Adapted from Pearson Education, Inc. Welcome to MM150! Kirsten Meymaris Unit 5 Plan for the hour MML...

Adapted from Pearson Education, Inc.

Welcome to MM150!Kirsten Meymaris

Unit 5

Plan for the hour MML Challenge!! Basic Terms in Metric System (5.1) Length, Area, Volume (5.2) Mass and Temperature (5.3) Conversions To and From Metric System (5.4)


MML Challenge!!Everyone score 60/60 this week, Unit 5?!

Challenge: Can everyone get 60/60 on your MML Graded Practice this week?! REMEMBER:

1- You can go in and out of the MML all Unit long (through next Tuesday at midnight) 2 - You can keep trying similar problems until you get that one right3 – You can view an example of this problem being worked out4 - You can step through this problem getting feedback at each step5 – You can send me an email with your questions about this problem.


5.1

Basic Terms and Conversions within the Metric System


Basic TermsCommon Use US Customary Metric System

Length inchfoot, yardmile

centimetermeterkilometer

Area inch2

feet2,yard2

acre

cm2

meter2

hectare

Volume (solid) inch3

foot3 yard3

cm3

meters3

Volume (non-solid, liquid)

ounce, cupquartgallon

milliliter, ccliter

Weight/Mass* ouncepound (lb)ton

gramkilogramtonne

Temperature Fahrenheit Celsius* Weight and mass are not the same but on Earth they are proportional and therefore are treated as the same.


Metric Prefixestera giga mega kilo hecto deka * deci centi mili micro nano pico

1012 109 106 103 102 101 1 10-1 10-2 10-3 10-6 10-9 10-12

Count how many prefixes/decimal places to move

Put in decimal point (if not already there) Move decimal point to the left/right (adding zeros

where necessary) Smaller to larger? (Left = L ~ Larger) Larger to smaller? (Right = R ~ Smaller)


Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MB


Metric Prefixes BA

SE


Example: Changing Units within Metric System Convert 54.6 m to km Convert 0.89 kg to cg Convert 1.5 TB to MBSolutions: 54.6 m = 0.0546 km. 0.89 kg = 89,000 cg 1.5 TB = 1,500,000 MB


5.2

Length, Area, and Volume


Common Use US Customary Metric System



Area inch2

feet2,yard2

acre

cm2

meter2

hectare


foot3 yard3

cm3

meters3



milliliter, ccliter


gramkilogramtonne



Length

The meter is used to measure things that we normally measure in yards and feet.

Areas are always expressed in square units.

Common Formulas:

2rA

wlA

circle

Area


Area Example

The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park.


Area Example

The length of a rectangular park is 82.5 m, and its width is 25.4 m. Find the area of the park.

A = 82.5 25.4

A = 2095.5 m2

Solution: Area = length width.


Volume in the Metric System

1 m3 = 1 kL

1 dm3 = 1 L

1 cm3 = 1 mL

Volume in LitersVolume in Cubic Units

cc = cubic centimeters = 1cm3

Common Formulas:

hrv

rV

hwlv

cylinder

sphere

2

3

34


Example: Volume Application

A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters?


Example: Volume Application

A cylindrical shampoo bottle has a diameter of 6 cm and a height of 12 cm. What is the volume in milliliters?

Solution:

V r 2h

V 3.14 3 2 12

V 339.12 cm3

V 339.12 mL


5.3

Mass and Temperature


Common Use US Customary Metric System



Area inch2

feet2,yard2

acre

cm2

meter2

hectare


foot3 yard3

cm3

meters3



milliliter, ccliter


gramkilogramtonne



Mass

Although weight and mass are not the same, on Earth they are proportional to each other. Mass is a measure of the amount of matter in

an object. Weight is the measure of gravitational pull on

an object.


Mass

Weight Mass

Earth

Moon


Volume and Mass of Water

Volume in Cubic Units

1 m3 = 1 kL = 1 t (1000 kg)

1 dm3 = 1 L = 1 kg

1 cm3 = 1 mL = 1 g

Mass of WaterVolume in Liters


Example: Capacity

A fish tank is 1 m long, 60 cm high and 260 mm wide.

Determine the number of liters that the tank holds.

What is the mass of the water in kilograms.


Example: Capacity


Determine the number of liters that the tank holds.


Example: Capacity


What is the mass of the water in kilograms.


Example: Capacity continued

Solution:

Since 1 m3 of water = 1 kL of water, 0.156 m3 = 0.156 kL, or 156 liters of water

Since 1L = 1 kg, 156 L = 156 kg of water.

V l w h

10.26 0.6

0.156 m3


Temperature

Water boils212ºF100ºC

Body temperature98.6ºF37ºC

Comfortable room71.6ºF22ºC

Water freezes32ºF0ºC

DescriptionºFºC

Temperature


Example: Choose ºF or ºC

The temperature of a can of frozen juice about 2 __.

The temperature of a person with a fever is about 101.5 __.

