CH 13, 14, 15, 16

0 KELVIN

-273 C

Convert 10,000 m into km (conversion factor 1000 m/km)

10,000m / 1000 m = 10 km

Convert 178,300 ml into l. (Conversion factor 1000 ml/ l)

178,300 / 1000 = 178.3 l

21 INCHES / 3 OZ

21 / 3 = 7 IN/ OZ (units are combined)

23 FEET + 19 FEET - 10 FEET =

23 + 19 = 42 42 - 10 = 32 FEET (units stay the same when you preform different operations)

DENSITY OF WATER

300 G/ 300 ML = 1G/ ML

Convert 5,300 km into m. (Conversion factor 1000 m/ km)

5,300 x 1,000 = 5,300,00

FREQUENCY DISTRIBUTION

A LIST OF HOW OFTEN EACH VALUE OCCURS (Make the list from lowest to highest)

A chart that shows the popularity or mode of a certain type of data is what?

A frequency table is a chart that shows the popularity or mode of a certain type of data. When we look at a frequency, we are looking at the number of times an event occurs within a given scenario.

1 MILLILITER =

CUBIC CENTIMETER

HISTOGRAM

GRAPHICAL REPRESENTATIONS OF THE VARIABLES (BAR GRAPH)

VOLUME

HOW MUCH SPACE SOMETHING TAKES UP

ENGLISH/ METRIC MEASUREMENT

IN METRIC: ALL MEASUREMENTS ARE BASE 10

CONVERTING MEASUREMENTS

MAKE SURE ALL UNITS ARE THE SAME: 10 feet x 12 = 120 inches

METER

MEASURE

GAUGES

MEASURE HOW MUCH OF SOMETHING WE HAVE EXAMPLE: fuel gauge on the car that shows us how much gas we have used and how much is left in the gas tank.

KELVIN

NEVER GOES NEGATIVE (0 kelvin is the lowest temp EVER)

Things that are more dense...

SINK TO THE BOTTOM

STEM AND LEAVES

THE COLUMN ON THE LEFT REPRESENTS THE 10'S VALUES ON EACH OF THE NUMBERS. Must have...0,1,2,3,4,5

MILLILITER

.001 (one thousandths of a liter, one milliliter = cubic centimeter)

MILLI

.001 UNITS (thousandths the size of the base unit)

FREEZING POINT OF WATER

0* C

KELVIN AND CELSIUS ARE PROPORTIONAL

0* C: 273 K

CENTI

0.1 UNITS (way to help memorize: 100 cents to a dollar, 100 years in a century)

DENSITY OF WATER

1 G/ ML

Convert 2,000 meters into kilometers.

1 kilometer/ 1,000 meters (solve from left to right)

METRIC CONVERSION

1. WHAT ARE YOU STARTING WITH 2. WHAT DO YOU WANT TO END UP WITH 3. WHAT DO YOU NEED TO GET THERE

10 CM - 6 CM =

10 CM - 6 CM = 4 CM (units stay the same when subtracting)

Convert 10 kg into grams (conversion factor 1000 g/ kg)

10 x 1000 = 10,000 g

BOILING POINT OF WATER

100* C

KILOMETER

1000 METERS

KILOMETER (Comparison to our mile but a bit shorter)

1000 METERS

Convert 13,000 milliliters into liters. (Conversion factor 1000 ml/l)

13 liters

Convert 1.5 kg into grams (conversion factor 1000 g/ kg)

1500 grams

8 M * 2 M

16 M^2 (units are squared when we multiply)

Divide 16 inches into fourths.

16 inches / 4 inches = 4 inches (units stayed the same)

Convert 19 l into ml (conversion factor 1000 ml/ l)

19 x 1000 = 19,000 ml

What is the closest to a mass of 500 ml of water?

500 ml * (1g / 1 ml) = 500 g

DIVIDING MEASUREMENTS

6 IN / 3 = 2 (UNITS ALL STAY THE SAME)

Your friend's car is going 70 miles every 2 hours.

70 mi / 2 hr = 35 mi / hr (KEEP IN FRACTION FORM)

VARIABLES

A SYMBOL FOR SOMETHING WE DON'T KNOW

What is a chart that shows the popularity or mode of a certain type of data based on the population sampled?

A relative frequency table is a chart that shows the popularity or mode of a certain type of data phased on the population sampled. When we look at relative frequency, we are looking at the number of times a specific event occurs compared to the total number of events.

