Math
Practicum in Commercial Photography
Lesson Plan
Performance Objective
Upon completion of this lesson, each student will be able to calculate the true focal length of a lens on
cameras with different sensor sizes.
Specific Objectives
 Students will explain the concepts of focal lengths, aspect ratios, sensor sizes and how they
relate to one another.
 Students will calculate equivalent focal lengths of various lenses on cameras with different
sensors.
 Students will explain the different types of sensors.
 Students will solve various equivalent focal length problems.
 Students will take photos, using various lenses and sensors and identify the equivalent focal
length.
This lesson should take 10-12 class days to complete, unless the teacher decides to teach the discount
material separately from mark-up.
Preparation
TEKS Correlations
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the activities
may result in the elimination of any or all of the TEKS listed.
Practicum in Commercial Photography
130.92(c)
(1) The student demonstrates professional standards/employability skills as required by
business and industry. The student is expected to:
(A) apply English language arts knowledge and skills to a variety of written documents;
and
(B) apply mathematics knowledge and skills in accordance with industry standards to
solve a problem.
(3) The student understands and examines problem-solving methods. The student is expected
to employ critical thinking and interpersonal skills independently and in teams to solve
problems.
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(10) The student is expected to employ planning and time-management skills to complete
work tasks, such as creating quotes and budgeting. The student is expected to:
(A) employ planning and time management skills to complete work tasks; and
(B) demonstrate skills in budgeting and creating quotes for freelance or contract
projects.
(11) The student develops an increased understanding of commercial photography. The
student is expected to:
(A) create photographs for defined purposes;
(B) apply the elements and principles of art to a variety of commercial photography
projects;
(C) demonstrate the principles of commercial photography such as working with
clients, interpreting client instructions, developing production schedules, and delivering
products in a competitive market;
(D) demonstrate the use of appropriate cameras and lenses;
(E) apply appropriate photographic composition and layout principles;
(G) apply effective photographic lighting techniques including 3 Point, studio,
portraiture, and product;
(H) produce professional quality photographs;
(K) demonstrate use of appropriate, current, and industry-standard production
processes to produce photographs; and
(L) evaluate photographs using principles of art, commercial photography standards,
and critical-thinking skills.
Interdisciplinary Correlations
Reading I, II, III
110.47(b)
(1) The student uses the following word recognition strategies. The student is expected to:
(A) Apply knowledge of letter-sound correspondences, language structure, and
context to recognize words;
(B) Use reference guides such as dictionaries, glossaries, and available technology to
determine pronunciations of unfamiliar words;
(2) The student acquires an extensive vocabulary through reading and systemic word study.
The student is expected to:
(A) Expand vocabulary by reading, viewing, listening, and discussing;
(B) Determine word meanings through the study of their relationships to other
words and concepts such as content, synonyms, antonyms, and analogies;
(4) The student comprehends text using effective strategies. The student is expected to:
(A) Use prior knowledge and experience to comprehend;
(B) Determine and adjust purpose for reading; and
(D) Summarize texts by identifying main ideas and relevant details.
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Public Speaking I, II, III
110.57 (b)
(4) Organization. The student organizes speeches. The student is expected to:
(B) Organize speeches effectively for specific topics, purposes, audiences, and
occasions.
(7) Delivery. The student uses appropriate strategies for rehearsing and presenting
speeches. The student is expected to:
(C) Develop verbal, vocal, and physical skills to enhance presentations.
Tasks
 Students will secure signatures on all forms, as specified by the teacher.
 Students will return all paperwork in a timely manner.
Accommodations for Learning Differences
It is important that lessons accommodate the needs of every learner. These lessons may be modified
to accommodate your students with learning differences by referring to the files found on the Special
Populations page of this website (cte.unt.edu).
Preparation
 Copy the handouts.
 Have multimedia presentations ready to show.
Instructional Aids
 Student Notes sheet
 Student worksheets
Materials Needed
 Copies
 Pencils
Equipment Needed
 Teacher computer
 Projector (for digital presentation)
 Calculators
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Introduction
Learner Preparation
 How do camera lenses work?
 What is the difference between a wide-angle lens and a telephoto lens?
 What is different about digital camera sensors from old film?
 Explain that focal length can change depending upon sensor size.
Lesson Introduction
 Ask the class if they get the same photo on a DSLR that they do on their camera phone?
