M5.B.1 Demonstrate an understanding of measurable attributes of objects and figures, and the units, systems and processes of measurement. M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements.

M5.B.1.2 Eligible Content M5.B.1.2.1 Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below – use a conversion chart or a “hint” with problems e.g., hint: 16oz = 1lb). • Metric using mm, cm, m and km; mL and L; g and kg • Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb M5.B.1.2.2 Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form).

M5.B.1.2.1 Convert using linear measurements, capacity, and weight (mass) within the same system to the unit immediately above or below the given unit (using only the units below – use a conversion chart or a “hint” with problems e.g., hint: 16oz = 1lb). • Metric using mm, cm, m and km; mL and L; g and kg • Customary using cup, pint, quart, gallon; in, ft, yd; oz, lb

PSSA Sample Item

Converting Customary Measurement Length, Capacity, and Weight

Customary Length 12 inches (in) = 1 foot (ft) Copy this in your booklet page 12 12 inches (in) = 1 foot (ft) 36 inches = 3 feet or 1 yard (yd) 5,280 feet = 1 mile (mi) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE.

This represents about 1 mile. Customary Length A mile is about half the length of Talladega Super Speedway. Talladega is 2.9 miles long. This represents about 1 mile. Talladega Super Speedway

Customary Length A yard is about the length of a walking stick.

Customary Length A foot is about the length of a floor tile.

Customary Length An inch is about the length of a drink bottle top.

Customary Capacity 4 quarts = 1 gallon (gal) 2 pints = 1 quart (qt) Copy this in your booklet page 12 4 quarts = 1 gallon (gal) 2 pints = 1 quart (qt) 2 cups = 1 pint (pt) 8 fluid ounces (fl oz) = 1 cup (c) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE.

Meet Mr. Gallon 1 gallon

Meet Mr. Gallon 4 quarts

Meet Mr. Gallon 8 pints

Meet Mr. Gallon 16 cups

Customary Weight 16 ounces (oz) = 1 pound (lb) Copy this in your booklet page 12 16 ounces (oz) = 1 pound (lb) 2,000 pounds = 1 ton (T) To change from a larger unit of measure to a smaller unit, MULTIPLY. To change from a smaller unit of measure to a larger unit, DIVIDE.

Customary Weight A small car weighs about a ton.

Customary Weight A bag of coffee weighs about 1 pound.

Customary Weight An ounce weighs the same as 8 nickels.

Practice

1.  8 qt  =  ________ c 2.  11 qt  =  ________ fl oz 3.  108 in  =  ________ yd 4.  384 in  =  ________ ft 5.  20 lb  =  ________ oz 6.  128 pt  =  ________ gal 7.  15 yd  =  ________ ft 8.  21 gal  =  ________ qt 9.  31 lb  =  ________ oz 10.  336 oz  =  ________ lb

11. 6 inches = ______foot 12. 10 feet = _____yards_____feet 13. 30 feet = ________inches 14.  24 qt = _______ gal 15. 8 pt = _______ qt 16.  192 oz = _______ lb 17.  4 pt = _______ qt 18.  33 ft = _______ yd 19. 1 yd = _______ in 20. 3 lb = _______ oz 21. 4 gal = _______ qt

Converting Metric Measurements Metric System

metres grams litres Converting Units kilometres centimetres kilograms Joanne Smithies Our Lady & St. Gerards RCP

We use different metric units to measure :- Distance Capacity Weight We can use our knowledge of multiplying and dividing by 10, 100 or 1000 to change or convert measurements in one unit to measurements in another unit.

Containers and objects come in various shapes and sizes Containers and objects come in various shapes and sizes. How can you tell if: one container holds as much liquid as another? one object weighs the same as another? Or if they have equal measurements? It is easy if you convert the measurements.

Liters measure volume of a liquid substance

Grams measure weight

Meters measure distance or length

Metric System The metric system is based on a base unit that corresponds to a certain kind of measurement Length = meter Volume = liter Weight (Mass) = gram Prefixes plus base units make up the metric system Example: Centi + meter = Centimeter Kilo + liter = Kiloliter

Metric System The three prefixes that we will use the most are: kilo centi milli kilo hecto deca Base Units meter gram liter deci centi milli

Metric System So if you needed to measure length you would choose meter as your base unit Length of a tree branch 1.5 meters Length of a room 5 meters Length of a ball of twine stretched out 25 meters

Metric System But what if you need to measure a longer distance, like from your house to school? Let’s say you live approximately 10 miles from school 10 miles = 16093 meters 16093 is a big number, but what if you could add a prefix onto the base unit to make it easier to manage: 16093 meters = 16.093 kilometers (or 16.1 if rounded to 1 decimal place)

Metric System These prefixes are based on powers of 10. What does this mean? From each prefix every “step” is either: 10 times larger or 10 times smaller For example Centimeters are 10 times larger than millimeters 1 centimeter = 10 millimeters kilo hecto deca Base Units meter gram liter deci centi milli

