Who turned off the lights?

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Presentation transcript:

Who turned off the lights? Factor Labeling who Who turned off the lights? Factor Labeling Factor Labeling Factor Labeling Factor Labeling Factor Labeling Factor Labeling Richard J. Terwilliger by

Thanks, that sure is bright! Factor Labeling Thanks, that sure is bright! Factor Labeling Factor Labeling Factor Labeling Factor Labeling Factor Labeling

Let’s review the method Factor Labeling Factor Labeling

we’ll determine the number of kilometers in 1 mile Using the we’ll determine the number of kilometers in 1 mile Factor Labeling Method Factor Labeling 1 mi = ? km

To do this we need to know some basic conversions. 1 mile = 5280 feet Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

You should learn these common conversions. 1 mile = 5280 feet Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

To start the conversion from miles to kilometers we draw a set of brackets. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Then draw a horizontal line that divides the brackets, top to bottom. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Again, we are converting 1 mi. Again, we are converting 1 mile into kilometers so we’ll place 1 mile above the line. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

There’s no denominator so we’ll leave the bottom blank. Leave this blank Leave this blank There’s no denominator so we’ll leave the bottom blank. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

We need to convert miles into feet, feet into inches, inches into centimeters, centimeters into meters and finally meters into kilometers. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Let’s get started and convert 1 mi. Let’s get started and convert the miles into feet! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Draw another set of brackets with a horizontal line next 1 mi. Draw another set of brackets with a horizontal line next to the first set. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

We’re going to match units in the 1 mi. mi. We’re going to match units in the numerator with units in the denominator. Place miles in the bottom of the second set of brackets. This matches the miles already on the top in the first set of brackets. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. ft. mi. We will change miles into feet so place feet directly above miles Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

To fill in the conversion, place 1 mi. 5280 ft. 1 mi. There’s 5280 feet in 1 mile. To fill in the conversion, place 5280 next to feet and 1 next to miles. Factor Labeling conversions 1 mile = 5280 feet 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

As you can see, the miles on the 5280 ft. 1 mi. As you can see, the miles on the top of the first set of brackets matches with the miles in the bottom of the second set of brackets. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

so we have changed to feet. 1 mi. mi. 5280 ft. 1 mi. reduces to one so we have changed to feet. mi. 1 Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Watch closely as it’s done. 1 mi. mi. 5280 ft. 1 mi. The same process will be used to change feet into inches! Watch closely as it’s done. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. 1 mi. Draw a set of brackets and then the horizontal line. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Match units top to bottom. 1 mi. mi. 5280 ft. 1 mi. ft. Match units top to bottom. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Place in the conversion units. (What are we converting to? 1 mi. mi. 5280 ft. in. 1 mi. ft. Place in the conversion units. (What are we converting to? In this case feet into inches.) Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Fill in the conversion numbers. 1 mi. mi. 5280 ft. 12 in. 1 mi. 1 ft. Fill in the conversion numbers. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Cross out the units that reduce. 1 mi. mi. 5280 ft. 12 in. 1 mi. 1 ft. Cross out the units that reduce. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. ft. 12 in. 1 mi. 1 ft. Again reduces to leaving inches. ft. 1 Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

The next step is to convert inches into centimeters. 1 mi. mi. 5280 ft. ft. 12 in. 1 mi. 1 ft. The next step is to convert inches into centimeters. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. 1 mi. 1 ft. 1 in. Follow the steps as I demonstrate!. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

centimeters into meters. 1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. 1 mi. 1 ft. 1 in. 100 cm. Now convert centimeters into meters. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

The final step, converting meters into kilometers. 1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. m. 1 km. 1 mi. 1 ft. 1 in. 100 cm. 1000 m. The final step, converting meters into kilometers. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. m. 1 km. 1 mi. 1 100 cm. 1000 m. Our units are now in kilometers! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

To finish up we multiply 1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. m. 1 km. 1 mi. 1 ft. 1 in. 100 cm. 1000 m. To finish up we multiply all of the numbers on the top. (1 x 5280 x 12 x 2.54 x 1 x 1) 160934 = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. m. 1 km. 1 mi. 1 100 cm. 1000 m. Multiply all of the numbers on the bottom and then divide. (1 x 1 x 1 x 100 x 1000 ) 160934 = 100000 = 1.61 km. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

