Today’s Lesson Dimensional Analysis. Materials needed for today’s session: Notepaper Pen/pencil calculator Your thinking cap on

Today’s LessonDimensional 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/wl-book-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.

TipsStep 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 milesx

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:


This way like units are diagonal from each other (in this case, miles)

and can cancel out when we solve the problem

2 milesx

5,280 ft

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

2 milesx

5,280 ft

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

2 milesx

5,280 ft

1 mile

=

1

10,560

SolveStrategize:

How many feet are in 2 miles?

Finally – divide

10,560 / 1 = 10,560 feet is your answer

2 milesx

5,280 ft

1 mile

=

1

10,560 ft

=

10,560 feet

Example 2: a multi-step problemConvert : 1100 feet per second into miles per hour

We are given 1100 feet per secondAnd want – miles per hour in the final answer

Setup your ProblemSetup 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

x = =1100 feet

1 second

Setup the next FenceStrategize:

Setup your problem with the Picket Fence


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?

x = =1100 feet

1 second

Find your Conversions

How many feet are in 1 mile? = 5280 Found from the conversion website:


How many seconds are in 1 hour?

60 seconds in 1 minute

60 minutes are in 1 hour

Setup the next Fence



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

x = =1100 feet

1 second

1 mile

5280 ft

* We are not done yet – need miles and hours in the final answer – not miles and seconds




How seconds are in 1 hour? = 60 seconds in 1 minute

x = =1100 feet

1 second

1 mile

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…




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

x = =1100 feet

1 second

1 mile

5280 ft

60 seconds

1 minute

60 minutes

1 hour=

Multiply across top & bottom

Given 1100 feet per second = how many miles per hour is this?

x x x1100 feet

1 second

1 mile

5280 ft

60 seconds

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?

x x x1100 feet

1 second

1 mile

5280 ft

60 seconds

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”

Conversions to Use:

1 hour = 3600 seconds 1 mile = 5280 feet 1 yard = 3 feet

1 meter = 3.28 feet 1 km = 0.62 miles 1 kg = 2.2 lbs

1 lb = 0.45 kg 1 quart = 0.946 liters

1 m/s = 2.2 miles/hour 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:


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

Documents

Today’s Lesson Dimensional Analysis. Materials needed for today’s session: Notepaper Pen/pencil calculator Your thinking cap on