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TitleNon-routine counting problems, Clip 2 of 8: Candy hearts interview with Jeff

PublisherNew Brunswick, NJ: Robert B. Davis Institute for Learning, 1990-02-26, c1990-02-26

Persistent URLhttps://doi.org/doi:10.7282/T3W66NF6

DescriptionIn the second of 8 clips with second grade students, researcher Amy Martino interviews Jeff about how he and his group, which had included Stephanie and Brian, approached the candy heart problems in their classroom session several days earlier. Jeff revisits his earlier solution, noting first that he had counted the bottom layer and found it to be 12, then states that they had "plussed" that number for the five layers and the total number would be 60. When questioned about the second problem, he said that each child would get 20 candies, basing this answer on his observation that there were three children in each group and that the teacher could join the one group that had only two children. When Martino asks the first extension problem, Jeff quickly says 72. For the second extension problem, Jeff is quiet for a bit and then responds 24, which he explains as adding 6 and 6 for 12 and then adding a second set of 12. When Martino calls Jeff's attention to the answer of 22 candies for each person that he had recorded on his paper, Jeff responds that the group had decided not to include the teacher and to distribute the 20 extra pieces among the children. He states that the group concluded that the result would be 22 pieces per child without further explanation. (Stephanie, in Clip 3 of this series, describes distributing the extra candies to the children. Although the original video of the classroom session has been lost, our notes indicate that there were 20 children in the class, six groups of 3 and one group of two, which raises questions about how there could be 2 extra candies for each child.)

First Candy Heart Problem Statement (on yellow paper)

This is a problem about a jar of candy hearts.

Each layer of candy in the jar has the same number

of pieces. Can you figure out how many candy

pieces are in the jar without opening it?

First, discuss this problem with the people in your group.

Next, explain how you solved the problem on this page.

You may draw pictures to help you explain your answer.

Second Candy Heart Problem Statement (on pink paper)

Our jar has _______pieces of candy.

All the jars have the same number of candy hearts.

Imagine that we collect all the jars of candy

and decide to share all the candy hearts.

Each person in the room has to get the same number

of candy hearts. Figure out how many candy hearts

Each person would get without opening the jars.

Explain how you solved the problem on this page.

You may draw pictures to help explain your answer.

First Candy Heart Problem Extension

Suppose we added another layer to the candy jar

with the same number of candy pieces as the other layers.

How many candy pieces would be in the jar?

Second Candy Bar Problem Extension

Imagine another candy jar with four layers.

Each layer has 6 candy pieces. How many candy pieces would be in this jar?

First Candy Heart Problem Statement (on yellow paper)

This is a problem about a jar of candy hearts.

Each layer of candy in the jar has the same number

of pieces. Can you figure out how many candy

pieces are in the jar without opening it?

First, discuss this problem with the people in your group.

Next, explain how you solved the problem on this page.

You may draw pictures to help you explain your answer.

Second Candy Heart Problem Statement (on pink paper)

Our jar has _______pieces of candy.

All the jars have the same number of candy hearts.

Imagine that we collect all the jars of candy

and decide to share all the candy hearts.

Each person in the room has to get the same number

of candy hearts. Figure out how many candy hearts

Each person would get without opening the jars.

Explain how you solved the problem on this page.

You may draw pictures to help explain your answer.

First Candy Heart Problem Extension

Suppose we added another layer to the candy jar

with the same number of candy pieces as the other layers.

How many candy pieces would be in the jar?

Second Candy Bar Problem Extension

Imagine another candy jar with four layers.

Each layer has 6 candy pieces. How many candy pieces would be in this jar?

Math ToolLayered candy jar

Math StrandArithmetic

Math ProblemCandy heart problem

NCTM Grade RangePreK-2

NCTM Content StandardNumber and operations

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

Forms of Reasoning, Strategies and HeuristicsCounting, Direct reasoning

Grade Level2

Student ParticipantsJeff (student)

MediatorsMartino, Amy Marie (Researcher)

SettingClassroom

Student GenderMale

Student EthnicityWhite

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 Captured1990-02-26

Local IdentifierB55-ARTH-CH-CLIP001

Source

__Title__: B55, Candy hearts interviews, Grade 2, February 26, 1990, raw footage.

__Identifier__: B55-19900226-KNWH-SV-CLASS-GR2-ARTH-CH-RAW