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Presentation Handouts - The Boat Challenge

By April Harper,2014-06-17 21:47
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Presentation Handouts - The Boat Challenge

We’ll Have Supplies; You Bring the

    Mathematics!

    Matt Kaufmann Bloomington High School, IL

    Darl Rassi Illinois State University

    kaufmannm@district87.org & mr.rassi@gmail.com

    NCTM Conference: Salt Lake City, Utah

    April 10, 2008

    Affiliated with the NSF PRISM Project

    http://www.gk12.ilstu.edu/presentation/

    Algebra I Boat Building Project

     Name:

     Group #:

    TASK 1: Build the boat out of a 5 x 8 index card with the side height as shown.

    _____ inches

    5 inches wide

     8 inches long

TASK 2: Calculate the following. SHOW WORK and unit analysis.

    1. Footprint (Area of the bottom of the boat). 2. Surface Area of the boat.

    3. Volume of the boat. 4. Perimeter of the top rim of the boat.

TASK 3: Check with the teacher to make sure your boat is seaworthy. Then in a tub of

    water, measure the amount of mass the boat can hold before it sinks.

     Mass Held: _____________

    pg 1.

TASK 4: Suppose I want to get into the boat building business. I want to know which of

    the characteristics (height, foot print, surface area, volume, perimeter) is the best

    predictor for the amount of Mass Held. Make an educated guess: __________________

TASK 5: Using Excel Spread Sheet make five scatter plots. One of each of the

    following:

     We want to find which of these variables the Mass Held depends upon. 1. Mass Held vs Height 2. Mass Held vs Footprint **Make Mass Held the dependent variable, and

    3. Mass Held vs Surface Area the other variable the independent variable.

    4. Mass Held vs Volume

    5. Mass Held vs Perimeter

TASK 6: Refer to your graphs.

    Explain the “story” that Mass Held vs. Height graph tells.

Was your educated guess made in the introduction correct? Which of the boat characteristics (height,

    foot print, surface area, volume, perimeter) is the best predictor for Mass Held? ____________________

Explain how you know by referring to the graphs. _________________________________________

__________________________________________________________________________________

TASK 7: Add a trend line to your capacity vs volume graph (Ask for instructions).

    1. What is the equation of the “best fit” line? ___________

    2. What is the slope? ______

    3. What does the slope mean? _________________________________

    pg 2.

    Writing Polynomial Expressions

    View Sketchpad File: (Dynamic Rectangles - Polynomials.gsp) BC = ABC

    CD =

     AF =GD

1. What is the variable in this situation?

     FEFE =2. Write an expression for the length of DE.

3. Write an expression for the length of AB.

4. The area of a rectangle is (length)(width). Write an expression for the area of the

    white square.

5. Write an expression for the yellow area.

6. Make a table of values (x, yellow area) and graph the points on a graph.

     TASK 8: Consider the Boat Problem

    _____ inches

    5 inches wide

    8 inches long

    1. What of this situation is best represented by a variable?

    2. Letting the variable x represent the height of the boat.

    a. Write an expression for the volume of the boat

    b. Rewrite this expression as a polynomial in descending order.

    pg 3.

TASK 9: Now let’s look at the 2-variable equation you found in Task 8. 32 V = 4x 26x + 40x

     Evaluate this 2-variable equation for the missing height values.

    x (height) V (volume) x (height) V (volume)

    0 1.5

    0.25 8.4 1.75 11.8

    0.5 2

    0.75 17.1 2.25 3.9

    1 2.5

    1.25 17.2

TASK 10:

    1. Plot the ordered pairs in the table in Task 9 below.

    2. Give the graph labels on the x and y axis and a title.

    15 | | | | 5

    | | | | | | | | | 0.5 1 1.5 2

Remember: The boat with the most volume will hold the most mass.

    3. Find the highest point on the graph and name it.

4. What does the highest point mean in terms of making a boat out of a 5 x 8 index card?

5. Where are the x-intercepts?

6. What do they mean in terms of making a boat out of a 5 x 8 index card?

    pg 4.

TASK 11:

    This is similar to Task 8, but instead of examining volume we will write expressions for

    the other characteristics.

    1. Letting the variable x represent the height of the boat.

    a. Write an expression for the foot print.

    b. Simplify this expression. Write as a polynomial in descending order.

    2. Letting the variable x represent the height of the boat.

    a. Write an expression for the surface area of the boat

    b. Simplify the expression and write it in descending order.

    3. Letting the variable x represent the height of the boat.

    a. Write an expression for the perimeter of the boat.

    b. Simplify the expression and write it in descending order.

    pg 5.

    The Calculus

    Boat

    Challenge

How many can fit on your boat

    before it sinks?

    Designed by:

    Matt Kaufmann & Darl Rassi

    Bloomington High School & Illinois State University

    pg 6.

Reflect on your boat design and trial float…

1. Could your boat have done better? _____

2. If given the chance, what would you do

    differently?

    ____________________________________

____________________________________

____________________________________

3. Generally speaking, boats that can carry a

    lot of weight have what characteristics?

    ____________________________________

    pg 7.

    Buoyancy: A boat floats when its weight in water is displaced.

4. Given the physical law of buoyancy,

    what characteristic do we want in our

    boats if we want them to carry the most

    weight? _______________

5. ____________ is the quantity of interest.

6. The boat that displaces the most water

    will carry the most weight!!

    pg 8.

Engineers are given problems like the boat

    challenge you just tackled. They are asked

    to achieve a goal while at the same time

    observing certain constraints.

7. What were your constraints? ________

8. What other constraints may engineers

    have to observe? ___________________

9. How might an engineer/mathematician

    approach the boat challenge?

    __________________________________

    _______________________

    Steps for Solving the Boat Challenge st

    1. ___________________ nd

    2. ___________________ rd

    3. ___________________ th

    4. ___________________ th

    5. ___________________

    pg 9.

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