students EXPERIENCE the new meaning of the sign. They quickly learn that the correct value of the unknown will make both sides have the same value.

For teachers not using Hands-On Equations, I would recommend an approach whereby the students experience the relational use of the equal sign in gradually more complex examples. In other words, the teacher gradually enables students to develop meaning to expressions such as 10= 4 + 6, 7 +3 = 9 + 1, and 10 + 2 = 2 + 5 + 5. Next, the teacher omits any one of the given numbers and asks the class for the missing number. In this manner the student soon learns to correctly answer examples such as 4+3+2= __ + 2.

In summary, there exist sound pedagogical interventions to enable even young students to understand the relational use of the equal sign.

Teaching 4th Graders How to Do Algebra

2010-12-15T04:18:00.007-05:00

December 12th, 2010 3:05 pm ET

Joe Sipper, Durham K-12, Examiner

In the spirit of making algebra more concrete and accessible to students, Dr. Henry Borenson invented a method of teaching variables in a concrete method. Hand-on Equations® is actually targeted toward a 4th grade audience, with some classes using it in as early as 3rd grade.

The system uses a structure (or a drawing) that resembles a double pan balance. An algebraic equation is given. The students “set up” the equation on the balance using game pieces and cubes with number values written on them. The numbered cubes literally represent the number written on them. The game pieces are “x”. The center of the balance is the equal sign.

Students begin by taking away equal amounts from each side until the equation is simplified. Then they do the simple arithmetic needed to solve for “x”. Maybe the best part is that students then have a way of checking their solution by seeing if both sides of the balance have an equal value.

Some video demos of elementary students using the device can be seen here.

Concerning the ideas that sparked his invention, Dr. Borenson allows:

"Even before the National Research Council issued a report in 1998 that included the statement, ‘We know from experience that the current school approach to algebra is too abstract and an unmitigated disaster for most students,’ I was already aware of this phenomenon. I wanted to find a way to make the abstract concepts of algebra visual, hands-on, and accessible to students of all ability levels-- and at much younger age. It turns out that the symbols and concepts of algebra related to solving equations such as 4x + 3 = 3x + 9 can be expressed perfectly via objects and actions. Using the Hands-On Equations® approach that I developed, even 3rd and 4th graders can solve equations that many 9th graders find difficult when presented abstractly."

The main idea behind the product is to take the fear out of algebra and allow students to strengthen applicable skills before actually enrolling in the class. Users and researchers swear by the results and hail it as a method for teaching how to think mathematically.

For more information about the teaching model, the Website offers free webinars. The Website also gives information on demonstrations and seminars.

About Joe Sipper

A former science teacher and coach, Joe Sipper also has experience as a content and assessment developer, project director, program manager, strategic planner, presenter, and director of staff of large educational publishing companies. Joe Sipper has experience on more than 20 testing programs across the United States, Puerto Rico, and Chile. Joe Sipper is owner of his own educational consulting company, iJS Education Services . His client list includes Pearson Educational Measurement, Educational Testing Service, the Educational Records Bureau, Education 2020, and several large school districts.

Sharing the Excitement of Hands-On Equations

2010-04-16T05:34:00.003-04:00

At the end of the workshop, one participant indicated that she had the materials in her building but had no knowledge of what they were or how to use them. She asked how she could get others excited about HOE. I told her my story and my first experience with HOE. I stated I was so excited about the presentation that I immediately went back and used my individual set with one student during our remediation/enrichment period and invited my principal to come and watch. After my principal saw how quickly my student was picking up on the concepts, he ordered me a class set of 30. I then used my planning period for several weeks to go to different classrooms and model HOE with individual teachers’ classes within my building with the stipulation that they had to remain and watch. After demonstrating HOE in their classrooms, they became excited and wanted the materials as well. I even went to resource classrooms to model the power of the program. She was excited about this suggestion and stated she would start with her principal first and share in a departmental meeting with her peers.
-Instructor Kathryn Dillard

COMMON CORE STATE STANDARDS

2010-04-16T04:31:00.004-04:00

General Comments on the Algebra-Related Standards, K - 6

Formulating and disseminating national math standards is an ambitious goal, but also one that can backfire if the standards are not capable of being attained by a large portion of the intended student population.

Before the draft Common Core State Standards are proposed for adoption, they need to be pilot-tested. Failure to conduct this pilot testing has the potential to cause more damage to students than the educational system that is already in place.

