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Mathematics Governor’s Institute 2003

Problem-in-a-bag Template

 

(Download as Microsoft Word document: Home Sweet Home)

 

Title of Project:                                  Home Sweet Home

Team Members:        Christopher Hoshaw, Laurie Johnson, Sandy Madden, Kathleen Polley

Grade Level and/or Course:             6th grade math

Concept(s) used:                    Finding Area, Measuring, Scale Modeling, Problem Solving, Writing,

PA Standards Addressed:

2.2 Computation and Estimation

            F. Identify the difference between exact value and approximation and determine which is            appropriate for a given situation.

2.3 Measurement and Estimations

            A. Develop formulas and procedures for determining measurement (e.g., area, volume, distance)

            D. Estimate, use and describe measures of distance, rate, perimeter, area, volume, weight, mass, and     angles.

            F. Use scale measurement to interpret maps or drawings.

            G. Create and use scale models.

2.4 Mathematical Reasoning and Connections

            F. Use measurements and statistics to quantify issues (e.g., in family, consumer science situations).

2.5 mathematical Problem Solving and Communication

            A. Invent, select, use, and justify the appropriate methods, materials and strategies to solve a     problem.

            B. Verify and interpret results using precise mathematical language, notation, and representations,           including numerical tables and equations, simple algebraic equations, and formulas, charts, graphs             and diagrams

            C. Justifies strategies and defends approaches used in conclusions reached.

            D. Determine pertinent information in problem situations and whether any further information is   needed for solution.

2.7 Probability and Predictions

            D. Compare and contrast results from observations and mathematical models.

 

NCTM Standard(s) Addressed:

Number Operations

  • Understand meanings of operations and how they relate to one another.
  • Compute fluently and make reasonable estimates.

Geometry

  • Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop        mathematical arguments about geometric relationships.
  • Use visualization, spatial reasoning, and geometric modeling to solve problems.

Measurement

  • Understand measurable attributes of objects and the units, systems, and process of measurement.         
  • Apply appropriate techniques, tools, and formulas to determine measurements.

 

Problem Solving

Reasoning and Proof

Communication

Representations

Introduction/applications

 

Question: 

Given specific guidelines, can you successfully design your dream home?

Model:

The students will describe their dream houses.  They will design them given

real world guidelines and see if what they design matches what they wanted.

Resources and Materials (estimated cost):

Graph paper                 $1.20

Markers                       $1.10

Scotch tape                  $2.30

Masking Tape              $2.80

Ruler                            $1.00

Compass                      $2.00

Poster Board                $5.75

Glue                             $2.20

Tape Measure              $5.50

File Cards                    $1.19  

Total (+ tax)                 $29.65

Procedures & Activities:

Task 1

The students will start by writing a short paragraph describing what they want their dream homes to be.

Task 2

The students will find the dimensions and areas of three rooms in their homes to get an idea of the size

of specific rooms.

Task 3

The students will be given graph paper to construct their land.  They will design the

outlines of their houses following given guidelines.

Task 4

The students will take their outlines and design the interiors of their homes.  They will calculate and label the dimensions and areas of each room.  They will also be allowed to add different items to their yards such as a pool or garden.

 

Task 5

When task four is completed, they are to write a narrative describing any changes that they made to their house.  In the narrative, they need to describe each change and why they made that change.

 

Answer/Rubric:

Each task will be graded as an individual assignment and then added together to produce their final grade out of 100 total points.

 

Task 1 (10 points total)

5 points:  Include the required rooms

                        plus     

5 points: Complete sentences and no grammatical errors

                        or

3 points: Not all complete sentences or grammatical errors

                        or

1 point: Not all complete sentences and grammatical errors 

 

 

Task 2 (15 points)

5 points for each completed section

 

Task 3 (25 points)

5 points            Area is correct 

5 points            Area is within the given range

15 points          Outline of the house is within the given guidelines

 

Task 4 (30 points)

Points will be deducted for the following mistakes:

            Walls are not drawn straight with a ruler                        5 points

            Rooms are not labeled                                                  5 points each

            Areas are not given                                                       5 points each

            Areas are not correct                                                    3 points each

 

Task 5 (20 points)

20 points –      Complete sentences and proper grammar and proper spelling is used     

                        All changes from task 1 are listed

                        Explanations for the changes are mentioned.

15 points –       Two of the three criteria are met

10 points –       One of the three criteria is met

5 points –         Task attempted; criteria are not met

0 points –         Task is not attempted           

 

Accommodations/Adaptations:

ESL:**            

ESL students will be paired with other students to help them with reading and writing.  Measurements may be given in metric units.

           

Special Ed:**

Special Education students will be paired with other students.  They will receive more one-on-one help.  They may use tiles instead of graph paper to help them determine the area.  

 

** Both ESL and Special Education students will be taught vocabulary words they will need to know for the project.

           

Enrichment:

  1. Add furnishings, windows, doors, closets and appliances to their floor plans.
  2. Add a second floor and a basement.
  3. Make three-dimensional models of their homes.
  4. Determine the cost of carpet and tile for the floors.

 

 

 

 

 

 

Home Sweet Home

 

Goal: To plan and design your dream home

 

Tasks:

                   1 – Write a short paragraph describing your ideal one-story home.

                             (10 points)

                  

                   2 – Find the dimensions and areas of the following rooms in your home:

                             A – kitchen

                             B – one bedroom

                             C – one bathroom with a bath/shower

                             (15 points – 5 points each)

 

                   3 – Create an outline of your ideal house. 