The temperature of a bowl of hot soup is about 175 __.


Example: Choose ºF or ºC

The temperature of a can of frozen juice about 2 __.

The temperature of a person with a fever is about 101.5 __.

The temperature of a bowl of hot soup is about 175 __.

Solution: a) ºC b) ºF c) ºF


Conversions

F

9

5C 32

C

5

9F 32


Example: Conversions The air temperature on a warm summer

day is about 85ºF. What is the equivalent temperature on the Celsius thermometer?

C

5

9F 32


Example: Conversions

The air temperature on a warm summer day is about 85ºF. What is the equivalent temperature on the Celsius thermometer? Solution:

C 5

9F 32

C 5

985 32

C 5

953

C 29.4

The equivalent temperature is about 29.4ºC.



The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer?

F

9

5C 32



The temperature of a cold glass of milk is about 5ºC . What is the equivalent temperature on the Fahrenheit thermometer?

Solution:

The equivalent temperature is about 41ºF.

F 9

5C 32

F 9

55 32

F 9 32

F 41


5.4

Dimensional Analysis and Conversions to and from the

Metric System


Dimensional Analysis

Dimensional analysis is a procedure used to convert from one unit of measurement to a different unit of measurement.

A unit fraction is any fraction in which the numerator and denominator contain different units and the value of the fraction is 1.


U.S. Customary Units

1 pint = 2 cups 1 year = 365 days

1 cup (liquid) = 8 fluid ounces

1 day = 24 hours1 ton = 2000 pounds

1 hour = 60 minutes1 pound = 16 ounces

1 minute = 60 seconds1 mile = 5280 feet

1 gallon = 4 quarts1 yard = 3 feet

1 quart = 2 pints1 foot = 12 inches

U.S. Customary Units


Dimensional Analysis

Examples of unit fractions:

16 oz

1 lb

1 hr

60 min

12 in.

1 ft


Conversion to and from the Metric System - Length

LENGTH

U.S. to Metric

1 inch (in.) ≈ 2.54 centimeters (cm)

1 foot (ft) ≈ 30 centimeters (cm)

1 yard (yd) ≈ 0.9 meter (m)

1 mile (mi) ≈ 1.6 kilometers (km)


Conversion to and from the Metric System - Area

AREA

U.S. to Metric

1 square inch (in.2) ≈ 6.5 square centimeters (cm2)

1 square foot (ft2) ≈ 0.09 square meter (m2)

1 square yard (yd2) ≈ 0.8 square meter (m2)

1 square mile (mi2) ≈ 2.6 square kilometers (km2)

1 acre ≈ 0.4 hectare (ha)


Conversion to and from the Metric System - Volume

VOLUME

U.S. to Metric

1 teaspoon (tsp) ≈ 5 milliliters (ml)

1 fluid ounce (fl oz) ≈ 30 milliliters (ml)

1 quart (qt) ≈ 0.95 liter (l)

1 gallon (gal) ≈ 3.8 liters (l)

1 cubic yard (yd3) ≈ 0.76 cubic meter (m3)


Conversion to and from the Metric System - Weight (Mass)

WEIGHT OR MASS

U.S. to Metric

1 ounce (oz) ≈ 28 grams (g)

1 pound (lb) ≈ 0.45 kilogram (kg)

1 ton (T) ≈ 0.9 tonne (t)


Example: Volume and Area

A gas tank holds 22.6 gallons of gas. How many liters is this?

The area of a box is 14.25 in2. What is its area in square centimeters?


Example: Volume and Area

A gas tank holds 22.6 gallons of gas. How many liters is this?

Solution:

The area of a box is 14.25 in2. What is its area in square centimeters?

Solution:

3.8 l

22.6 gal = 85.88 lgal

14.25 in2 6.5 cm2

1 in2

92.625 cm2


Example: Converting Speed

A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.


Example: Converting Speed

A road in Toronto, Canada shows that the speed limit is 62 kph. Determine the speed in miles per hour.

Solution:

Since 62 km equals 38.75 mi, 62 kph is equivalent to 38.75 mph.

62 km

1 mi

1.6 km

62

1.6mi 38.75 mi


Example: Weight (Mass) Conversion for Medication

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?


Example: Weight (Mass) Conversion for Medication

A newborn baby weighs 8 pounds 4 ounces. If 20 mg of a medication is given for each kilogram of the babies weight, what dosage should be given?

Solution:

The dosage of the medication is 73.92 mg.

8 lbs 16 oz

1 lb

4 oz 128 oz 4 oz 132 oz

132 oz28 g

oz

1 kg

1000 g

20 mg

1 kg

73.92 mg


Remember to Ask, Ask, Ask!

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Adapted from Pearson Education, Inc. Welcome to MM150! Kirsten Meymaris Unit 5 Plan for the hour MML...

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Transcript of Adapted from Pearson Education, Inc. Welcome to MM150! Kirsten Meymaris Unit 5 Plan for the hour MML...