STEM AND LEAF DISPLAY

A visual representation of data where the stem, the data on the left side of the chart, shows one part of the value while the leaves, the data on the right side of the chart, shows the other.

Histograms are very similar to what other graphical representation of numbers?

BAR GRAPH

GRAM

BASIC UNIT FOR MASS (use a scale, a penny is 2.5 grams)

LITER

BASIC UNIT FOR VOLUME (example: soda comes in a 2 liter bottle)

METER

BASIC UNIT OF LENGTH IN THE METRIC SYSTEM (One meter is a tiny bit longer than a yard)

FAHRENHEIT TO CELSIUS

C = (F - 32) * 5/9 C = (98.6 - 32) * 5/9 C = (66.6) * 5/9 (66.6 multiplied by 5 then divided by 9) C = 333/ 9 C = 37

FREQUENCY TABLE

CHART THAT SHOWS THE POPULARITY OR MODE OF A CERTAIN TYPE OF DATA AND THE NUMBER OF TIMES AN EVENT OCCURS WITHIN A GIVEN SCENARIO (Remember mode: most frequent number in a set)

RELATIVE FREQUENCY TABLE

CHART THAT SHOWS THE POPULARITY OR MODE OF A CERTAIN TYPE OF DATA BASED ON THE POPULATION SAMPLED. THE NUMBER OF TIMES A SPECIFIC EVENT OCCURS COMPARED TO THE TOTAL NUMBER OF EVENTS.

WHAT DO YOU DO IF MEASUREMENTS ARE NOT THE SAME UNIT?

CONVERT ALL UNITS TO THE SAME EXAMPLE: 3 FEET + 36 INCHES = (36 INCHES EQUALS 3 FEET) THEN ADD LIKE TERMS...

FREQUENCY DISTRIBUTION CHART

DIVIDE EACH SCORE BY THE TOTAL PEOPLE POLED TO FIND THE PERCENT. 5 / 55 = 9.1 %

What is the density of a solid that has a mass of 9.2 grams and a volume of 12.3 cm^3? Would this object float or sink in water?

Density = mass / volume. The units for density remain the same as the units you used for mass over the units you used for volume. This gives us 0.75 g/ cm ^3, which is less than water, meaning it will float.

What is the mass of a liquid with a density of 2.12 g/ ml and a volume of 53.0 ml (to the nearest gram)?

Density = mass/ volume So, mass = density * volume Mass = 2.12 g/ ml * (53.0 ml) = 112 g

DENSITY = MASS/ VOLUME

EXAMPLE: 8.3G / 3.5 CM^3 = 2.4 G/ CM^3

CELSIUS TO FAHRENHEIT

F = (C * 9/5) + 32 F = (27 * 9/5) + 32 (multiply by 9 then divide by 5) F = (48.6) + 32 F = 80.6

Things that are less dense...

FLOAT TO THE TOP

MULTIPLYING UNITS

FORMULA: L x W = AREA FEET^2 6 INCHES / BY 12 INCHES TO GET DECIMAL CONVERT INCHES TO FEET 0.5 + 7 = 7.5 7.5 FEET + 10 FEET = 75 SQUARE FEET (This is because you measured two feet units together so there are two "feet" being combined so it becomes feet squared)

HISTOGRAM

GRAPHICAL REPRESENTATION OF THE DISTRIBUTION OF DATA...SHOWS THE POPULARITY OR MODE OF DATA

What is a graphical representation of the distribution of data?

HISTOGRAM

SCALES

HOW MUCH AN OBJECT WEIGHS EXAMPLE: bathroom scale that tells us how much we weigh

CUMULATIVE PERCENTAGE

HOW MUCH OF SOMETHING THERE IS IN TOTAL

MASS

HOW MUCH OF SOMETHING YOU HAVE or THE AMOUNT OF MATTER IN AN OBJECT

DENSITY

HOW TIGHTLY PACKED THE PARTICLES OF AN OBJECT ARE HIGH DENSITY = PARTICLES CLOSELY PACKED TOGETHER LOW DENSITY = PARTICLES SPREAD FAR APART

