Books Mentioning Hands-On Equations

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 ... Limited preview - About this book - Add to my library

The Hands-On Equations Learning System‎ by Henry Borenson - Mathematics - 1994 - 66 pages No preview available - About this book - Add to my library - More editions

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... No preview available - About this book - Add to my library - More editions

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. ... Snippet view - About this book - Add to my library - More editions

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. ... Limited preview - About this book - Add to my library - More editions

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. ... Limited preview - About this book - Add to my library - More editions

Educators' Opinions of the Product Hands-on-equations TMlearning System‎ by Nancy C Ray - 2002 No preview available - About this book - Add to my library

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." No preview available - About this book - In my library (Remove)

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. No preview available - About this book - Add to my library

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 ... Snippet view - About this book - Add to my library - More editions

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. ... Limited preview - About this book - Add to my library

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 ... Limited preview - About this book - Add to my library - More editions

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. ... Limited preview - About this book - Add to my library - More editions

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 ... Snippet view - About this book - Add to my library

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® ... Limited preview - About this book - Add to my library - More editions

The development of arithmetic concepts and skills: constructing adaptive ...‎ - Page 186 by Arthur J. Baroody, Ann Dowker - Education - 2003 - 494 pages Hands-on equations. ... Limited preview - About this book - Add to my library - More editions

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). ... Limited preview - About this book - Add to my library

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 ... Limited preview - About this book - Add to my library - More editions

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 ... Snippet view - About this book - Add to my library

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* ... Limited preview - About this book - Add to my library

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 ... Limited preview - About this book - Add to my library - More editions

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. ... No preview available - About this book - Add to my library - More editions

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. ... Limited preview - About this book - Add to my library - More editions

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 ... No preview available - About this book - Add to my library - More editions

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 ... No preview available - About this book - Add to my library

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 ... Snippet view - About this book - Add to my library

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. ... Snippet view - About this book - Add to my library - More editions

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 ... Snippet view - About this book - Add to my library - More editions

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, ... Snippet view - About this book - Add to my library - More editions

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 ... No preview available - About this book - Add to my library

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, ... No preview available - About this book - Add to my library - More editions

Fostering children's mathematical power: an investigative approach to K-8 ...‎ by Arthur J. Baroody, Ronald T. Coslick - Education - 1998 - 632 pages [ Sorry, this page's content is restricted ] Limited preview - About this book - Add to my library

IDRA newsletter‎ by Intercultural Development Research Association (Tex.) - Education, Bilingual - 1994 [ Sorry, this page's content is restricted ] Snippet view - About this book - Add to my library - More editions

Developing Mathematical Talent: A Guide for Challenging and Educating Gifted ...‎ by Ann Lupkowski-Shoplik - Education - 2003 - 387 pages [ Sorry, this page's content is restricted ] Limited preview - About this book - Add to my library

Visual-Spatial Learners: Differentiation Strategies for Creating a ...‎ by Alexandra Shires Golon - Education - 2008 - 169 pages [ Sorry, this page's content is restricted ] Limited preview - About this book - Add to my library

Upside-down brilliance: the visual-spatial learner‎ by Linda Kreger Silverman - Psychology - 2002 - 400 pages [ Sorry, this page's content is restricted ] Snippet view - About this book - Add to my library

The Homeschooling Book of Answers: The 88 Most Important Questions Answered ...‎ by Linda Dobson - Education - 1998 - 350 pages [ Sorry, this page's content is restricted ] Snippet view - About this book - Add to my library

9th Grade Algebra I vs. 4th Grade Hands-On Equations

How do your Algebra I students compare with 4th – 8th grade Hands-On Equations students on these questions?


2x = 6; x+ 3 = 10; 2x + 1 = 7; 3x = x + 2; 4x + 3 = 3x + 7; 2(2x + 1) = 2x + 10


Would you like to find out?

Students in grades 4 to 8 who have had the first seven lessons of Hands-On Equations score above 80% on a post-test consisting of the above questions. Wouldn’t you like to know if the students in your Algebra 1 classes -- near the end of the academic year -- can do at least as well on these basic equations? If so, we invite you to participate in this preliminary study.

We can provide you with the instruction for administering the survey, the Equation Survey, Teacher Questionnaire and Summary Form. You may ask the teachers to return the Summary Form and Questionnaire to you, or they may submit them directly to us at the address noted on the document. We will analyze the results and submit a report back to each teacher.


Why would you wish to conduct this study?


