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Mathematics Governor’s Institute 2003

Problem-in-a-Bag Project

 

(Download as Microsoft Word document: Playground Placement)

 

Title of Project:                                                       Grade Level:  3

Playground Placement

 

Team Members:                                                      Concepts Used:    

Amy Barshinger                                                        area

Vicky Edinger                                                            spacial relations

Susan Kappenstein                                                  factors

Danielle Retallack                                                     multiplication arrays

Colleen Wellstein

 

PA Standards Addressed:

2.1.3C  Represent equivalent forms of the same number through the use of concrete objects, drawings, word names and symbols

 

2.2.3C  Demonstrate the concept of multiplication as repeated addition and arrays

 

2.3.3F  Use concrete objects to determine area and perimeter

 

2.3.3G  Estimate and verify measurements

 

2.5.3A  Use appropriate problem-solving strategies

 

2.5.3B  Determine when sufficient information is present to solve a problem and explain how to solve a problem

 

2.5.3C  Select and use appropriate method, materials and strategy to solve problems, including mental mathematics, paper and pencil and concrete objects

 

2.8.3A  Recognize, describe, extend, create, and replicate a variety of patterns including attribute, activity, number and geometric patterns

 

2.8.3B  Use concrete objects and symbols to model the concepts of variables, expressions, equations and inequalities

 

2.9.3I  Predict how shapes can be changed by combining or dividing them

 

NCTM Standards Addressed:

  1. Understand the meanings of operations and how they relate to each other
  2. Use visualization, spacial reasoning and geometric modeling to solve problems

Introduction/Applications:

The old school parking lot is going to be removed and the space will be turned into a playground.  Students will show how to fit six playground items into the space provided.  They will determine if there are unused units. 

 

Question:

Using their knowledge of factors, is there more than one way for students to create the rectangles and arrange them in a given space? 

 

Model:

By completing two different playgrounds, students will demonstrate a conceptual understanding of multiplication. 

 

Resources & Materials: 

 

Procedures:

  1. The teacher will distribute enough student materials to complete two playgrounds.  Suggestion:  complete playgrounds one at a time. 
  2. Students will create different playgrounds including the following six items in each: 

Playground Equipment/Space         Total Units                Color

Sliding Board                                          6                                  Red

Swing                                                       8                                  Yellow

Merry-go-round                                        10                                Blue

Jungle Gym                                              12                                Orange

Basketball Court                                     16                                Brown

Kickball Field                                           20                                Purple

 

  1. Playgrounds may not be identical.  Requirement:  at least one item (ex. sliding board) must be shaped differently on each playground. 
  2. Students must determine the appropriate shape of each rectangle based on whether or not all six pieces fit inside the playground.  They may need to try a variety of rectangular shapes for any/all items.  The intention is, for example, that students will discover that the six-unit sliding board can be created using a 1x6 or 2x3 rectangle.  (Model as needed.)  Once the rectangles are cut out, students must label and color appropriately.  Students should arrange rectangles on playground - making sure they all fit - prior to gluing them in place. 

 

Answers/Rubric:

Advanced – 5 

All pieces of both playgrounds are correctly formed, labeled and colored.  All pieces are placed on the two playgrounds correctly with no overlapping.  Eight units remain uncovered. 

 

Satisfactory – 4 

All pieces of both playgrounds are correctly formed.  All pieces are placed on the two playgrounds correctly with no overlapping.  Eight units remain uncovered.  Minor errors in coloring and/or labeling occur. 

 

Almost Satisfactory – 3

All pieces of one playground are correctly formed and placed with no overlapping.  Minor errors in coloring and/or labeling occur.  Attempt at second playground is incorrect or incomplete. 

 

Partial Understanding – 2

Most pieces of one playground are correctly formed with 1-2 pieces not formed correctly.  Overlaps occur.  No attempt at second playground. 

 

Minimal Understanding – 1

Attempt is made to solve one problem.  Many errors occur. 

 

Incorrect – 0

Nothing correct.  Blank or off-task response. 

 

Accommodations/Adaptations: 

ESL:  Students will see how to create a rectangle through teacher modeling.  Students may be successful with partners to help them follow directions. 