For the pilot testing to be effective, it cannot be conducted with teachers who volunteer to participate. Rather, districts and teachers must be selected at random from the inner city, suburban and rural areas and asked to participate so that a reasonable assessment can be made.

Proposed standards should be one that can reasonably be attained by at least 80% of the intended student populations through instructional means which teachers can reasonably be expected to learn and implement.

This pilot testing will determine, for example, if some of the math standards related to algebra in grades K – 6 are overly formalistic and, whereas they may have some value for mathematically gifted students who may have the intention of becoming professional mathematicians, they would further discourage the average and below average student.

For an example, in the 6th grade standard students are expected to see the need for and to understand that through the use of the multiplicative identity and the distributive and commutative laws they can get from y + y + y to 3y as follows: y + y + y = y(1+1+1) = y(3)= 3y. This is only one of many examples where a formalistic approach is used for an obvious result.

Indeed, in the standard for grade 3 the students have been informed that multiplication by a whole number can be considered as repeated addition. Hence, adding the same item three times, namely y, is the same thing as having three of those items, that is 3y.

So that while on the one hand there is an excessive formalism in many of the standards in the area of algebra -- a formalism which is not likely to endear many students to mathematics, but rather cause them to wonder why the subject is so obtuse and dry -- standards that would give students an early and solid foundation for algebra through concrete and pictorial means, is lacking.

For example, in kindergarten or the 1^st grade (and not in grade 6) the students can learn to represent an apple by the letter "a". They can then work with questions such as 2a + 3a (2 apples and 3 apples are 5 apples), so 2a + 3a =5a. Likewise, "g" can represent a grape. Hence students can be asked, “What is the total number of apples and grapes that we have in basket containing: 3a + 2a + 2g – g?” In this manner, young students can become comfortable working with mathematical expressions containing letters.

Later on, in grades 2 or 3, "a" and "g" can represent the cost of an apple and the cost of a grape, respectively and the students can be asked for the total cost of 4a + g (4 apples and one grape) if each apple costs 25 cents and each grape is 5 cents.

Additionally, in the current set of standards it is only in grade 6 that students are asked to use the idea of maintaining equality to solve equations of the form x + p = q and px = q where x, p, and q are all non-negative rational numbers. In other words, at the same grade level the students are being asked to use properties of equality to solve x + 3 = 10 and 4x = 20, they are also expected to solve x + 2/5 = 3/4 and 2/5x = 3/4. It should be clear to the reader that the former are much more simple and obvious than the latter and should therefore be presented several years earlier.

Indeed, using concrete or pictorial methods, it is know that 4th and 5th graders, including inner city minority students, can solve equations such as 4x + 2 = 3x + 10 with unknowns on both sides of the equation. They do so by first transforming the abstract equation into a physical or pictorial representation (the same physical or pictorial icon is used for each x, e.g., 4x is represented by 4 of the icons; the constants can be represented by numbered cubes or boxes) and then physically or pictorially maintaining the balance by removing the same number of icons (x's) from each side of the equation or the same value from the constants.

Students in the 4th and 5th grade can then transfer this learning to solving word problems such as, "Four times a number, increased by 2, is the same as twice the number, increased by 10."

By moving away from the formalism that is suggested in a number of the standards related to algebra and instead replacing those with standards that recommend concrete and pictorial representation and solution of algebraic equations -- an activity that students enjoy doing because they can understand the process and experience success-- the standards will be empowering younger students and laying a foundation for later success in algebra. Otherwise, algebraic equations will continue to be seen as abstract even by students who have strong arithmetic skills.

In summary, this educator believes it would be a grave error to propose the draft core standards for national implementation absent an extensive pilot testing with a broad population of students and teachers. This testing will likely take from one to three years.

Recommending the draft core standards, absent this pilot testing, poses the risk that the attempt to raise the level of mathematics education in the United States via the formalistic and "rigorous" algebra-related standards, may backfire, that is, it may lead to a higher level of failure and frustration then already exists in the mathematics classroom and may therefore result in a very strong back-to-basics movement.

Hands-On Equations in Virginia Beach

2010-02-18T15:32:00.002-05:00

Consecutive Integer Problem Solved with Hands-On Equations

2010-01-30T16:55:00.002-05:00

The Day2 Hands-On Equations Verbal Problems Workshop or webinar is designed to show teachers of Hands-On Equations how to present verbal problems to their students. In the example below a gifted student going into the 6th grade solves a consecutive integer problem which most likely would be a challenge to many Algebra 1 students.