The ability to work with simple algebraic linear equations is crucial to success in Algebra I. Knuth, Alibali, et al (2008) quote Carpenter, Franke, and Levi (2003) saying that “a limited conception of what the equal sign means is one of the major stumbling blocks in learning algebra. Virtually all manipulations on equations require understanding that the equal sign represents a relation.” If your Algebra I students cannot solve the vary basic equations noted above, is it any wonder that they are having difficulty with the subject?


We invite you to participate in this preliminary study to give us initial feedback on how Algebra I students compare to younger students who have had Level I of Hands-On Equations. Your assistance is appreciated.


Sincerely,



Henry Borenson, Ed.D.



References

Carpenter, Thomas, Megan Franke, and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in the Elementary School. Portsmouth, NH: Heinemann 2003

Knuth, Eric J, Martha W. Alibali, Shanta Hattikudur, Nicole M. McNeil, and Ana C. Stephens. “The Importance of Equal Sign Understanding in the Middle Grades.” Mathematics Teaching in the Middle School. Vol. 13, No. 9, May 2008:514-519


HOW TO PARTICIPATE:

Administer the survey to one or more of your Algebra 1 classes. Complete the teacher questionnaire and summary form (no student names please), submit it to us, and as a token of our appreciation we will provide you with a complimentary copy of the Hands-On Equations Verbal Problems Book containing more than 350 verbal problems, including consecutive number, age and distance problems. If you wish to participate, mail your inquire to info@borenson.com and we will send the survey documents to you. Thank you.

Hands-On Equations Workshops- Instructor Letter

Hands-On Equations Instructor Kendra Jensen just completed conducting a Day1 and Day2 workshop in Hot Springs, AR.

The comments below, submitted by the instructor, are typical of the high value that workshop participants place on this training.

Hot Springs, AR

Day 1

Tuesday, April 21, 2009

Thank you for sending me to Arkansas! I learned about it's geography by driving into Hot Springs on a winding, mountainous highway for the last 2 hours of the drive! Beautiful scenery, challenging drive. All was fine.

Participants:

Our participants readily volunteered. Their teaching experience ranged from 10 years to 28 years and they were just as eager to learn as an educator with less experience. Great group.

From Bryant, Carol taught 7th grade; Heather 8th; Jaime was a special ed teacher who teaches with them. Elisabeth was also a special ed teacher.

Our two participants not from Bryant were Shannon who teaches K-6 gifted and Kittena who is a K-12 Math Coordinator.

Day 1 teacher quotes and conversations:

Carol wanted to know early on if there were worksheets and teacher manuals. Heather was excited about the smartboard application.

"This is so cool ... When I saw the demonstration at my school, it was too fast."

Lesson 7: "I've always done the numbers first. I guess you get stuck in your ways. I like that HOE teaches the removal of pawns first." Heather repeated this when asked what the highlight of the morning session was for her.

Shannon knows of a school who uses HOE and has Level l taught in 3rd grade, Level ll in 4th and Level lll in 5th grade. They like it.

Shannon especially liked the fact that we're reaching so many learning styles with this approach!

Kittena loved both days! "I have a monthly math focus for various grades. I demonstrate or model teach on that focus topic. I'll use HOE for this! I'm going to buy a kit for each school (or teacher?)." Kittena took such detailed notes because she plans to present this to the many teachers she helps. I told her to enquire about overheads from our office.

Day 2

Wednesday, April 22, 2009

Additional Participants:

For Day 2, Michelle joined us and teaches 6,7, and 8th grades.

Corrie and Laurie were 3rd and 4th grade teachers from the same school. They said they registered for the half day. They were a little concerned about the level of math necessary but were encouraged to find their 3rd and 4th graders could do many of our verbal problems.

Day 2 teacher quotes and conversations:

The Arkansas Benchmark test was mentioned several times. "Oh, if our kids had HOE before that test, they would have aced it!"

Kittena, the Math Coordinator, expressed a concern about open response questions on the Benchmark. There are two people grading a student's answer to the open response. Each grader has 4 points to give for a total of 8 points. "How would individual graders view the pictoral solution. Is there enough there to earn a full 4 points?" Heather, an 8th grade teacher responded enthusiastically, "The student has to solve and then verify the answer. For word problems, there's also the full sentence answer to show understanding. I definitely think there's enough here to earn each grader's 4 points."

When asked what they liked most about this approach, the participants replied:

"I like setting game pieces on the scale phrase by phrase through the word problem." It makes sense.

