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TitleEarly algebra ideas involving two variables: Romina and Brian work on Guess My Rule problems 3 and 4

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 1993-10-01, c1993-10-01

Persistent URLhttps://doi.org/doi:10.7282/T3JD4V59

DescriptionThis video comes from a 6th grade class session in which the researcher, Robert B. Davis, introduces algebraic equations with two variables, using a square “box” and a “triangle” as symbols to represent the variables. The objective of the activity is to create a “rule” for each problem on the worksheet, where the rule is the equation for a truth set presented in table form with "box" column as input values and "triangle" column as output values. Tables for problems 3 and 4 appear below. In this clip, the Romina and Brian work as partners. At this point they have moved to problem 3 on their worksheets and express to the researcher that they are progressing well. When comparing rules for problem number three, however, Romina says that she thinks “it” (the y-intercept) is 1. When Brian challenges her conjecture, she works to convince Brian. For the next problem, Romina asserts that the slope for the new linear function rule is “ten.” Romina soon leans over and corrects the rule Brian is writing on his paper. She explains her method for identifying the y-intercept for the function rule: “All you have to do, Brian, is take the first number and add it.” Brian then asks her if the rest of the rule is “blank times four” or “times seven.” Romina describes that she finds the slope by looking for “whatever is between seven and seventeen” – two of the entries in the triangle column. Then Brian writes the correct rule for problem number four as a linear function with a slope of ten and y-intercept seven.

Table for Problem 3:

□ ∆

0 1

1 4

2 7

3 10

Table for Problem 4:

□ ∆

0 7

1 17

2 27

3 37

4 47

5 57

Table for Problem 3:

□ ∆

0 1

1 4

2 7

3 10

Table for Problem 4:

□ ∆

0 7

1 17

2 27

3 37

4 47

5 57

Math ToolWorksheet with problem statements

Math StrandAlgebra

Math ProblemOpen sentence in two variables

NCTM Grade Range6-8

NCTM Process StandardProblem solving, Reasoning and proof, Communication, Connections, Representation

Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Recognizing a pattern

Grade Level6

Student ParticipantsRomina (student)

MediatorsDavis, Robert B. (Researcher)

SettingClassroom

Student GenderFemale

Student EthnicityWhite

Camera ViewsStudent view, Work 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 Captured1993-10-01

Local IdentifierA51A52A53-ALG-GMR-CLIP019

Related Publication

__Type__: Related publication

__Label__: Ed.D. dissertation references the video footage that includes Early algebra ideas involving two variables: Romina and Brian work on Guess My Rule problems 3 and 4

__Date__: 2010

__Author__: Steffero, Maria (Rutgers, the State University of New Jersey)

__Name__: Tracing beliefs and behaviors of a participant in a longitudinal study for the development of mathematical ideas and reasoning [electronic resource] : a case study.

__Reference__: http://hdl.rutgers.edu/1782.2/rucore10001500001.ETD.000052894

Related Publication

__Type__: Related publication

__Label__: Ed.D. dissertation references the video footage that includes Early algebra ideas involving two variables: Romina and Brian work on Guess My Rule problems 3 and 4

__Date__: 2008

__Author__: Giordano, Patricia (Rutgers, the State University of New Jersey)

__Name__: Learning the concept of function: Guess my rule activities with Dr. Robert B. Davis

__Reference__: QA.G497 2008

Source

__Title__: A51, Early algebra ideas involving two variables (student view), Grade 6, October 1, 1993, raw footage.

__Identifier__: A51-19931001-KNWH-SV-CLASS-GR6-ALG-GMR-RAW

Source

__Title__: A52, Early algebra ideas involving two variables (side view), Grade 6, October 1, 1993, raw footage.

__Identifier__: A52-19931001-KNWH-SV-CLASS-GR6-ALG-GMR-RAW

Source

__Title__: A53, Early algebra ideas involving two variables (classroom view), Grade 6, October 1, 1993, raw footage.

__Identifier__: A53-19931001-KNWH-CV-CLASS-GR6-ALG-GMR-RAW