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Title of Project:
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Tiling on a
Budget
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Team Members: |
Shad Greco, Charlene Keen, Elizabeth Shimko, Tania Stoker
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Grade Level
and/or Course: |
Geometry (10th or 11th grade)
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Concept(s) used: |
Polygons, angles, patterns,
area, perimeter, cost, estimating, relationships, modeling
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PA Standard(s) Addressed: |
- 2.2.11 (Computation &
Estimation) A, B, E
- 2.3.11 (Measurement & Estimation) A
- 2.4.11 (Mathematical Reasoning & Connections) B, E
- 2.5.11 (Mathematical Problem Solving & Communication) A, C, D
- 2.9.11 (Geometry) A, H, I, J
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NCTM Standard(s) Addressed: |
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Understand meanings of operations and how they relate to one another
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Compute fluently and make reasonable estimates
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Analyze characteristics and properties of two and three dimensional
geometric shapes and develop mathematical arguments about geometric relationships
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Apply
transformations and use symmetry to analyze mathematical
situations
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Use
visualization, spatial reasoning and geometric modeling
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Build
new mathematical knowledge through problem solving
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Solve
problems that arise in mathematics and in other contexts
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Apply
and adapt a variety of appropriate strategies to solve problems
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Monitor and reflect on the process of mathematical problem solving
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Introduction / applications: |
You have decided to
cover the 9’ x 12’ floor in your new home with tile.
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Questions: |
After reviewing your budget, you determine that you can spend no more
than $200 for the job. The home improvement store offers five different
shapes of tile at various costs (see below). This week they are running
a sale; if you select three or more types of tile, delivery is free. You
decide to take the offer.
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Model: |
- 9” x 12” grid
board (1/4” scale)
- Foam shapes as
previously described
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Resources and Materials: |
Do-It-Yourself Kit
Estimated cost $5.00
- Minimum of six 9” x 12”
pieces of colored foam (for shapes)
- 9” x 12” grid board
(scale model of room)
Pre-fabricated,
commercially sold, wooden tiles and grid board
Estimated cost $15-$23
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Procedures: |
- Trial and error/estimation to
determine patterns that fit grid board
- Multiplication & addition to determine
cost
- Reassess technique to achieve
acceptable cost requirement
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Possible Solutions: |
$64.00--16 red squares
$48.00--8 blue parallelograms
$12.00--4 purple trapezoids
$64.00--8 orange large triangles |
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| $188.00—Total
cost |
$48.00--12 red squares
$80.00--8 yellow small triangles
$32.00--4 orange large triangles
$24.00--8 purple trapezoids
$36.00--6 blue parallelograms |
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| $220—Total cost |
$16.00--4 red squares
$60.00--10 blue parallelogramss
$12.00--4 purple trapezoids
$96.00--12 orange large triangles
$80.00--8 yellow small triangles |
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| $264--Total cost (did not meet req’s) |
$24.00--6 red squares
$54.00--18 purple trapezoids
$48.00--6 orange large triangles |
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$126.00—Total cost
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Accommodations/Adaptations
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ESL: |
- Read and clarify
directions and procedures in native
language
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Special Ed: |
- Read and clarify directions and
procedures and model example(s).
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Enrichment: |
- Decrease the total
amount of money you
have available
- Increase/decrease the
cost of each shape
- Increase/Limit the
number of shapes
- Increase/Change the
type of shapes
- Compute the
area/perimeter of the shapes
- Ratio of the area of
one shape type to the
total area
- Determine angles and
slopes for the shapes
- Use the cost/ft2
minimize the total cost
- Require symmetry or
unique color patterns
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