M5.B.1.2 Solve problems using simple conversions and/or add and subtract measurements.

1. 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.

2. 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).

3. 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

4. PSSA Sample Item

5. ConvertingCustomary MeasurementLength, Capacity, and Weight

6. Copy this in your booklet page 12 Customary Length • 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.

7. 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

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

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

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

11. Customary Capacity 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.

12. Meet Mr. Gallon 1 gallon

13. Meet Mr. Gallon 4 quarts

14. Meet Mr. Gallon 8 pints

15. Meet Mr. Gallon 16 cups

16. Copy this in your booklet page 12 Customary Weight • 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.

17. Customary Weight • A small car weighs about a ton.

18. Customary Weight • A bag of coffee weighs about 1 pound.

19. Customary Weight • An ounce weighs the same as 8 nickels.

26. Practice

27. 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

28. 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

29. Converting Metric Measurements Metric System

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

31. 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.

32. 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.

33. Liters measure volume of a liquid substance

34. Grams measure weight

35. Meters measure distance or length

36. 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

37. Metric System • The three prefixes that we will use the most are: • kilo • centi • milli

38. 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

39. 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)

40. 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

41. 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 40 41 1 cm

42. 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)

43. 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

44. 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)

45. 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

46. Metric System • Now let’s start from centimeters and convert to kilometers 400000 centimeters = 4 kilometers 400000 centimeters = 4.00000 kilometers

47. Metric System • Now let’s start from meters and convert to kilometers 4000 meters = 4 kilometers • Now let’s start from centimeters and convert to meters • 4000 centimeters = 40 meters

48. Metric System • Now let’s start from meters and convert to centimeters 5 meters = 500 centimeters • Now let’s start from kilometers and convert to meters • .3 kilometers = 300 meters

49. 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

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