 Have students use a 50mm lens on both a cropped sensor camera and a full-frame sensor
camera. Compare the results. How are they different?
 Explain how equivalent focal length affects what a camera sees.
 Explain that in order to really know what to expect from a lens, a consumer must know the
sensor size of their camera, the focal length of their desired lens, and the crop factor of the
camera (if it is a cropped sensor camera).
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Outline
NOTES TO TEACHER
OUTLINE
MI
The teacher has the discretion to teach
these two lessons back to back or
separately.
I.
II.
III.
IV.
V.
Math in photography
Focal Length
Sensors
Different Sensor Sizes
Equivalent Focal Length
I.
II.
III.
IV.
V.
Math in Photography
ISO
Aperture
Shutter Speed
Using Aperture, ISO and Shutter
Speed together
The teacher will use the multimedia
presentation to explain the concept of
equivalent focal lengths. Students will take
notes using the Student Notes outline and
then will complete the worksheets.
These concepts may be somewhat difficult
for the students to grasp. It may be
necessary for the teacher to make up
additional problems.
One suggestion is to put students into
groups or pairs and have them craft five or
10 problems (and work the answer keys)
that could be compiled and shared with the
entire class.
Multiple Intelligences Guide
Existentialist
Interpersonal
Intrapersonal
Kinesthetic/
Bodily
Logical/
Mathematical
Musical/Rhythmic
Naturalist
Verbal/Linguistic
Visual/Spatial
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Application
Guided Practice
The teacher will use the multimedia presentations to teach the material. The teacher will monitor
students’ guided and independent work.
Independent Practice
Students will complete the math worksheets independently. The teacher has the option to go over
these in class, hold a debriefing to discuss and work through problem issues, etc. Answer keys are
provided.
Summary
Review
 Why are lens measurements not always accurate?
 What are a few ways that sensors can differ from one another?
 What are the terms for the different types of sensors?
 What is a crop factor?
 What size film are all digital sensors compared to?
Evaluation
Informal Evaluation:
 Teacher will check for understanding
 Very small work group option (students help each other)
Formal Evaluation:
 Tests over the material
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Math: Equivalent Focal Lengths – Student Notes Outline
A.
Math in Photography
B.
You use math a lot in photography.
C.
D.
1.
ISO, apertures and ___________ ___________ all deal with math.
2.
___________ ___________ also deals with math.
What Focal Length isn’t
1.
You’ve probably discussed focal length before.
2.
Focal length is not how “____________ ________” you are.
3.
The higher the ___________ of a lens, the more telephoto it is.
What is Focal Length?
1.
Focal length is the distance in millimeters from the optical center of a lens to a
camera’s ___________.
E.
35mm Equivalent
1.
The term ___________ ___________ is based upon old film cameras that used
35mm film.
2.
The term describes the field of view with a lens through cameras that have
different ___________ ___________.
F.
Example
1.
In the past, a 28mm lens gave the same field of view on all cameras because
they all used ___________ ___________.
2.
With digital cameras, there is _______ ___________ ___________ between
the focal length of a lens and the angle of view that is received.
3.
A 28mm lens on a film camera would not produce the same field of view on a
small digital camera.
G.
Different Sensor Sizes
1.
Sensors come in all shapes and ___________.
2.
The size and shape of a camera’s sensor determines the “___________
___________.”
3.
Most medium or large format cameras produce images with a square aspect
ratio because they have a ___________ shaped sensor.
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H.
Cropped vs. Full Frame
1.
I.
Most modern day cameras fall into _________ categories:
a)
Full frame cameras
b)
Cropped sensor cameras
Full Frame Sensors
1.
_________ ___________ sensors are the size and shape as 35mm film.
2.
A lens with a focal length of 50mm would look the ___________ on an old film
camera and a modern day DSLR with a full frame sensor.
J.
Cropped Sensors
1.
A ___________ sensor produces images that are of a different size and shape
than 35mm film.
2.
Most of the time their “___________ ______ ___________” is smaller than a
full frame camera sensor.
K.
Field of View
1.
A DSLR with a full frame sensor sees a ___________ field of view than a
cropped sensor camera.
L.
Buying a Lens
1.
Most lenses are named according to their focal length when attached to a
___________ ___________ camera.
2.