                             You will be given guidelines that you will need to follow.

                             You will calculate the total area of your house and explain how you found it.

                             (25 points)

 

                   4 – Design the inside of your house.

                             Label each room and hallway.

                             Find the area of each room and hallway.

                             (30 points)

 

                   5 – Write a short narrative describing any changes that were made to your original idea and explain why the changes were made.

                             (20 points)

                                                  

 

 

 

 

 

 

 

 

 

 

 

 

Home Sweet Home

Task 1 – (10 points)

 

Name ____________________________________     Date ___________

 

Write a short paragraph describing your dream one-story home.           

1.     Use complete sentences, proper grammar, and spelling. 

2.     Make sure to include at least one bedroom, one bathroom, and a kitchen along with any other rooms or hallways you wish to include.

3.     Be specific.

4.     Remember that it is only one floor and there is no basement.

 

 

You may include any of the following items or any other items not mentioned:

          Living Room                                                Pool

          Dining Room                                               Driveway with a garage

          Multiple Bathrooms                                      Driveway without a garage

          Multiple Bedrooms                                                Garden

          Den                                                             Pond

          Porch/Patio/Deck                                         Fountain                                  

          Game Room                                                Basketball Court

          Hallways

          Computer Room/Office

          Weight Room/Gym

          Foyer

 

 

 

 

 

 

 

Scoring (10 points total)

5 points if you include the required rooms

                   plus  

5 points:  Complete sentences and no grammatical errors

3 points:  Not all complete sentences or grammatical errors

1 point:   Not all complete sentences and grammatical errors 

      

                                                                                                          Points: _________

 

 

 

Home Sweet Home

Task 2 – (15 points)

 

Name ____________________________________     Date ___________

 

Find the dimensions and areas of the following rooms in your home:

                             A – Kitchen

                             B – One bedroom

                             C – One bathroom with a bath/shower

 

A.   Using a ruler, yardstick or measuring tape, find the length of each wall to the closest foot. **If you have trouble finding the lengths of a wall because of furniture, appliances, or cabinets, use a best estimate according to the length of the opposite wall.

B.    Using the measurements you found and find the area of each room.

C.   Have a parent/guardian initial each room.

 

A –Kitchen

 

          Length: __________ft                           Width: __________ft

 

          Area: ____________ft2                         Initial: __________

 

B –Bedroom

 

          Length: __________ft                           Width: __________ft

 

          Area: ____________ft2                         Initial: __________

 

C –Bathroom with a Bath/Shower

 

          Length: __________ft                           Width: __________ft

 

          Area: ____________ft2                         Initial: __________

 

 

Scoring (15 points – 5 points for each completed section)

 

 

 

 

 

Home Sweet Home

                                  Task 3 – (25 points)

Name ____________________________________     Date ___________

Create an outline of your dream house.

1 – Take four pieces of graph paper and tape them together to form a rectangle.                          

          Make sure the grids are lined up.

          This represents the land on which you will build your house.

 

2 – Draw the outline of your house using the following guidelines:

A.   You need at least 12 feet between the front of your house and the edge of your land.

B.    You need at least 10 feet between the rest of your house and the edge of your land.

C.  The area of your house must be between 1500 ft2 and 2500 ft2.

 

3 – Label the front of your house.

 

4 – Calculate the area of your house.

 

                                                                                      Area = __________________ ft2

Scoring (25 points)

5 points       Area is correct 

5 points       Area is within the given range

15 points     Outline of the house is within the given guidelines

 

 

 

 

 

 

 

 

 

 

 

Home Sweet Home

Task 4 – (30 points)

Name ____________________________________     Date ___________

 

Design the inside of your house.

                            

1 - Design the inside of your house. 

          Use a ruler to draw each wall.

          Neatly label each room with the name and its dimensions.

2 - Find the area of each room and hallway.

          Write the area in each room.

 

 

Reminder: You may use any of the following items or any other items not listed.

 

          Living Room                                      Pool

          Dining Room                                      Driveway with a garage

          Multiple bathrooms                             Driveway without a garage

          Multiple Bedrooms                                     Garden

          Den                                                    Pond

          Porch/Patio/Deck                               Fountain                                  

          Game Room                                      Basketball court

          Hallways                                            Shed

          Computer Room/Office

          Weight Room/Gym

          Foyer

 

Scoring: (30 points)

Point Deductions

Points will be deducted for the following mistakes:

          Walls are not drawn straight with a ruler                  5 points

          Rooms are not labeled                                           5 points each

          Areas are not given                                                5 points each

          One or two incorrect areas                                     5 points

          Three or more incorrect areas                                 10 points

 

 

 

 

 

 

 

 

Home Sweet Home

Task 5 – (20 points)

Name ____________________________________     Date ___________

 

Write a narrative describing any changes that were made to your home.

         

1.     Use complete sentences, proper grammar, and proper spelling.  

2.     Explain any changes that you made from your idea in Task 1.

3.     Explain why you made each change.

 

Scoring:

 

20 points –  1) Uses complete sentences, proper grammar, and proper spelling.      

                   2) Lists all changes from Task 1.

                   3) Explains changes.

 

15 points – Two of the three criteria are met.

 

10 points – One of the three criteria is met.

 

5 points –    Task attempted; criteria are not met.

 

0 points –    Task is not attempted.              

 

 

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