Metric System Centimeters are 10 times larger than millimeters so it takes more millimeters for the same length 1 centimeter = 10 millimeters Example not to scale 40 41 1 mm 40 41 1 cm

Metric System For each “step” to right, you are multiplying by 10 For example, let’s go from a base unit to centi 1 liter = 10 deciliters = 100 centiliters 2 grams = 20 decigrams = 200 centigrams ( 1 x 10 = 10) = (10 x 10 = 100) (2 x 10 = 20) = (20 x 10 = 200) kilo hecto deca meter liter gram deci centi milli

Metric System An easy way to move within the metric system is by moving the decimal point one place for each “step” desired Example: change meters to centimeters 1 meter = 10 decimeters = 100 centimeters or 1.00 meter = 10.0 decimeters = 100. centimeters kilo hecto deca meter liter gram deci centi milli

Metric System Now let’s try our previous example from meters to kilometers: 16093 meters = 1609.3 decameters = 160.93 hectometers = 16.093 kilometers So for every “step” from the base unit to kilo, we moved the decimal 1 place to the left (the same direction as in the diagram below) kilo hecto deca meter liter gram deci centi milli

Metric System If you move to the left in the diagram, move the decimal to the left If you move to the right in the diagram, move the decimal to the right kilo hecto deca meter liter gram deci centi milli

Metric System Now let’s start from centimeters and convert to kilometers 400000 centimeters = 4 kilometers 400000 centimeters = 4.00000 kilometers kilo hecto deca meter liter gram deci centi milli

Metric System Now let’s start from meters and convert to kilometers 4000 meters = 4 kilometers kilo hecto deca meter liter gram deci centi milli Now let’s start from centimeters and convert to meters 4000 centimeters = 40 meters kilo hecto deca meter liter gram deci centi milli

Metric System Now let’s start from meters and convert to centimeters 5 meters = 500 centimeters kilo hecto deca meter liter gram deci centi milli Now let’s start from kilometers and convert to meters .3 kilometers = 300 meters kilo hecto deca meter liter gram deci centi milli

Metric System Now let’s start from kilometers and convert to millimeters 4 kilometers = 4000000 millimeters or 4 kilometers = 40 hectometers = 400 decameters = 4000 meters = 40000 decimeters = 400000 centimeters = 4000000 millimeters kilo hecto deca meter liter gram deci centi milli

We are going to use our knowledge about multiplying and dividing by 100 to convert centimetres to metres and to convert metres to centimetres.

Prefixes for Unit Measurements Kilo- hecto- deca- Unit deci- centi- milli-

When you walk up the steps, you move the decimal to the left one position for each step you take. Add a zero to hold each step.

When you walk down the steps, you move the decimal to the right one position for each step you take. Add a zero to hold each step.

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

4 2 7 ÷100 100 Remember! This is how we change 427cm into metres:- H T There are 100 centimetres in 1 metre When we change from cm to m we divide by:- 100 Remember! When we divide by 100 the units move two places to the right. This is how we change 427cm into metres:- H T U th hth 4 2 7 ÷100

Therefore:- 427cm = 4.27m cm m H T U t h th 3 2 6 H T U t h th 3 2 6 ÷100 H T U t h th 4 7 6 H T U t h th 4 7 6 ÷100 H T U t h th 1 6 5 3 H T U t h th 1 6 5 3 ÷100

Convert from centimetres to metres 354cm 15.4cm 779cm 52.4cm 939cm 395cm 25.8cm 3.54m 0.154m 7.79m 0.524m 9.39m 3.95m 0.258m ÷100

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

3.51m = 3 5 1 To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = H T U t h th 3 5 1

To change from metres to centimetres we MULTIPLY BY 100. REMEMBER When we multiply by 100 we move each digit two places to the left:- 3.51m = 351cm H T U t h th 3 5 1

Try changing these measurements in metres into centimetres 540cm 620cm 1270cm 300cm 760cm 54cm 30cm 5.4m 6.2m 12.7m 3m 7.6m 0.54m 0.3m x100

Let’s Practice! Convert 4 deciliters to kiloliters. Step 1: On the stairs, write the number 4 on the correct level. Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right? Step 3: Count the number of stairs you moved, either up or down. Step 4: Write the 4 and place the zeroes to the left of the 4 to hold the spot. Step 5: The decimal comes before your last zero. .0004 Kilo- 4 deci- Answer: 4 deciliters = .0004 kiloliters

Let’s Practice! Convert 3 grams to centigrams. Step 1: On the stairs, write the number 3 on the correct level. Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right? Step 3: Count the number of stairs you moved, either up or down. Step 4: Write the 3 and place the zeroes to the right to hold the spot. Step 5: The decimal comes after your last zero. 3 gram 300. Centi- Answer: 3 grams = 300. centigrams