Hands-On Equations for the SMART Board

2009-08-18T14:24:00.000-04:00

Click to on the arrow to play.

The kinesthetic component of Hands-On Equations is one of the facets of the program which produces such strong student gains. Hence, the use of Hands-On Equations for the SMART Board should not replace the physical elements of the program. Students should still use the game pieces at their desks and the teacher should still use the Teacher's Demonstration Scale at the front of the classroom.

The Smartboard application is simply another means to illustrate the teaching problems of each lesson. For example, the teacher can illustrate the simultaneous removal of three pawns from each side of the scale.

Each of the examples that are presented in each lesson of the Hands-On Equations red, blue and green booklets is presented on its own slide. In addition, there is a blank template slide if the teacher wishes to provide additional examples on the Smartboard. The Table of Contents enables the teacher to go directly to the desired lesson.

A number of the lessons have teaching points to be presented to the students as a summary of the lesson. These are available via a pull-out tab such as that shown below.

As noted, the Hands-On Equations program is fully effective without the SMART Board application. Hands-On Equations for the SMART Board is available for purchase via download and very soon via disk.

Cost: for one teacher $125. License for five teachers: $500

Borenson and Associates, Inc.
800-993-6294
info@borenson.com

HANDS-ON EQUATIONS WEBINARS

2009-07-16T01:34:00.006-04:00

(Broadband connection and computer headset or microphone is requred)

Test your browser and operating system by joining a test meeting

Fall 2009 Schedule of Public Webinars

Choose the time that is best for you for each webinar:

9:00 a.m. - 11:00 a.m. EST

3:00 p.m. - 5:00 p.m. EST

7:00 p.m. - 9:00 p.m EST

Making Algebra Child's Play Webinar (Each module is two hours in length)

Introduction and Level I (Red) Manual: Monday, October 26, 2009

Registration Fee: $59 includes the Hands-On Equations Learning System

Level II (Blue) Manual: Monday, November 9, 2009 ($29)

Registration Fee: $29 (no materials included)

Level III (Green) Manual: Monday, November 16, 2009 (29)

Registration Fee: $29 (no materials included)

Hands-On Equations Verbal Problems* Webinar(Each module is two hours in length)

Introduction: Wednesday, October 28, 2009 ($59)

Registration Fee: $59 includes the Hands-On Equations Verbal Problems Book and a student set of game pieces

Level I Verbal Problems: Thursday, October 29, 2009 ($29)

Registration Fee: $29 (no materials included)

Level II Verbal Problems: Wednesday, November 11, 2009 ($29)

Registration Fee: $29 (no materials included)

Level III Verbal Problems: Wednesday, November 18, 2009 ($29)

Registration Fee: $29 (no materials included)

Making Algebra Child’s Play® Webinar (for teachers of grades 3–8 and high school teachers of students struggling with algebra)

Hands-On Equations® Verbal Problems Webinar (for teachers of grades 4 -8,elementary teachers of the gifted and high school teachers of students struggling with algebra.)

*Important: Participation in a verbal problems webinar presumes the individual has participated in theMaking Algebra Child's Play webinar covering the same level,e.g. someone wishing to participate in a Level II Verbal Problems Webinar should first participate in the Making Algebra Child's Play Webinar on Level II.

To register for a webinar, please click here.

Books Mentioning Hands-On Equations

2009-07-15T16:58:00.002-04:00

Teaching Middle School Mathematics‎ - Page 216

by Douglas K. Brumbaugh, Enrique Ortiz, Gina Gresham - Education - 2006 - 328 pages

Hands-On Equations Hands-On Equations is another manipulative that helps develop
algebraic concepts. These materials may be used to solve equations like the ...

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The Hands-On Equations Learning System‎

by Henry Borenson - Mathematics - 1994 - 66 pages

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The Hands-on Equations Learning System‎

by Henry Borenson, Borenson and Associates - 2004

Demonstration game piece set for teacher use has: 8 white pawns, 8 blue pawns and 8
number cubes (4 green, 4 red); each student game set has the same types and...

