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Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions [video]. Retrieved from https://doi.org/doi:10.7282/T3XS5T98

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TitleEarly algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions
PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, , c1999-09-30
Persistent URLhttps://doi.org/doi:10.7282/T3XS5T98
DescriptionIn the first of eleven clips from the first day of the Early Algebra Ideas sessions, the researcher, Robert B. Davis, introduces ideas about algebraic equations with one variable and truth sets to a class of 6th grade students. Davis begins with the first problem statement printed below to introduce ideas about algebraic sentences or equations with one variable that can be true, false or open. The concept of a variable is introduced by varying the values that can be inserted into a printed ”box” that is a term within the equation. He introduces the idea of a truth set with brackets before demonstrating the mathematical Rule of Substitution, which says that in evaluating any mathematical expression or equation, if a variable appears more than once, for a legal substitution, the same value must be inserted into each “box”. Using the second problem statement below, which has two “boxes” in the equation, Davis asks the students for values to substitute into each “box” in order to create sentences that are legal and false; illegal and false; illegal and true; or legal and true. Observers present included researchers Amy Martino and Alice Alston and Kenilworth mathematics supervisor, Marcia O'Brien.
Problem Statements:
1. True, False or Open?
3 + □ = 5
Is there a number that would make the statement False/True?
Use { } Truth set – rather than “filling in the box and erasing it “.
3. Open sentences with two of the same variable (two “boxes”)
□ + □ = 8
Legal and false? Illegal and false? Illegal and true? Legal and true?
Math ToolColor markers
Math StrandAlgebra
Math ProblemOpen sentence in one variable
NCTM Grade Range6-8
NCTM Content StandardAlgebra
NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation
Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Substituting numbers for variables, Generalizing
Grade Level6
Student ParticipantsBrian (Kenilworth, student), Michael A. (Kenilworth, student), Jeff (student), Robert (student), Matt (student), Romina (student), Stephanie (student), Amy-Lynn (student), Michelle I. (student), Michelle R. (student), Ankur (student), Milin (student)
MediatorsDavis, Robert B. (Robert Benjamin) (Researcher), Maher, Carolyn Alexander (Researcher), Alston, Alice S. (Researcher), Martino, Amy Marie (Researcher), O'Brien, Marcia Joan (Teacher)
CorporateHarding Elementary School (Kenilworth, N.J.)
SettingClassroom
Student GenderMixed
Student EthnicityMixed
Camera ViewsTeacher view, Side view
RightsThe video is protected by copyright. It is available for reviewing and use within the Video Mosaic Collaborative (VMC) portal. Please contact the Robert B. Davis Institute for Learning (RBDIL) for further information about the use of this video.
Date Captured1999-09-30
Local IdentifierA54A55-ALG-PIB-CLIP001
Related Publication
   Type: Related publication
   Label: Ed.D. dissertation references the video footage that includes Early algebra ideas involving one variable, Clip 1 of 11: Open sentences that can be made True or False with Legal or Illegal substitutions.
   Date: 2009
   Author: Spang, Kathleen E. (Rutgers Graduate School of Education)

   Name: Teaching algebra ideas to elementary school children : Robert B. Davis' introduction to early algebra
   Reference: QA.S735 2009
Source
   Title: A54, Early algebra ideas involving one variable (teacher view), Grade 6, September 30, 1993, raw footage.
   Identifier: A54-19930930-KNWH-TV-CLASS-GR6-ALG-PIB-RAW