1 mi. mi. 5280 ft. ft. 12 in. in. 2.54 cm. cm. 1 m. m. 1 km. 1 mi. 1 100 cm. 1000 m. 1 mile = 1.61 kilometers 160934 = 100000 = 1.61 km. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 mi = ? km 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

complicated conversion? Ready to do a more complicated conversion? Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s OK, Lets convert 70 kilometers/hour to meters/second? Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s We start the conversion the same way as before. Draw a set of brackets and a horizontal line. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. hr. Next, fill in the 70 kilometers per hour. Kilometers on the top, hours on the bottom. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. hr. For right now ignore the hours and convert kilometers to meters. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. hr. To change km to m, draw another set of brackets with the horizontal line. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. hr. km. Fill in your units… km on the bottom to match the km on the top . 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

And then meters on the top. 70 km. m. hr. km. And then meters on the top. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. hr. 1 km. There are 1000 meters in 1 kilometer. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. hr. 1 km. The reduce and drop out. km. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. hr. 1 km. We now have meters per hour and have to change hours into seconds. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. hr. 1 km. Another bracket set and horizontal line. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km. 1000 m. hr. hr. 1 km. min. Place hours on top and minutes on the bottom. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km. 1000 m. 1 hr. hr. 1 km. 60 min. There are 60 minutes in 1 hour! 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km. 1000 m. 1 hr. hr. 1 km. 60 min. The hours reduce to one and drop out. 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. 1 hr. hr. 1 km. 60 min. Now, convert minutes into seconds! 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. 1 hr. 1 min. hr. 1 km. 60 min. 60 sec. By now you should have the hang of it so, watch me do it! 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. 1 hr. 1 min. hr. 1 km. 60 min. 60 sec. We now have meters on the top and seconds on the bottom! 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m = hr s 70 km. 1000 m. 1 hr. 1 min. hr. 1 km. 60 min. 60 sec. All that is left is to... 70 km ?m hr s = Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

And then divide the bottom into the top 70 km. 1000 m. 1 hr. 1 min. 70000 m. 19.4 m. sec. hr. 1 km. 60 min. 60 sec. sec. 3600 Multiply the top, 70 km ?m hr s = Multiply the bottom, And then divide the bottom into the top Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

70 km ?m Whew ! = hr s 70 km. 1000 m. 1 hr. 1 min. 70000 m. 19.4 m. sec. hr. 1 km. 60 min. 60 sec. sec. 3600 70 km ?m hr s = Whew ! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Now let’s do a real tough one!, 1 mile = 5280 feet 1 foot = 12 inches Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

How about changing 1 mile = 5280 feet 1 foot = 12 inches Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

We’re going to solve this exactly the same way as the 2 m min 3 We’re going to solve this exactly the same way as the other examples and for now we’ll IGNORE the exponents. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

2 m min 3 100 cm 1 m First change meters into centimeters. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

and between the numbers 2 m min 3 SPACE 100 cm SPACE SPACE 1 SPACE m Notice the SPACE I left after the units and between the numbers and the units! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

to be used for the exponents. 2 m min 3 100 cm 1 m This SPACE is going to be used for the exponents. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Since the meters is squared in the first set of brackets, 2 2 m 100 cm 3 1 2 min m Since the meters is squared in the first set of brackets, we will square the meters in the second set. Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

square everything else! 2 2 2 2 m 100 cm 3 2 1 2 min m Now, If we square the meters, we MUST square everything else! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

We’ll do the same thing again cm 1 100 2 2 2 m 1 min 3 min 60 sec We’ll do the same thing again changing into 3 min sec Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Remember to leave SPACE cm 1 100 2 2 2 m 1 min 3 min 60 sec Remember to leave SPACE for the exponents! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

We’re changing from minutes cubed so everything in the third bracket cm 1 100 2 3 3 2 2 m 1 min 3 3 3 min 60 sec We’re changing from minutes cubed so everything in the third bracket is cubed Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

m cm 1 100 2 3 3 2 2 m 1 min 3 3 3 min 60 sec Lets REDUCE Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

m cm 1 100 2 m cm 1 100 2 3 3 2 2 m 1 min 3 3 3 min 60 sec And we’re left with…. cm sec 2 3 Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

To finish up, multiply the top and divide by the bottom! cm 1 100 2 m cm 1 100 2 3 3 2 2 m 1 min 3 3 3 min 60 sec To finish up, multiply the top and divide by the bottom! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

m cm 1 100 2 m cm 1 100 2 3 3 2 .09 cm sec 2 3 2 m 1 min 3 3 3 min 60 sec 2 x 1002 603 Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

m cm 1 100 2 m cm 1 100 2 3 3 2 2 2 m 1 min cm .09 3 3 3 3 min 60 sec sec Now, wasn’t that easy! Factor Labeling conversions 1 mile = 5280 feet 1 foot = 12 inches 1 inch = 2.54 centimeters 1 meter = 100 centimeters 1 kilometer = 1000 meters

Factoring Labeling by Richard J. Terwilliger Suffern High School

Hey, Who turned out the lights?