"This makes fractions more meaninful."

"I love the fact there's so much going on here. There are so many topics buried in this program!"

The highlight of Day 2 for me personally was bringing volunteers up to demonstrate the travelling scooters and trains. These participants loved it and fully participated. I heard several "This is good!" "They'll understand this." - type comments.

Observations:

I used the Effective Learning transparency #13 from Day 1 to help in the review for Day 2.

These participants noticed two minor discrepancies on the transparencies. On transparency # 32, the verbal problem is actually number 6 not 5 on VPB page 42. and on transparency #37, the verbal problem is number 10 not 9 on VPB page 57.

The Velda Rose Hotel was a grand hotel in its day. My room was nice. The meeting room showed signs of age ... with worn trim and scratched doors, even a broken window down the hall from it. The hotel smelled of smoke when you walked in the front door. I asked Kittena Bell, a participant who stayed overnight there, what she thought just in case I was being too picky ... maybe it was a local attraction. She told me she actually called a friend to come stay with her because she wouldn't stay in such a place by herself. She also said "it wasn't a positive draw for such an awesome workshop."

Respectfully,

Kendra Jensen

Verbal Problems Blackline Masters

for Level I


VP-BM1 $25


This publication of blackline masters contains more than 200 Level I verbal problems (taken from the Hands-On Equations Verbal Problems Book), one per page to make it easy fo the teacher to use with an image projector or to copy and distribute to the class. An example is shown below:


VPB Pg. 10/Ex. 28; Solution Pg. 20/Ex. 28

28. Bill had two water jugs that each held 7 gallons. Tom had one jug that held 2 gallons and three others that held equal amounts. If all the jugs together held 28 gallons, how much did each of the three equal jugs hold?



VPB Pg. 25/Ex. 5; Solution Pg. 30/Ex. 5

5. Jamie guessed a number. Rob guessed a number that was double the sum of 3 and the number guessed by Jamie. If the sum of the numbers guessed by Jamie and Rob is 18, what are the numbers?

HANDS-ON EQUATIONS VERBAL PROBLEMS BOOK

The examples below are taken from the Hands-On Equations Verbal Problems Book. This book contains more than 300 verbal problems including number, consecutive number, age and distance problems for all three Levels of Hands-On Equations. A sampling of the types of problems presented in the book is shown below. Within each section of the book the problems are graduated in increasing order of difficulty. This makes the book a valuable resource for teachers in grades 4 to 6, as well as for teachers of pre-algebra and Algebra I students. (The number in parenthesis indicates where the problem can be found in the verbal problems book.)

Level I

1. Kathy's plant grew the same amount in January and February. In March, it grew 3 inches. If the plant grew a total of 13 inches during these three months, how much did it grow during each of the other months? (Page 8/7)

2. Heather can buy 4 pizzas for the same price as 2 pizzas and 8 one-dollar drinks. How much does each pizza cost? (Page 9/16)

3. Celeste is 12 years older than Rosa. In four years, she will be twice as old as Rosa will be then. How old is each now? (Page 58/17)

4. Charlene has a container 1/2 filled with pennies. She realizes that if she adds 12 pennies to the container, it will then be 2/3 filled. How many pennies does the container hold? (Page 77/18)

5. The average speed of an express train is 14 miles per hour more than 1/3 the speed of a freight train. In two hours the express train travels the same distance as the freight train in three hours. Find the average speed of each train. (Page 102/18)

NEW: HANDS-ON EQUATIONS VERBAL PROBLEMS BLACKLINE MASTERS FOR LEVEL I
More than 200 Level I verbal problems taken from the verbal problems book, one per page (VB-BM1.......................................................................................................$25)

Level II

1. The sum of two numbers is 10. Twice the first, increased by the second number, is 10. Find the numbers. (Page 27/18)

2. Jim has two lists of three consecutive even numbers. The sum of the first number on each list is 10. If twice the second number on the first list has the same value as the first number on the second list, what are the two set of consecutive even numbers? (Page 43/18)

3. If Jim's age is added to Sandra's age, the sum is 18. If twice Jim's age is subtracted from Sandra's age, the difference is 3. How old is each? (Page 68/22)

4. Charlotte has a total of 18 coins consisting of dimes and nickels. If the number of nickels is 12 more than the number of dimes, how many of each coin does she have? (Page 92/28)

5. Bobby can paddle a canoe at 3 miles per hour. For 1 hour, Bobby paddles with the current and travels 4 miles further then when paddling back against the current for one hour. What is the canoe's speed when it travels with the current? (Page 104/29)