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Teaching Kids with Learning Difficulties in the Regular Classroom ...‎ - Page 218

by Susan Winebrenner, Pamela Espeland - Education - 1996 - 237 pages

... Box 3328 Allentown, PA 18106 1-800-993-6284 "Hands-On Equations* Learning
Systems" provide hands-on understanding of algebraic concepts for grades 3-12.
...

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Smart kids with learning difficulties: overcoming obstacles and realizing ...‎ - Page 85

by Rich Weinfeld, Linda Barnes-Robinson, Sue Jeweler, Betty Roffman Shevitz - Family & Relationships - 2006 - 195 pages

Using interactive, hands-on programs (eg, Hands-on Equations), manipulatives,
and math tools help students grasp content and concepts. ...

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Mathematics education at highly effective schools that serve the poor ...‎ - Page 100

by Richard S. Kitchen, Sylvia Celedon-pattichis, Julie Depree, Jonathan Brinkerhoff - Education - 2006 - 231 pages

... 2003) stated, "I think the students really understand those concepts [
variables, combining like terms] better because of hands on equations. ...

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Educators' Opinions of the Product Hands-on-equations TMlearning System‎

by Nancy C Ray - 2002

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The Effectiveness of Hands-On-Equations on Students with Learning Disabilities‎

by Quinn Edward Karlinsey, School of Education, Weber State University - 2005

"July 13, 2005."

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Teaching Pre-algebra to Seventh Grade Resource Room Students Using the Hands ...‎

by Mary E O'Shea, Gratz College, RTC Division - 2003

A research project submitted to the faculty of Gratz College in partial fulfillment of
the requirements for the degree of Master of Arts in Education, 2003.

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Good Stuff: Learning Tools for All Ages‎ - Page 93

by Rebecca Rupp - Education - 1993 - 386 pages

There's more to Go than initially meets the eye. Generally available from toy
and game stores. Hands-On Equations Hands-On Equations is an introduction to ...

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Winning at Math‎ - Page 128

by Dr. Paul Nolting - Education - 2002 - 301 pages

... balance beam with top like objects to represent variables and dice to
represent numbers. Your math lab can order the Hands On Equations by going to
www. ...

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From Idea to Funded Project: Grant Proposals for the Digital Age‎ - Page 68

by Julia M. Jacobsen, Jan Fay Kress, Jane Colburn Belcher - Education - 2008 - 157 pages

... more inquiry Already noted this on 2 other forms . . . math manipulations in
general and hands on equations Workshops are wonderful Electricity Inquiry ...

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Developing math talent: a guide for educating gifted and advanced learners ...‎

by Susan Goodsell Assouline, Ann Lupkowski-Shoplik - Education - 2005 - 387 pages

So far that year, the students had been studying “Hands-On Equations” (an
algebra program for elementary students), which Arthur enjoyed very much. ...

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The complete home learning sourcebook: the essential resource guide for ...‎ - Page 173

by Rebecca Rupp - Education - 1998 - 865 pages

... Hands-On Equations This innovative math program, developed by ex- teacher
Henry ... and a laminated balance sheet, $34.95 Hands-On Equations ...

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Purposeful Co-Teaching: Real Cases and Effective Strategies‎ - Page 49

by Greg Conderman, Conderman,bresnahan,pedersen, Val Bresnahan, Theresa Pedersen - Education - 2008 - 176 pages

... 2004), Discovering Algebra: An Investigative Approach (Murdock, Kamischke, &
Kamischke, 2002), Hands-On Algebra (Thompson, 1998), Hands-On Equations® ...

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The development of arithmetic concepts and skills: constructing adaptive ...‎ - Page 186

by Arthur J. Baroody, Ann Dowker - Education - 2003 - 494 pages

Hands-on equations. ...

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Equations: Webster’s Quotations, Facts and Phrases‎ - Page 64

by Icon Group International, Inc. - Reference - 2008 - 487 pages

Author of "The hands-on equations learning system (kit). ...

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Expert Approaches to Support Gifted Learners: Professional Perspectives ...‎ - Page 285

by Margaret Wayne Gosfield, California Association for the Gifted - Education - 2008 - 306 pages

... Hands-on Equations, Mortenson Math, Math-U-See, and more. Maybe If We Ignore
It, They'll Outgrow It! Preferred learning styles don't affect just ...