For example, a 50mm lens would ___________ have the same field of view on a
cropped sensor camera that it would on a full frame camera.
3.
lens.
M.
Keep what type of sensor you have on your camera in mind when purchasing a
Crop Factor
1.
___________ ___________ measures how far a cropped sensor is from a full
frame sensor.
2.
Most cropped sensors have a crop factor of either ___________ _____
_______.
3.
___________ cameras have a crop factor of two.
a)
This means that a 40mm lens would actually have a focal length of
___________ on a mirrorless camera.
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N.
Other Ways Photography Deals with Math
1.
Equivalent focal length isn’t the only way photography deals with math.
2.
Photographers adjust aperture, ISO and shutter speed all while keeping in mind
the inverse relationship that exists between them.
3.
The seasoned photographer will also keep in mind their ___________ ______
___________ and how their aperture, focal length and distance from the subject all
affect it.
O.
Review
1.
Focal length is often different depending upon the size and shape of your
camera’s ___________.
2.
Sensors that are the size and shape of 35mm film are called _________
___________ sensors.
3.
Sensors that are of a different size and shape than 35mm film are called
___________ ___________.
4.
Different sensors have different ___________ ___________.
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Math: Focal Lengths – Student Notes Answer Key
A.
Math in Photography
B.
You use math a lot in photography.
C.
D.
1.
ISO, apertures and shutter speeds all deal with math.
2.
Focal length also deals with math.
What Focal Length isn’t
1.
You’ve probably discussed focal length before.
2.
Focal length is not how “zoomed in” you are.
3.
The higher the millimeters of a lens, the more telephoto it is.
What is Focal Length?
1.
Focal length is the distance in millimeters from the optical center of a lens to a
camera’s sensor.
E.
35mm Equivalent
1.
film.
The term 35mm equivalent is based upon old film cameras that used 35mm
2.
The term describes the field of view with a lens through cameras that have
different sensor sizes.
F.
Example
1.
In the past, a 28mm lens gave the same field of view on all cameras because
they all used 35mm film.
2.
With digital cameras, there is no universal relationship between the focal
length of a lens and the angle of view that is received.
3.
A 28mm lens on a film camera would not produce the same field of view on a
small digital camera.
G.
Different Sensor Sizes
1.
Sensors come in all shapes and sizes.
2.
The size and shape of a camera’s sensor determines the “aspect ratio.”
3.
Most medium or large format cameras produce images with a square aspect
ratio because they have a square shaped sensor.
10
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H.
Cropped vs. Full Frame
1.
I.
Most modern day cameras fall into two categories:
a)
Full frame cameras
b)
Cropped sensor cameras
Full Frame Sensors
1.
Full frame sensors are the size and shape as 35mm film.
2.
A lens with a focal length of 50mm would look the same on an old film camera
and a modern day DSLR with a full frame sensor.
J.
Cropped Sensors
1.
A cropped sensor produces images that are of a different size and shape than
35mm film.
2.
K.
Most of the time their “field of view” is smaller than a full frame camera sensor.
Field of View
1.
A DSLR with a full frame sensor sees a wider field of view than a cropped sensor
camera.
L.
Buying a Lens
1.
Most lenses are named according to their focal length when attached to a full
frame camera.
2.
For example, a 50mm lens would not have the same field of view on a cropped
sensor camera that it would on a full frame camera.
3.
lens.
M.
Keep what type of sensor you have on your camera in mind when purchasing a
Crop Factor
1.
Crop factor measures how far a cropped sensor is from a full frame sensor.
2.
Most cropped sensors have a crop factor of either 1.6 or 1.5.
3.
Mirrorless cameras have a crop factor of two.
a)
This means that a 40mm lens would actually have a focal length of
80mm on a mirrorless camera.
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N.
Other Ways Photography Deals with Math
1.
Equivalent focal length isn’t the only way photography deals with math.
2.
Photographers adjust aperture, ISO and shutter speed all while keeping in mind
the inverse relationship that exists between them.
3.
The seasoned photographer will also keep in mind their depth of field and how
their aperture, focal length and distance from the subject all affect it.
O.
Review
1.
Focal length is often different depending upon the size and shape of your
camera’s sensor.
2.
Sensors that are the size and shape of 35mm film are called full frame sensors.
3.
Sensors that are of a different size and shape than 35mm film are called
cropped sensors.
4.
