Imperial Units: Mass and Capacity - · PDF fileImperial Units: Mass and Capacity Lesson 11. Mathematics – MAT1L Unit 3 ... Convert each measurement to the imperial unit given. a

Imperial Units:

Mass and Capacity

Lesson 11

Mathematics – MAT1L Unit 3 – Lesson 11

Lesson Eleven Concepts

Investigate, discuss and describe applications from the everyday life and the workplace that would involve the measurement of mass and capacity.

Record measurements, using commonly accepted abbreviations for the chosen units.

Investigate, identify and use personal referents to aid in the estimation of mass and capacity.

Estimate and use measurements of mass and capacity in everyday situations. Measure of Mass and Capacity in the Imperial System

How much does it weigh? (mass) How much does it hold? (capacity) In the imperial system there are two main units of measurement that are used for mass.

1. pounds (lb) 2. ounces (oz)

Here are some examples of what each measurement might look like.

Pound (lb) ounce (oz) About 1 lb About 1 oz In the imperial system there are two main units of measurement that are used for capacity.

1. gallon (gal) 2. quart (qt)

Copyright © 2005, Durham Continuing Education Page 2 of 35


Here are some examples of what each measurement might look like. Gallon (gal) Quart (qt)

About 1 Gallon About 1 quart

Key imperial system conversions for mass and capacity There are 16 ounces in one pound (mass) There are 4 quarts in one gallon (capacity) Example a. Choose the best measure for the mass of a baseball.

1 oz 5 ozs 30 ozs Answer: A baseball’s mass is approximately 5 ozs.

b. Choose the best measure for the capacity of a glass of milk.

½ quart 4 quarts 19 quarts Answer: The capacity of a glass of milk is approximately ½ quart.



Support Questions 1. Choose the best measure.

a. Mass of newborn child 1 lbs 7 lbs 20 lbs

b. Mass of a bag of potato chips 1 oz 8 oz 20 oz

c. Mass of a mid-sized car 50 lbs 1 500 lbs 10 000 lbs

d. Mass of a cat 1 lbs 6 oz 8 lbs 2 oz 45 lbs 13 oz

e. Mass of an adult male 18 lbs 170 lbs 500 lbs

2. Choose the best measure.

a. Small glass of juice 1/2 qt ½ gal

b. Jug of milk 4 qts 4 gals

c. Can of soup 2 qts 8 gals

d. Bottle of mouthwash 2.2 qts 2.2 gal

e. A full bathtub of water 35 qts 35 gal 3. Choose the best measure for each.

a. Can of apple juice 2 qts 20 qts 80 qts

b. Plate 2 oz 2 lbs 20 lbs

c. tennis ball 2 oz 2 lbs 20 lbs

d. Swimming pool 50 qts 50 gals 5 000 gals 4. Estimate each measurement using appropriate units.

a. Capacity of a cup of hot chocolate in quarts. b. Mass of a stove in pounds c. Capacity of tea kettle in gallons d. Mass of a Barbie doll in ounces.



Key Question #11

1. Choose the best measure for capacity. a. Bottle of baby shampoo 1 qt 1 gal

b. Kitchen sink full of water 2 qts 2 gals

c. Large container of juice ½ qt ½ gal

2. Choose the best measure for the mass of each object.

a. Pair of jeans 2 oz 2 lbs

b. Bar of soap 3 oz 3 lbs

c. teaspoon of sugar ½ oz ½ lb 3. Choose the best measure for each.

a. Bottle of pop 1/2 qt 4 qts 12 qts

b. Flintstone multi-vitamin ¼ oz 1 oz 15 oz

c. Apple 1 oz 1 lb 5 lbs

4. Estimate each measurement.

a. Mass of CD player in ounces b. Mass of a horse in pounds c. Capacity of cereal bowl in quarts

5. Even though Canada has adopted the metric system can you think of two

examples where Canadians still use the imperial system as a form of measurement?


Conversions of Imperial Units

Lesson 12


Lesson Twelve Concepts

Explain and use correctly prefixes in the imperial system. Convert between imperial units commonly used in everyday applications.

Converting To and From Various Imperial Units Length When Converting from a larger unit to a smaller unit multiplication is needed.

miles yards feet inches Multiply by 1760 by 3 by 12 When Converting from a smaller unit to a larger unit division is needed.

inches feet yards miles Divide by 12 by 3 by 1760 Example

a. Convert each measurement to the imperial unit given.

6 ft = ? yds Answer: 6 ÷ 3 = 2 yards

Example

b. Convert each measurement to the imperial unit given.

38’ = ? “ Answer: 38 x 12 = 456”



Capacity and Mass When Converting from a larger unit to a smaller unit multiplication is needed.

gallons quarts pounds ounces Multiply by 4 by 16 When Converting from a smaller unit to a larger unit division is needed.

quarts gallons ounces pounds Divide by 4 by 16 Example

c. Convert each measurement to the imperial unit given.

2 gal = ? qts Answer: 2 x 4 = 8 quarts

Example

d. Convert each measurement to the imperial unit given.

