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TitleEarly algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 5 of 6: James modeling the Museum problem with rods

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 2005-12-15, c2005-12-15

Persistent URLhttps://doi.org/doi:10.7282/T3HQ3WWJ

DescriptionIn the fifth of six clips from an after-school enrichment session in an urban middle school, James, a 7th grade boy completing a unit about linear functions, has finished his written solution for the Museum problem. When researcher Markus Hahkioniemi asks James if he could use the Cuisenaire rods to model this problem, James begins by building a "ladder" with two rungs and counts the rods as he had for the earlier Ladder problem. He soon discards this model and instead indicates that each rod in his resulting group of eight should represent a craft piece and a value of three dollars. He concludes that the value of the eight rods or craft pieces would be $24 and that there would be a need for two more dollars for the entrance fee. He selects two additional rods, assigning each a value of one dollar, but keeps them separate from the others. Regardless of the questions from the researcher, James tenaciously holds to his interpretation that the different groups of rods represent different things and therefore have different values.

The worksheet wording for the Museum Problem:

The Museum Problem - Version One

A museum gift shop is having a craft sale. The entrance fee is $2. Once inside, there is

a special discount table where each craft piece costs $3.

How could you represent the total amount that you would spend if you were to buy any number of craft pieces at the discount price?

The worksheet wording for the Ladder Problem:

A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. Build a rod model to represent a 3-rung ladder.

How many rods did you use? How could you represent the number of rods needed if you were to build a ladder with any number of rungs?

The questions as posed to James:

How might you use the Cuisenaire rods to model the Museum problem?

What does each rod represent?

Is there a way that all of the rods can have the same value?

The worksheet wording for the Museum Problem:

The Museum Problem - Version One

A museum gift shop is having a craft sale. The entrance fee is $2. Once inside, there is

a special discount table where each craft piece costs $3.

How could you represent the total amount that you would spend if you were to buy any number of craft pieces at the discount price?

The worksheet wording for the Ladder Problem:

A company makes ladders of different heights, from very short ones to very tall ones. The shortest ladder has only one rung, and looks like this (we could build a model of it with 5 light green Cuisenaire rods.) A two-rung ladder could be modeled using 8 light green rods, and looks like this. Build a rod model to represent a 3-rung ladder.

How many rods did you use? How could you represent the number of rods needed if you were to build a ladder with any number of rungs?

The questions as posed to James:

How might you use the Cuisenaire rods to model the Museum problem?

What does each rod represent?

Is there a way that all of the rods can have the same value?

Math ToolCuisenaire rods, Color markers

Math StrandAlgebra

Math ProblemMuseum problem

NCTM Grade Range6-8

NCTM Content StandardAlgebra

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

Forms of Reasoning, Strategies and HeuristicsDirect reasoning, Multiplicative reasoning, Generalizing

Grade Level7

Student ParticipantsJames T. (student)

MediatorsHähkiöniemi, Markus (Researcher)

SettingInformal learning

Student GenderMale

Student EthnicityBlack

Camera ViewsStudent 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 Captured2005-12-15

Local IdentifierB19B20-ALG-VAR-CLIP005

Related Publication

__Type__: Related publication

__Label__: Ed.D. dissertation references the video footage that includes Early algebra, investigating linear functions, series 6 of 7, Museum problem, Clip 5 of 6: James modeling the Museum problem with rods

__Date__: 2009

__Author__: Baldev, Prashant V. (Rutgers, the State University of New Jersey)

__Name__: Urban, seventh-grade students building early algegra ideas in an informal after school program

__Reference__: QA.B175 2009

Source

__Title__: B19, Early algebra, investigating linear functions, series 6 of 7, Museum problem (student view), Grade 7, December 15, 2005, raw footage.

__Identifier__: B19-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW

Source

__Title__: B20, Early algebra, investigating linear functions, series 6 of 7, Museum problem (student view), Grade 7, December 15, 2005, raw footage.

__Identifier__: B20-20051215-PFLD-SV-IFML-GR7-ALG-VAR-RAW