Different sensors have different crop factors.
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Equivalent Focal Lengths Math Problems
Use your knowledge of equivalent focal lengths and their relationship to crop factor and full frame
camera sensors to figure out the following problems.
1. What is the 35mm equivalent of a 50mm lens on a camera with a crop factor of 1.6?
2. What is the 35mm equivalent of a 200mm lens on a camera with a crop factor of 1.5?
3. What is the 35mm equivalent of a 24mm lens on a micro 4/3rds camera with a crop factor of
two?
4. What is the 35mm equivalent of a 85mm lens on a full frame camera?
5. What is the 35mm equivalent of a 35mm lens on a camera with a crop factor of 1.6?
6. What is the 35mm equivalent of an 18-55mm lens on a camera with a crop factor of 1.5?
7. What is the 35mm equivalent of a 8mm lens on a micro 4/3rds camera with a crop factor of
two?
8. What is the 35mm equivalent of a 24-70mm lens on a full frame camera?
9. Full frame sensors are modeled after what size film?
10. Which has a larger sensor size: a full frame or cropped sensor camera?
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Math KEY
Equivalent Focal Lengths
Use your knowledge of equivalent focal lengths and their relationship to crop factor and full frame
camera sensors to figure out the following problems.
1. What is the 35mm equivalent of a 50mm lens on a camera with a crop factor of 1.6?
80mm
2. What is the 35mm equivalent of a 200mm lens on a camera with a crop factor of 1.5?
300mm
3. What is the 35mm equivalent of a 24mm lens on a micro 4/3rds camera with a crop factor of
two?
48mm
4. What is the 35mm equivalent of a 85mm lens on a full frame camera?
85mm
5. What is the 35mm equivalent of a 35mm lens on a camera with a crop factor of 1.6?
56mm
6. What is the 35mm equivalent of a 18 - 55mm lens on a camera with a crop factor of 1.5?
27-82.5mm
7. What is the 35mm equivalent of a 8mm lens on a micro 4/3rds camera with a crop factor of
two?
70mm
8. What is the 35mm equivalent of a 24 - 70mm lens on a full frame camera?
24-70mm
9. Full frame sensors are modeled after what size film?
35mm film
10. Which has a larger sensor size; a full frame or cropped sensor camera?
Full frame
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Math:
Mix and Match Cameras and Lenses
DIRECTIONS: Utilize your knowledge of sensor sizes, focal lengths, and how the two relate to one
another to figure out what the equivalent focal length would be with the following lenses attached to
the front of the following sensors.
A 50mm lens
Mirrorless Camera –
DSLR with a 1.5 crop factor –
DSLR with a 1.6 crop factor –
Full Frame DSLR –
An 18-55mm lens
Mirrorless Camera –
DSLR with a 1.5 crop factor –
DSLR with a 1.6 crop factor –
Full Frame DSLR –
A 100mm lens
Mirrorless Camera –
DSLR with a 1.5 crop factor –
DSLR with a 1.6 crop factor –
Full Frame DSLR –
A 35mm lens
Mirrorless Camera –
DSLR with a 1.5 crop factor –
DSLR with a 1.6 crop factor –
Full Frame DSLR –
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Math:
Mix and Match Cameras and Lenses KEY
DIRECTIONS: Utilize your knowledge of sensor sizes, focal lengths and how the two relate to one
another to figure out what the equivalent focal length would be with the following lenses attached to
the front of the following sensors.
A 50mm lens
Mirrorless Camera – 100mm
DSLR with a 1.5 crop factor – 75mm
DSLR with a 1.6 crop factor – 80mm
Full Frame DSLR – 50mm
An 18-55mm lens
Mirrorless Camera – 36-110mm
DSLR with a 1.5 crop factor – 27-82.5mm or 83mm
DSLR with a 1.6 crop factor – 30-88mm OR 31-88mm
Full Frame DSLR – 18-55mm
A 100mm lens
Mirrorless Camera – 200mm
DSLR with a 1.5 crop factor – 150mm
DSLR with a 1.6 crop factor – 160mm
Full Frame DSLR – 100mm
A 35mm lens
Mirrorless Camera – 70mm
DSLR with a 1.5 crop factor – 52.5mm (or 53mm)
DSLR with a 1.6 crop factor – 57.6mm (or 58mm)
Full Frame DSLR – 70mm
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