48 oz = ? lbs Answer: 48 ÷ 16 = 3 lbs



Support Questions 1. Convert each measurement to the imperial unit given.

a. 2 miles = ? yds b. 12 yds = ? ft c. 27 ft = ? in d. 144 ft = ? yds e. 144 ft = ? in f. 12 yds = ? in g. 7040 yds = ? miles h. 3 miles = ? ft i. 1 mile = ? in

2. Convert each measurement to the imperial unit given. a. 8 qts = ? gals b. 3 gals = ? qts c. 12 lbs = ? oz d. 160 oz = ? lbs e. ½ lbs = ? oz f. ½ gal = ? qts g. 24 oz = ? lbs and oz h. 2 qts = ? gal



Key Question #12

1. Convert each measurement to the imperial unit given. a. 84 ft = ? yds b. 15 yds = ? ft c. 36 ft = ? in d. 48 ft = ? in e. 10 miles = ? yds f. 7 yds = ? in g. 255 ft = ? yds h. 2 mile = ? in i. 3520 yds = ? miles j. 1/2 mile = ? ft

2. Convert each measurement to the imperial unit given.

a. 32 oz = ? lbs b. 2½ lbs = ? oz c. 6 lbs = ? oz d. 3 qts = ? gal e. 12 qts = ? gals f. 4½ gal = ? qts g. 30 oz = ? lbs and oz h. 8 gals = ? qts

3. David says his piece of wood is longer because it is 240” and Joe’s is only 15’

long. Is he correct? Explain with words and calculations. 4. Explain in words and with an example the process of converting to and from

pounds and ounces.


Converting to and from Metric to Imperial Units

Lesson 13


Lesson Thirteen Concepts

Explain and use correctly prefixes in the imperial and metric system. Convert between imperial and metric units commonly used in everyday applications.

Converting To and From Metric and Imperial Units Listed following are the main units of conversion from metric to imperial and then from imperial to metric for length, mass and capacity. (See next page for chart)



First, find the unit being converted in the far left column.

Second, multiply by the value in the far right column to complete the conversion.



Example

a) Convert 2 yards to metres. Answer: 2 x 0.9144 = 1.8288 m

Use the tables above to answer this question.

a) Convert 8.5 L to gallons.

Answer: 8.5 x 0.2642 = 2.2457 gal

b) Convert 11.45 kg to pounds.

Answer: 11.45 x 2.2046 = 25.24267 lbs



Support Questions

1. Convert each measurement. a. 2 miles to km b. 12 in to cm c. 27 ft to m d. 144 in to cm e. 144 m to yds f. 100 cm to in g. 7040 km to miles h. 3 miles to km

i. 100 mm to in j. 250 yds to m k. 8 L to gals l. 3 gals to L m. 12 lbs to kg n. 160 kg to lbs o. 2 oz to g p. 100 g to oz

Key Question #13

1. Convert each measurement to the imperial unit given. a. 84 ft to m b. 15 in to cm c. 6 ft to m d. 48 cm to in e. 10 miles to km f. 7 yds to m g. 251 m to yds h. 2 mile to km i. 3520 km to miles

j. 1/2 lbs to kg k. 32 oz to g l. 2½ lbs to kg m. 6 g to oz n. 3 in to mm o. 12 mm to in p. 4½ gal to L q. 30 cm and in r. 8 L to gal

2. Nathan has a piece of string that is 30 feet long and needs a piece of string that

is 10 m long. Does he have enough string? Explain with words and calculations.

3. Jill is emptying one 8 L container of apple juice into two 1 gallon jugs. Will the two gallon jugs hold all of the apple juice? Explain with words and calculations.

4. Brianna can drive 325 miles on a full tank of gas. She has a full tank and needs

to drive 590 km. Does she have enough gas to drive the entire 590 km?


Perimeter

Lesson 14


Lesson Fourteen Concepts

Explore and describe situations from everyday life and the workplace that require calculation or measurement of perimeter.

Estimate, measure, and calculate perimeters drawn from applications in everyday life and the workplace.

Explain and illustrate how to determine the perimeter of any figure bounded by straight line segments.

Select the most appropriate standard unit to measure perimeter. Solve problems involving perimeter in applications drawn from everyday situations. Organize measurement information, using a simple framework Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of

investigations, using appropriate terminology, symbols and form.



Perimeter Perimeter is the distance around an object.

Formulas to be used to calculate perimeter. P = Perimeter



Example Find the perimeter of each of the following shapes.

a) b)

8”

6cm 10 cm 8 cm

c) d) 4 m 2.8 m 2.6 m 6.1 m

15 cm 8 c

8 cm

Solution

a)

6cm 10 cm 8 cm

6 8 1024

P a b cPP cm

= + += + +=

b)

This symbol tells us that all sides with the same symbol are equal.