Level III

1. When a number decreased by 4 is doubled, the result is the same as the number increased by 6. Find the number. (Page 28/25)

2. Charlotte has two lists of consecutive odd numbers. The sum of the first number on each list is 10. When the 4th number on the 1st list is doubled and then subtracted from the first number on the second list, the result is the same as the second number from the firs list, decreased by 14. Find the two sets of numbers. (Page 44/28)

3. Ten years ago, Marlene was 6 years older than 1/3rd of her present age. How old is she now. (Page 60/30)

4. Two-thirds of a collection of 90 coins consists of nickels. Of the remaining coins, the number of dimes is 10 more than 1/3rd the number of quarters. How many of each type of coin is in the collection? (Page 78/24)

5. A private plane flying for two hours meets a headwind that reduces its speed by 20 miles per hour. If it took the plane a total of 5 hours to travel 440 miles, find the speed of the plane prior to meeting the headwind. (Page 106/40)

Press Release: Hands-On Equations in Africa & Asia

Hands-On Equations to be implemented in 1,000 classrooms in Africa and Asia

Contact: Henry Borenson, henry@borenson.com, 800-993-6284,
Or Patti Davis, patriciadavis@opportunityeducation.org, 402-660-2174

October 28, 2008--Borenson and Associates, Inc., an Allentown, PA firm known for its innovative algebra teaching system that enhances learning performance in U.S. schools, has been selected to provide its program to more than 1,000 classrooms in Asia and Africa.

Under the agreement, Hands-On Equations®, which is the name of the proprietary algebra program developed by Henry Borenson, will be implemented in 5th, 6th and 7th grade classrooms in Uganda, Tanzania, South Africa, Ghana, Sierra Leone, India, Sri Lanka and Nepal by Opportunity Education, a charitable foundation that provides educational tools for children in developing countries around the world.

“We are delighted to be chosen to provide our program to these students in developing nations,” said Borenson. “I’m confident the teachers in these classrooms will be very satisfied with the success they will see in their students.”

Borenson’s algebra teaching system uses manipulatives – similar to game pieces – to help students visualize an equation. Students use the manipulatives to make chess-like moves to balance an equation. “The program helps demystify the language of algebra and helps take an abstract concept and make it an intuitive process,” he said.

The Hands-On Equations® program has been introduced to over 25,000 teachers in the U.S. and is used in schools across the nation.

Opportunity Education chose to distribute Hands-On Equations® because the organization’s director of education, Patti Davis, had used the program as a classroom elementary school teacher, and had seen the improvement in her students’ abilities to learn algebraic principles and retain the skill set.

“I recommended Hands-On Equations® because I had had personal success using it in my classroom,” said Davis. “We chose the program because it is the easiest to understand, has the most applicability in classrooms in other parts of the world, and produces results.”

Providing the learning program to schools in developing nations supports the organization’s overall mission to supply curriculum and materials to classrooms in order to give children in developing countries the advantages of a U.S. education. “Providing the program and the materials the teacher needs to use to teach the program is imperative to help these countries meet their educational standards,” says Davis.

Opportunity Education was founded by Joe Ricketts, founder of TD Ameritrade. It is a charitable foundation that provides educational tools for children in developing countries around the world. For more information, go to www.opportunityeducation.org.

Borenson and Associates was founded by Henry Borenson in 1986. Borenson had taught honors mathematics classes at the Stuyvesant High School in New York City. For more information, go to www.borenson.com.

Hands-On Equations Pre and Post-Tests for Level I

Complete instructions for administering pre- and post-tests for Level I are now available online. These instructions include a Summary Form for the teacher to record student scores and compare class results on each test, as well as class performance on each question.

On the pre-test, especially with students in grades 3 - 5, the scores are expected to be very low since these concepts and examples are not normally presented at these grades. The teacher should not be too surprised by low pre-test scores. If the teacher has gone through the training and implements the program as designed, he/she will see significant gains on the Lesson #6 post-test. This improvement is expected to be maintained as the students move away from using the game pieces to the pictorial notation in Lesson #7.

Pre-Test- 15 minutes

Post-Test After Lesson #6

(Students may use the game pieces on this post-test- time limit: 15 minutes)

Post-Test after Lesson #7
(Students do not use the game pieces-- just the pictorial notation)
Time Limit: 15 minutes

http://www.borenson.com/LevelIPrePostTestsOct08.pdf