Gold Seal Lesson:
Filling A Wedge

Copernicus Education Gateway

 

Subject:

 

Mathematics

Grade:

 

 

9-12

 

 

 

ICLE Standards:

 

 

Geometry and Measurement: 

  • Find volume of solid objects

  • Work with metric and English units of length, volume and capacity.

  • Work to a scale

Algebra:    

  • Interpret real situations graphically

  • Model real situations with a formula

Technology:   

  • Use formulas in spread sheets

 

 

 

Performance Task:

 

 

Jaycar Construction Company is filling a foundation for a building that is to be built on a slope. Figure the volume (in cubic yards) of a wedge 125' long, 85' wide and 3' tapering to O' high.

The foundation will be laid in 6" layers so that each layer can be compacted before the next is laid. Calculate the number of cubic yards of fill material that must be ordered each day. Remember that the wedge gets smaller each day. Interpret your results graphically. 

Jaycar finds that it is filling such foundations often. Develop a function that models the problem so that a computer can be used to order each day's fill.

Using metric units, make a cardboard scale model of the foundation. Show that your solution works (using units of capacity) to fill the wedge.

 

 

 

Knowledge / Skills:

 

 

Perform operations with signed (positive and negative) numbers, including decimals, ratios, percents, and fractions. M.1

Understand the best procedures for statistical data collection, organization, and display. M.5

Compute the volume of three-dimensional figures (solids). M.17

Use the technique of dimensional analysis to convert units of measure (e.g., convert km/hr to m/min). Understand and use various techniques for estimating, making and converting measure; and using these to perform dimensional analysis. M.33

Find the solution of linear equations and inequalities where the variable appears on both sides and in which one or both sides must be simplified before solving the equation (e.g., solve x+2(x-3) = -4x+5 for x). M.35

Plan and apply real or hypothetical models and constructions to facilitate investigation and learning and the solution to practical problems. 115

 

 

 

Rubric:

 

 

4 POINTS: Student completes all four parts of the problem without help, justifying each step. 

 

 

3 POINTS: Student needs extensive help on or is unable to complete one part of the problem correctly.

 

 

2 POINTS: Student needs extensive help on or is unable to complete two or more parts of the problem correctly.

 

 

1 POINT: Even with help, student does not complete at least two parts of the problem correctly.

 

 

 

Keywords:

 

 

GEOMETRY
THREE-DIMENSIONAL OBJECTS
VOLUME STATISTICS
DATA ANALYSIS
DATA COLLECTION
GRAPHS
COMPUTATION
MODELS AND CONSTRUCTION 
RATIOS

 

 

 

Grades:

 

 

Kg [] - 1 [] - 2 [] - 3 [] - 4 [] - 5 [] - 6 [] - 7 [] - 8 [] - 9 [x] - 10 [x] - 11 [x] - 12 [x]

 

 

 

ICLE Application:

 

 

D

 

 

 

 

 

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