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

By May 8, 2009July 4th, 2023No Comments

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.


Henry Borenson, Ed.D.


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


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 and we will send the survey documents to you. Thank you.