My garden has a length of 34 decimeters and a width of 2 meters My garden has a length of 34 decimeters and a width of 2 meters. Which measurement is larger? On a separate piece of paper, show your work and explain your answer. Choose which number to convert. Draw the stairs. Step 1: On the stairs, write that number. Step 2: Decide where the new unit is that you want to have as your end measurement. Is it to the left or to the right? Step 3: Count the number of stairs you moved, either up or down. Step 4: Write that number on the new step. (Ask yourself if you moved left or right) Step 5: Place the zeroes on the correct side of the number(s). Then place the decimal point in the correct position. Answer: Conversion of 34 decimeters to meters. 34 decimeters = 3.4 meters Answer: Conversion of 2 meters to decimeters. 2 meters = 20. decimeters

Practice

Prefixes for Unit Measurements Kilo- hecto- deca- Unit deci- centi- milli-

On Your Own On a separate sheet of paper, convert the following measurements. 23 kilograms = ___ centigrams 2. 23 grams= ____ milligrams 62 meters = ____ decimeters 4. 62 centimeters = ____ meters 5. 375 milliliters = ____ kiloliters 6. 375 deciliters = ____ milliliters

On Your Own On a separate sheet of paper, convert the following measurements. 23 kilograms = 2300 centigrams 2. 23 grams= 23,000 milligrams 62 meters = 620 decimeters 4. 62 centimeters = .62 meters 5. 375 milliliters = .000375 kiloliters 6. 375 deciliters = 37500 milliliters

More Practice 2,570 L = ____ DL 2. 25 mm = ___ m 3. 54.5 mg = ____ g 4. 15 mm = ____Km 5. 340 cL = ____ L 6. 250 Kg=____g 7. 8750 mL = ____L 8.125,000 cm = _____Km 270 cm = _______mm

More Practice 2,570 L = 257 DL 2. 25 mm = .025 m 3. 54.5 mg = .0545 g 4. 15 mm = .000015 Km 5. 340 cL = 3.4 L 6. 250 Kg=250,000 g 7. 8750 mL = 8.75 L 8.125,000 cm = 1.25 Km 270 cm = 2,700 mm

M5.B.1.2.2 Add or subtract linear measurements, (feet and inches) or units of time (hours and minutes), without having to regroup with subtraction (answer should be in simplest form).

PSSA Sample Item

PSSA Sample Item

PSSA Sample Item

PSSA Sample Item

Adding and Subtracting Time Advice: Add or Subtract the hours and minutes separately. But you may need to do some adjusting if the minutes end up 60 or more, or less than zero!

Adding Times Follow these steps: Add the hours Add the minutes If the minutes are 60 or more, subtract 60 from the minutes and add 1 to hours Easy example: What is 2:45 + 1:10 ? Add the Hours: 2+1 = 3 Add the Minutes: 45+10 = 55 The minutes are ok, so the answer is 3:55 Hard example: What is 2:45 + 1:20 ? Add the Hours: 2+1 = 3 Add the Minutes: 45+20 = 65 The minutes are 60 or more, so subtract 60 from minutes (65-60 = 5 Minutes) and add 1 to Hours (3+1 = 4 Hours) ... so the answer is 4:05

Subtracting Times Follow these steps: Subtract the hours Subtract the minutes If the minutes are negative, add 60 to the minutes and subtract 1 from hours. (Note: the easiest way to add 60 to the negative minutes is to start with 60 and subtract the minutes) Easy example: What is 4:10 - 1:05 ? Subtract the Hours: 4-1 = 3 Subtract the Minutes: 10-5 = 5 The minutes are fine, so the answer is 3:05 Hard example: What is 4:10 - 1:35 ? Subtract the Hours: 4-1 = 3 Subtract the Minutes: 10-35 = -25 The minutes are less than 0, so add 60 to Minutes (-25+60 = 60-25 = 35 Minutes) and subtract 1 from Hours (3-1 = 2 Hours) ... answer is 2:35

Measurement Conversion: Scavenger Hunt You will need to add, subtract, multiply, and divide measurements on the worksite. With your partner, find the following measurements around your classroom and work through the problems. Use scratch paper to record your “work.” See the example below for how to convert inches to feet. Example: Measure the length of two tables in the room. Add the two measurements together.What is the total? (L. table #1) = 6 feet, 4 inches (L. table #2) = 3 feet, 9 inches 9 feet, 13 inches Simplify: 10 feet, 1 inch

1. Find the height of two doors in the room 1. Find the height of two doors in the room. Add the two heights together. 2. What is the length of a table plus the height of a chair? 3.Measure four sides around a window. Add the total of all four sides. 4.Measure the total height of a bookshelf. Measure the height of the tallest book on the shelf. Subtract the height of the book from the height of the bookshelf. 5. Find the height of a door in the room.Measure your or your partner’s height. Subtract your (or your partner’s) height from the height of the door.