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Mathematics Governor’s Institute 2003

Problem-in-a-Bag Template

 

 

(Download as Microsoft Word document: Halloween Candy)

 

 

 

Title of Project:  Halloween Candy

 

Team Members:  Marge Bittner, Evelyn Jackson, Jerry O’Brien, Debbie Roberts

 

Grade Level and/or Course:  K-3

 

Concept(s) used:

 

Recording data, organizing data, recognizing patterns, classifying objects, number sense, addition computation

 

PA Standard(s) Addressed:

 

            2.1.3.C

            2.1.3.G

            2.2.3.A

            2.5.3.A

            2.5.3.C

            2.6.3.A

            2.8.3.B

            2.8.3.C

            2.8.3.G

 

NCTM Standard(s) Addressed:

 

Understanding numbers, ways of representing numbers, relationships among numbers, and number systems

 

Understand patterns, relations, and functions

 

Represent and analyze mathematical situations and structures using algebraic symbols

 

Using mathematical models to represent and understand quantitative relationships

 

Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them

 

Introduction/Applications:

 

To introduce the activity, the teacher will tell a story about Halloween candy.  A child with a chocolate allergy offers to share his chocolate treats with his teacher.  The child tells the teacher he received eleven pieces of candy while trick-or-treating, but fails to mention how many pieces in his bag are chocolate.

Question:

           

            The teacher then poses this question to the students:

           

            What are all of the possible combinations of chocolate and non-chocolate

candies in the trick-or-treat bag?

 

Model:

 

            Student-developed mathematical model

 

Resources and Materials (estimated cost):

 

Two-sided counters, small manipulatives (Popsicle sticks, cubes, links, etc.), pencil and paper, bags of candy

 

Procedures and Activities:

 

Students are given paper and pencil to record their data.  Various manipulatives are made available for their use.  They are given 10-15 minutes to formulate their answers.  The teacher briefly interviews individuals to assess their problem solving strategies.  The whole group is then brought together to share their conclusions and their strategies.  Through a teacher guided discussion all combinations are discovered and recorded.  Students discuss which strategy was most efficient.  Students are given a piece of candy as a treat to conclude the lesson.

 

Answers/Rubric:

 

            Answers: 0,11; 1,10; 2,9; 3,8; 4,7; 5,6; 6,5; 7,4; 8,3; 9,2; 10,1; 11,0

Rubric:       4 points

> Child lists all 12 correct combinations

> Child presents sequential list

> Child includes headings (chocolate, not chocolate)

> Child has a logical strategy

> Child can explain the strategy

 

                                3 points

> Child lists 8-11 correct combinations

> Child presents mostly sequential list

> Child has a strategy

> Child can explain the strategy

 

                                2 points

                               > Child lists 4-7 correct combinations

                               > Child presents partially sequential list

> Child has a random strategy

 

                              1 point

                               > Child lists 1-3 combinations

 

0 points

> Child lists nothing

 

 

                               

 

Accommodations/Adaptations

 

            ESL:

 

            Pair the student with a buddy

 

            Special Ed:

 

            Use less candy in the original problem

 

            Enrichment:

 

            Use more candy in the original problem

 

            Increase the variables (types of candy)

 

           

 

 

 

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