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Perspectives on Latinos‎ - Page 82

by Luis Ortiz-Franco, Norma G. Hernandez, Yolanda De la Cruz - Education - 1999 - 168 pages

... Who Had Seen and Used Various Types of Manipulatives Type of Manipulative
Percent Algebra tiles 26.8 Fraction bar 51.9 Hands-On Equations® 41.4 Geometry
...

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Kits, games, and manipulatives for the elementary school classroom: a source ...‎ - Page 195

by Andrea C. Hoffman, Ann M. Glannon - Education - 1993 - 605 pages

... decimal numbers from tenths tbrough thousandths. Includes gameboards,
decimal cards, decimal pieces, and markers. 230-O34 TITLE: Hands On Equations*
...

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Igniting Creativity in Gifted Learners, K-6: Strategies for Every Teacher‎ - Page 222

by Joan Franklin Smutny, Sarah von Fremd - Education - 2008 - 344 pages

(The kit Hands- On-Equations uses an excellent approach for teaching this topic.
) Creative Constructions Student-designed structures made from stacks of ...

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Home learning year by year: how to design a homeschool curriculum from ...‎

by Rebecca Rupp - Education - 2000 - 415 pages

Page 191

HANDS-ON EQUATIONS A hands-on progam using simple manipulatives (pawns and
number cubes) to teach algebraic concepts to kids in grades 3-8. ...

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Guide to math materials: resources to support the NCTM standards‎ - Page 19

by Phyllis Jean Perry - Education - 1997 - 127 pages

Activity suggestions for groups of four promote cooperative, logical thinking.
Uses maps, science, and mapping skills. ** Hands-on Equations. Allentown, Pa.
...

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It Happened in Glacier National Park‎

by Vince Moravek - History - 2005 - 128 pages

Page 78

The mechanical challenges of technical climbing were hands-on equations crying
out for a solution. On one of their trips, Mark and his father had ...

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The Kid's Address Book: Over 3,000 Addresses of Celebrities, Athletes ...‎

by Michael Levine - Biography & Autobiography - 1997 - 304 pages

Page 191

... DC 20004 William R. Fry, Executive Director Oldest and largest organization
of Americans for legal reform Hands-On Equations National Media Coordinator ...

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The Elementary Math Teacher's Book of Lists: With Ready-to-use Patterns and ...‎ - Page 20

by Sonia M. Helton, Stephen J. Micklo - Education - 1997 - 398 pages

... Grades 1-8 Great Source 95 Hayden Avenue Lexington, MA 02173 1-617-860-1777
Grades K-12 Hands-On Equations ...

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Programs focused on improving academic achievement, producing quality ...‎ - Page 63

by United States. Congress. House. Committee on Education and the Workforce. Subcommittee on Early Childhood, Youth, and Families - Education - 2000 - 78 pages

... development and training in the areas of Hands on Equations and Everyday
Counts Calendar Math, as well as training in a new physical science curriculum.
...

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The federal role in K-12 mathematics reform: joint hearing before the ...‎ - Page 181

by United States. Congress. House. Committee on Education and the Workforce. Subcommittee on Early Childhood, Youth, and Families, United States. Congress. House. Committee on Education and the Workforce. Subcommittee on Postsecondary Education, Training, and Life-long Learning - Mathematics - 2000 - 169 pages

... full implementation of Hands-On Equations and the Wil- liam A Mary Reading/
Language Arts program; some exciting elementary school curriculum initiatives
...

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Official gazette of the United States Patent and Trademark Office‎ - Page 45

by United States. Patent and Trademark Office - Law - 1987

HANDS-ON EQUATIONS NO CLAIM IS MADE TO THE EXCLUSIVE RIGHT TO USE "EQUATIONS",
APART FROM THE MARK AS SHOWN. FOR TEACHING APPARATUS, NAMELY CUBES AND PAWNS,
...

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The Mislabeled Child: How Understanding Your Child's Unique Learning Style ...‎

by Brock Eide, Fernette Eide - Family & Relationships - 2007 - 528 pages

Page 489

... (Hands On Equations: This is a simple, inexpensive, yet useful manipulative
program to help children "get the idea" behind math calculations and ...

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Uncovering student thinking in mathematics: 25 formative assessment probes‎

by Cheryl M. Rose, Leslie Minton, Carolyn Arline - Education - 2006 - 181 pages

Page 175

Hands-on equations. Retrieved December 31, 2005, ...

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