Today’s Lesson
Dimensional Analysis
Materials needed for today’s session:

 Notepaper
 Pen/pencil
 calculator
Your thinking cap on
Learning Objectives we are covering
today:
 Use base and derived metric units to solve problems.
 Converting/Changing from 1 unit to another
 Meets: Common Core Math Standard-Algebra
 SSE – Seeing Structure in Expressions
 Write expressions in equivalent forms to solve
problems
What is “Dimensional Analysis”?
Examples:
How many wheels are on 350 Ford pick-up trucks?
How many seconds are in a day?
If you are going 50 miles per hour, how many feet per second are you
traveling?
186,282 miles per second into how many meters per second?
First watch a video
to get started
Pick one of these:
http://www.phschool.com/atschool/academy123/english/academy123_content/wlbook-demo/ph-165s.html
http://www.youtube.com/watch?v=lAan6L9UjsE
Let’s Begin!
Using what’s called Dimensional Analysis or the Factor-Label
Method –
You can convert from one unit of measurement to another
 You use the relationship of one unit to another
 For Example: 12 inches = 1 foot in length
 These 2 values are equivalent to each other.
 For every 12 inches = you get 1 foot or for every 1 foot – there are
12 inches.
Tips
Step 1: Strategize – find your conversion factor.
Step 2: Set up the problem, write it out fully
Step 3: Muliply/Divide, and simplify
Step 3: Solve
Step 4: Check your work
Example 1:
 The problem: How many feet are in 2 miles?
Strategize & The Setup:
The problem: How many feet are in 2 miles?
1. Strategize:
given that 5,280 feet are in 1 mile
I used this website to help find out how many feet are in 1 mile:
http://quizzes.cc/metric-conversion-charts.php
2. The Setup: Picket Fence– draw a Fence on your paper
Strategize & The Setup:
The problem: How many feet are in 2 miles?
1. Strategize:
Start with what you are given in the problem and put your amount in the
first fence on the top
And put multiplication signs in-between each fence picket
2. The Setup:
2 miles
x
The Setup:
Next – fill in the next Track with a conversion, (how many feet are in every 1 mile?)
putting miles in the denominator.
5,280 feet are found in every 1 mile.
I used this website to help find out how many feet are in 1 mile:
http://quizzes.cc/metric-conversion-charts.php
This way like units are diagonal from each other (in this case, miles)
and can cancel out when we solve the problem
5,280 ft
2 miles
x
1 mile
Let’s Solve
The unit miles cancels out since miles are diagonal from each other – one in the
numerator and in the denominator.
This is the same method for multiplying fractions; such as
1
2
-- x ---- = 1/5
2
5
5,280 ft
2 miles
x
1 mile
Strategize & The Setup:
Strategize:
How many feet are in 2 miles?