 

Special Education:  Depending on individual needs, partners may help these students understand and follow directions.  Rectangles may be manipulated using magnets and a cookie sheet. 

 

Enrichment:  These students may be asked to find the area and perimeter of each rectangle and the entire playground.  A more detailed explanation can be expected from these students. 

 

Name ________________________________             Date  ________________

 

Playground Placement

 

Directions

Part A:  Create a playground including each of the six items listed below.  All items must be rectangles.  You may arrange them in any way as long as they fit in the playground without overlapping.  Label and color-code the items according to the chart. 

 

*BE CAREFUL:  2x10 is not the only way to make 20

 

Playground Equipment/Space   Total Units                Color

Sliding Board                                    6                                  Red

Swing                                                 8                                  Yellow

Merry-go-round                                  10                                Blue

Jungle Gym                                        12                                Orange

Basketball Court                               16                                Brown

Kickball Field                                     20                                Purple

 

Question:  Is there any extra space?  __________________________________

 

If so, how many units are left?  _______________________________________

 

Part B:  Now, create a different playground.  You must change the shape of at least one rectangle. 

 

Question:  Is there any extra space?  __________________________________

 

If so, how many units are left?  _______________________________________

 

Part C:  Why were you able to create two different playgrounds? 

 

________________________________________________________________

 

________________________________________________________________

 

________________________________________________________________

 

________________________________________________________________

 

________________________________________________________________

 

________________________________________________________________

Answers/Rubric:

Advanced – 5 

All pieces of both playgrounds are correctly formed, labeled and colored.  All pieces are placed on the two playgrounds correctly with no overlapping.  Eight units remain uncovered. 

 

Satisfactory – 4 

All pieces of both playgrounds are correctly formed.  All pieces are placed on the two playgrounds correctly with no overlapping.  Eight units remain uncovered.  Minor errors in coloring and/or labeling occur. 

 

Almost Satisfactory – 3

All pieces of one playground are correctly formed and placed with no overlapping.  Minor errors in coloring and/or labeling occur.  Attempt at second playground is incorrect or incomplete. 

 

Partial Understanding – 2

Most pieces of one playground are correctly formed with 1-2 pieces not formed correctly.  Overlaps occur.  No attempt at second playground. 

 

Minimal Understanding – 1

Attempt is made to solve one problem.  Many errors occur. 

 

Incorrect – 0

Nothing correct.  Blank or off-task response. 


Accommodations/Adaptations: 

 

ESL:  Students will see how to create a rectangle through teacher modeling.  Students may be successful with partners to help them follow directions. 

 

Special Education:  Depending on individual needs, partners may help these students understand and follow directions.  Rectangles may be manipulated using magnets and a cookie sheet. 

 

Enrichment:  These students may be asked to find the area and perimeter of each rectangle and the entire playground.  A more detailed explanation can be expected from these students. 


Resources & Materials:

·        1” graph paper (two labeled “playground” and 4 or more per student to cut out playground pieces)

·        colored pencils or crayons

·        glue

·        scissors

·        instructional handout

 

Procedures:

1.    The teacher will distribute enough student materials to complete two playgrounds.  Suggestion:  complete playgrounds one at a time. 

2.    Students will create different playgrounds including the following six items in each: 

 

Playground Equipment/                   Total Units         Color

Space                     

 

Sliding Board                              6                           Red

Swing                                           8                           Yellow

Merry-go-round                           10                        Blue

Jungle Gym                                 12                        Orange

Basketball Court                         16                        Brown

Kickball Field                              20                        Purple

 

3.    Playgrounds may not be identical.  Requirement:  at least one item (ex. sliding board) must be shaped differently on each playground. 

4.    Students must determine the appropriate shape of each rectangle based on whether or not all six pieces fit inside the playground.  They may need to try a variety of rectangular shapes for any/all items.  The intention is, for example, that students will discover that the six-unit sliding board can be created using a 1x6 or 2x3 rectangle.  (Model as needed.)  Once the rectangles are cut out, students must label and color appropriately.  Students should arrange rectangles on playground - making sure they all fit - prior to gluing them in place. 

 

 

 

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