POUNDS TO KILOGRAMS

KG = LB / 2.2046 EXAMPLE: 15O LB TO KG KG = 150/ 2.2046 KG = 68.04

METRIC MEASUREMENT UNITS

KILOGRAMS, CENTIMETERS, AND LITERS

MILES TO KILOMETERS

KM = MI/ 0.6214 KM = 25/ 0.6214 KM = 40.23

METRIC CONVERSION CHART

King Henry Died By Drinking Chocolate Milk

KILOGRAMS TO POUNDS

LB = KG * 2.2046 LB = 70 * 2.2046 LB = 154.32

METERS

MEASURE HOW MUCH OF SOMETHING WE HAVE OR ARE USING EXAMPLE: a parking meter that shows us the amount of time we have used vs we have left

DEGREES CELSIUS

METRIC UNIT FOR TEMPERATURE (Memorize the rhyme)

KILOMETERS TO MILES

MI = KM * 0.6214 MI = 50 * 0.6214 MI = 31.07

10.5 KILO TO METER

MOVE DECIMAL PLACE 3 JUMPS TO THE RIGHT: 10,500.

Smallest unit to largest unit?

Mm is 1000th of a meter, cm is 100th of a meter, a meter is the standard measurement, and km is 1000 meters.

US MEASUREMENT UNITS

POUNDS, INCHES, AND GALLONS

UNITS OF MASS

POUNDS, KILOGRAMS

CREATING FREQUENCY TABLES (example 1)

Plug in information within the table to get an overall picture of frequency and choice of those being polled.

STEM AND LEAVES

THE COLUMN ON THE LEFT REPRESENTS THE 1'S VALUE OF EACH THE NUMBERS. Must fill into the table by adding the ones to the tens in the column on the left.

WEIGHT

THE FORCE OF GRAVITY ON AN OBJECT

Which axis of a histogram usually shows the categories into which the various members of a data set fall?

THE HORIZONTAL AXIS (the vertical axis displays the frequency of each choice)

What can we show using a histogram?

THE MODE OF THE DATA SET (mode is the most frequent number in a set)

MEASUREMENTS

THE NUMBERS LINKED TO THINGS THAT SHOW THEIR SIZE, AMOUNT, OR MAGNITUDE

SKEWED

THE SHAPE OF A GRAPH PEAKS TO THE LEFT OR THE RIGHT OF THE CENTER. HIGHER SKEWS HAVE LESS HIGHER NUMBERS TO THE RIGHT OF THE GRAPH. (The example peaks to the right of the center)

SKEWED

THE SHAPE OF A GRAPH PEAKS TO THE LEFT OR THE RIGHT OF THE CENTER. LEFT SKEWED HAVE FEWER LOWER VALUES TO THE LEFT.

HOW TO CALCULATE

THE UNITS OF THE INGREDIENTS MUST ALWAYS BE ON THE OPPOSITE SIDE OF THE FRACTION BAR IN ORDER TO CANCEL OUT! 2000/ 1000 = 2 km

CREATING FREQUENCY TABLES (example 1 cont.)

TO FIND THE RELATIVE FREQUENCY DIVIDE THE RESULT BY THE TOTAL NUMBER OF PEOPLE POLLED. THE RELATIVE FREQUENCY COULD THEN BE SWITCHED INTO A PIE CHART TO SHOW PARTS OF THE WHOLE.

UNITS OF VOLUME

US: GALLONS, OUNCES WORLD: LITERS, MILLILITERS

STANDARD UNITS OF LENGTH

US: MILES, INCHES, FEET, YARDS, WORLD: KILOMETERS, CENTIMETERS, MILLIMETERS, METERS

HISTOGRAM

USED TO VISUALLY REPRESENT A SERIES OF DATA

How many ml are in 3.4 l?

Working in multiples of 10, we know that 3.4 liters needs to be multiplied by 1000 ml, to give us 3,400 ml.

MULTIPLYING VARIABLE MEASUREMENTS

YOU CAN HAVE TWO DIFFERENT UNITS AND IT IS OK (If you can convert units however go ahead and do so) EXAMPLE: 1 FEET x 1 INCH = 1X x 1Y = 1XY

DIVIDING VARIABLE MEASUREMENTS

YOU CAN HAVE TWO DIFFERENT UNITS AND IT IS OK (If you can convert units however go ahead and do so) EXAMPLE: 7 feet 6 inches / 10 feet 1. CONVERT TO A DECIMAL 6 / 12 then 0.5 x 7 = 7.5 2. Divide 7.5 by 10

COMPLETED STEM AND LEAVES DISPLAY

YOU CAN SEE NOT ONLY EACH OF THE EXACT NUMBERS BUT THE FREQUENCY IT APPEARS IN THE DATA.