Multiply across the top: 2 x 5,280 = 10,560
Multiply across the bottom: 1= 1
10,560
5,280 ft
2 miles
x
=
1 mile
1
Solve
Strategize:
How many feet are in 2 miles?
 Finally – divide
10,560 / 1 = 10,560 feet is your answer
10,560
ft
5,280 ft
2 miles
x
=
1 mile
1
10,560 feet
=
Example 2: a multi-step problem
Convert : 1100 feet per second into miles per hour
We are given 1100 feet per second
And want – miles per hour in the final answer
Setup your Problem
Setup your problem with the Picket Fence – putting your given in the
first fence – top & bottom. Feet per second
Given 1100 feet per second = 1100 feet / 1 second
1100
feet
1
second
x
=
=
Setup the next Fence
Strategize:
Setup your problem with the Picket Fence
Given 1100 feet per second = 1100 feet / 1 second
Want – miles per hour in the final answer
1. Let’s work on changing feet into miles and then seconds into hours
How many feet are in 1 mile?
How many seconds are in 1 hour?
1100
feet
1
second
x
=
=
Find your Conversions
How many feet are in 1 mile? = 5280
Found from the conversion website:
http://quizzes.cc/metric-conversion-charts.php
How many seconds are in 1 hour?
60 seconds in 1 minute
60 minutes are in 1 hour
Setup the next Fence
Given 1100 feet per second = 1100 feet / 1 second
Want – miles per hour in the final answer
How many feet are in 1 mile? 5280
** Feet are across from each other in the fence so they will cancel out – we want to
end up with miles and hours in final answer
1100
feet
1
second
1 mile
x
=
=
5280 ft
* We are not done yet – need
miles and hours in the final
answer – not miles and
seconds
Setup the next Fence
Given 1100 feet per second = 1100 feet / 1 second
Want – miles per hour in the final answer
How seconds are in 1 hour? = 60 seconds in 1 minute
1100
feet
1
second
1 mile
x
=
5280 ft
60
seconds
1 minute
=
We are so close!
Seconds has been
cancelled out – but
answer needs hours
not minutes. One
more Fence needed…
Setup the next Fence
Given 1100 feet per second = 1100 feet / 1 second
Want – miles per hour in the final answer
How seconds are in 1 hour? = 60 seconds in 1 minute
60 minutes in 1 hour
** Cross out like units that are diagonal from each other
= now units in feet, seconds, and minutes have cancelled
1100
feet
1
second
1 mile
x
60
seconds
=
=
5280 ft
1 minute
60
minutes
1 hour
=
Multiply across top & bottom
Given 1100 feet per second = how many miles per hour is this?
1100
feet
1
second
60
seconds
1 mile
x
x
x
5280 ft
1 minute
60
minutes
1 hour
=
3960000 miles
____________
5280 hours
Divide & Solve for your Final Answer
Given 1100 feet per second = how many miles per hour is this?
1100
feet
1
second
60
seconds
1 mile
x
x
x
5280 ft
1 minute
60
minutes
1 hour
=
3960000 miles
____________
5280 hours
= 750 Miles per Hour
Assignment time
–
1. Unit Conversion Practice Problems
Convert the following quantities. Show ALL your work – all steps to get the answer:
1. 2678 cm into feet
2. 165 pounds into kilograms
3. 43 miles into feet
4. 60 miles per hour into meters per second
5. 130 meters per second into miles per hour
* Type these up on a Document with your name. Save your document & send to
class dropbox called “Unit Conversions Practice”
*You can also hand write on paper – then scan or take a clear digital picture of
your paper and send that to me in the class dropbox called “Unit Conversion
Practice”
1 hour = 3600 seconds
1 meter = 3.28 feet
1 lb = 0.45 kg
1 m/s = 2.2 miles/hour
Conversions to Use:
1 mile = 5280 feet
1 yard = 3 feet
1 km = 0.62 miles
1 kg = 2.2 lbs
1 quart = 0.946 liters
1 foot = 12 inches
1 inch = 2.54 cm
2. Create your Own
Dimensional Analysis Problem
 Post to the class discussion board titled, Dimensional Analysis
 You may create a 1 step (like Example 1) or 2-3 step problem
(like Example 2)
 Here is a helpful website for conversion factors you can use in
your problem:
 http://quizzes.cc/metric-conversion-charts.php

Also remember time conversions that you can use: 60 seconds in 1 minute, 60
minutes in 1 hour, 24 hours in 1 day
To turn into Class by Friday:
1. Your completed Unit Conversion Practice Problems
5 problems; 5 points each = 25 points total possible
Turn it into the class dropbox titled “Unit Conversions Practice”
2. Your own created Dimensional Analysis Problem posted to the class
discussion board titled, Dimensional Analysis.
Then your reply / answer/comment on at least 2 of your classmate’s postings –
due in 1 week
Remember these items are due
Friday:
1. Unit Conversion Practice problems, 1-5
calculated out on a computer document or written neatly by
hand – and submitted to the class dropbox
2. Your dimensional analysis problem posted to the
discussion board
Practice Your Conversions
1. Helpful Website for Dimensional Analysis Practice
 http://www.alysion.org/dimensional/fun.htm
 Work through the given 10 examples
Questions – Concerns?
Contact me for any questions about the class lessons, help, and to
stay informed!
 Kmail
 Office Phone: 360-329-6867