For Mathguru

1

Math 30-1 Midterm Project: At the movies

In 2010, Canadian and American movie-goers spent $10.6 billion on tickets, or 33% of the

worldwide box office ticket sales. Of the films released in 2010, only 25 were in 3D, but they

brought in $2.2 billion of the ticket sales! You will examine box office revenues for newly

released movies, investigate graphs of the revenue over time, determine the function that best

represents the data and graph, and use this function to make predictions. In this project, you will

explore the use of mathematics to model box office revenues for a movie of your choice.

PART1: Modelling a curve

It is not easy to determine the best mathematical

model for real data. In many situations, one model

works best for a limited period of time, and then

another model is better. Work with a partner. Let x

represent the time, in weeks, and let y represent the

cumulative box office revenue, in millions of

dollars.

• The curves for Avatar and Dark Knight appear to have a horizontal asymptote. What do you

think this represents in this context? Do you think the curve for Titanic will eventually exhibit

this characteristic as well? Explain.

• Consider the curve for Titanic.

➢ If the vertex is located at (22, 573), determine a quadratic function of the form y = a(x -

h)2 + k that might model this portion of the curve.

➢ Suppose that the curve has a horizontal asymptote with equation y = 600. Determine an

exponential function of the form y = -35(0.65) 0.3(x - h) + k that might model the curve.

➢ Which type of function do you think better models this curve? Explain.

PART 2: Modelling Data

The table shows box office receipts for a popular new movie.

• Determine the equation of a logarithmic function of the form y = 20 log1.3 (x - h) + k that fits the

data.

• Determine the equation of an exponential function of the form y = -104(0.74)x - h + k that fits

the data.

• Compare the logarithmic function to the exponential function. Is one model better than the

other? Explain.

2

PART 3: At the Movies

• Investigate one of your favourite movies. Find and record the box office revenues for the first

10 weeks. You may wish to change the time period depending on the availability of data, but try

to get about ten successive data points.

• Graph the data.

• Which type of function do you think would best describe the graph? Is one function appropriate

or do you think it is more appropriate to use different functions for different parts of the domain?

• Develop a function (or functions) to model the movie’s cumulative box office revenue.

• Use your function to predict the cumulative revenue after week 15.

• Discuss whether this model will work for all movies. Record a video of yourself giving a brief

presentation of your findings.

3

Project Checklist

I Need To …

 choose one of my favourite newly-released movies, and then find and record the box office revenues for the first 10 weeks of its run (this time period can be adjusted

depending on the information that is available)

 graph the box office data from my research

 determine whether a single function can be used to describe the graph, or if it is more appropriate to use different functions for different parts of the domain

 develop a function (or functions) to model the movie’s cumulative box office revenue

 use my function to predict the cumulative revenue after week 15

 consider whether my model can be used to evaluate the box office revenue for all movies, and be prepared to present my findings to the class

Ana-Holistic Project Rubric

Criteria Level 1 Level 2 Level 3 Level 4 Level 5

Understanding

• strategies and

mathematical

processes

• develops an

initial start

• develops

some

relevant

strategies

and

procedures

• develops

relevant

strategies

and

procedures

• develops

thoroughly

• develops

thoroughly

• comparisons

and

connections

• absent or

inappropriat

e

• makes

minimal

number that

lead to a

partial

solution

• makes some

that

demonstrate

a basic

understandi

ng

• are

reasonable;

demonstrate

a clear

understandi

ng

• are

significant;

demonstrate

a

comprehensi

ve

understandin

g

Connections

• procedures • reflects a

correct start

• may be

partially

correct

• are basic • are

reasonable

• are efficient

and effective

4

• reflect level of

understandin

g

• could lead

to a correct

solution

• may contain

several

major

mathematic

al errors

• may contain

a major

error or

omission

• may contain

a minor

mathematic

al error that

may hinder

understandi

ng in one

part

• may contain

a minor

mathematica

l error that

does not

affect

understandin

g or the final

response

Communicating

• use of

mathematical

language

• uses poorly

or does not

use

• uses little or

none

• uses

common

language

• uses

appropriate

language

• uses

significant

language

• level of

support for

conclusions

• provides

weak or no

support

• provides

little or no

support

• provides

minimal

support

• provides

clear

support

• provides

in-depth

support

Criteria Level 1 Level 2 Level 3 Level 4 Level 5

Presenting

•

appropr

iateness of

format

• includes an

initial start

to a format

• uses format

that may

not be

appropriate

or well

developed

• uses

reasonable

format

• uses

appropriate

format

• uses

appropriate

format with

significant

authority

• clarity •

communicat

ion is weak

• may

communica

te at a basic

level

•

comm

unicates

with some

difficulty

• provides

clear

communicati

on

• provides

clear

communicat

ion that is

easy to

follow

• audience

appeal

• audience is

not

considered

• provides

weak

appeal to

audience

• may not

consistently

communicat

e directly to

audience or

consider

needs/intere

sts of

audience

•

comm

unicates

directly to

audience

• focusses on

needs and

interests of

intended

audience

5

• accuracy of

information

• information

is not

supported

by the

research

• information

is

minimally

supported

by the

research

• information

is basic and,

for the most

part, is

supported

by the

research

• information

is accurate

• information

is accurate

and in-

depth

Holistic Project Rubric

Score/Leve

l Holistic Descriptor

5

(Standard

of

Excellence)

Applies/develops thorough strategies and mathematical processes making

significant comparisons/connections that demonstrate a comprehensive

understanding of how to develop a complete solution

Procedures are efficient and effective and may contain a minor

mathematical error that does not affect understanding

Uses significant mathematical language to explain their understanding, and

provides

in-depth support for their conclusion

Presentation is well organized and appropriate for the material to be

presented, appeals to the audience, and is supported by the mathematics

of the research and its conclusions

4

(Above

Acceptabl

e)

Applies/develops thorough strategies and mathematical processes for

making reasonable comparisons/connections that demonstrate a clear

understanding

Procedures are reasonable and may contain a minor mathematical error

that may hinder the understanding in one part of a complete solution

Uses appropriate mathematical language to explain their understanding,

and provides clear support for their conclusion

Presentation is organized and appropriate for the material to be presented,

generally appeals to the audience, and is generally supported by the

mathematics of the research and its conclusions

6

3

(Meets

Acceptabl

e)

Applies/develops relevant strategies and mathematical processes making

some comparisons/connections that demonstrate a basic understanding

Procedures are basic and may contain a major mathematical error or

omission

Uses common language to explain their understanding, and provides

minimal support for their conclusion

Presentation is somewhat organized and appropriate for the material

being presented, may lack audience appeal or interest, and includes some

inconsistencies or omissions, with possible inconsistencies between the

presentation and the mathematics of the research and its conclusions

2

(Below

Acceptabl

e)

Applies/develops some relevant mathematical process(es) making minimal

comparisons/connections that lead to a partial solution

Procedures are basic and may contain several major mathematical errors

Communication is weak

Presentation lacks organization, has weak audience appeal, and includes

evident inconsistencies and omissions, with some inconsistencies between

the presentation and the mathematics of the research and its conclusions

1

(Beginning

)

Applies/develops a start that may be partially correct or could have led to

a correct solution

Procedures are very basic and contain several major mathematical errors

Communication is weak or absent

Presentation organization is minimal or non-existent. There is little

audience appeal and many inconsistencies and omissions, with

inconsistencies between the presentation and the mathematics of the

research and its conclusions