8 8 8 832"

P s s s sPP

= + + += + + +=



d)

4 6.1 2.8 2.615.5

P a b c dPP m

= + + += + + +=



Support Questions

1. Estimate then calculate the perimeter for each of the following objects.

a) b) c) 7cm 4cm 8.25 cm

3 cm 5cm 3cm 2 cm d) e) f) 11 cm 6 cm 11’ 16.28’ 2.5 cm 12’

h)



Key Question #14

1. Estimate then calculate the perimeter for each of the following objects.

a) b) c) 4cm 8 cm 9.25 cm

2 cm 6 cm 5 cm 7 cm d) e) f) 12 m 9‘ 6 cm 10 cm 4’ 8 cm

h)



Key Question #14 (con’t)

2. Complete the table where P is the perimeter and a, b and c are the lengths of the sides.

P a b c 8.5 6.2 11.3 32.7 6.1 7.4 48.6 5.4 22.7

3. A tennis court measures 23.6’ by 14.7’. What is the perimeter of the tennis

court? 4. The yard of a mansion in Toronto is rectangular in shape. The length of the yard

is 244.3 m and the width is 125.7 m. What is the perimeter of the yard? 5. The building at Much Music on the corner of Queen St. and John St. in Toronto is

square and has a perimeter of 420 feet. What is the length of each side of the building?

6. A softball diamond is a square that measures 60’ on each side. What is the

distance a person must run when hitting a home run? 7. Measure the perimeter of the object below in millimetres.

8. Where in everyday life would a person use perimeter? Explain with an example.


Area

Lesson 15


Lesson Fifteen Concepts

Explore and describe situations from everyday life and the workplace that require calculating and measuring area.

Investigate the areas of a variety of rectangles, using concrete materials. Estimate, measure, and record rectangular areas found in everyday life and the

workplace, using uniform non-standard units. Predict and explain, from experiences involving concrete materials that the area of

any rectangle can be found by multiplying its length by its width. Estimate and calculate the areas of rectangles, drawn from applications in everyday

life and the workplace. Estimate and calculate the areas of regions that can be broken into rectangles. Organize measurement information, using a simple framework Explain their reasoning used in problem solving and in judging reasonableness. Communicate, in writing, the solutions to measurement problems and the results of

investigations, using appropriate terminology, symbols and form.



Area

Area is the number of square units needed to cover a region.

Area of a Square

Example Find the area of the square given below.

a.



Answer:

Remember the tick marks on the edges tell us that the sides are all of equal lengths.

2

Area = Length x Width 11 11 121

A L x WA xA m

==

=

Notice that the units are now squared. (exponent of 2). It takes 121 squares to cover the area of the rectangle shape given.

Area of a Rectangle

Example Estimate then find the area of the rectangle given below.

b.



Answer:

2

2

Estimated Area = Length x Width 15 10 150

Calculated Area = Length x Width 17 9 153

A L x WA xA cm

A L x WA xA cm

==

=

==

=

The estimation tells us that our calculation seems reasonable.

Area of Shapes that can be broken into Rectangles and/or Squares



Support Questions 1. Estimate then calculate the area for each of the following objects.

a. b.

c.

2. A credit card measures 8.4 cm by 5.6 cm. Find the area of the card. 3. Find the area of the shaded object below. Each unit represents . 21 cm

a. b.



Support Questions (con’t)

4. Copy and complete the chart for rectangles.

Length Height Area in Smaller Units

Area in Larger Units

9 m 650 cm 120 mm 15 cm 25 cm 120 mm 12 km 1100 m 8’ 12”


Length Height Area 4 cm 100 cm 2

9 m 36 m 2

15 km 225 km 2

Key Question #15

1. Estimate then calculate the area for each of the following objects.

a. b.

c.



Key Question #15 (con’t) 2. A picture frame measures .65 m by 1.25 m. Find the area of the picture frame. 3. Find the area of the shaded object below. Each unit represents . 2 1cm

a. b.


Length Height Area in Smaller Units

Area in Larger Units

6 m 630 cm 110 mm 15 cm 25 m 120 cm 5 200 m 120 km 6’ 24”


Length Height Area 4 cm 64 cm 2

5 m 45 m 2

20 km 300 km 2

6. An average rectangular NHL rink is approximately 61 m long and 26 m wide. A rectangular Olympic rink measures 61 m by 30.5 m. About how much More playing surface do Olympic players have than NHL players?



Key Question #15 (con’t)

7. Mrs. Vaughan is laying floor tile in her kitchen. The cost of floor tile is $10.25/ m 2 . Use the diagram below to estimate and calculate the area of the kitchen and the cost of the flooring tile.

8. The cost of grid system to located missing articles cost $2 500/km . Find the

cost for locating an item in a grid that measures .5 km by 900 m. 2

9. Describe two situations, not already mentioned in this lesson, from everyday life

and the workplace that requires calculating and measuring area.


Mathematics – MAT1L Unit 3 – Support Question Answers

Answers to Support Questions Lesson Eleven 1. a. 7 lbs b. 8 oz c. 1 500 lbs d. 8 lbs 2 oz e. 170 lbs 2. a. ½ qt b. 4 qts c. 2 qts d. 2.2 qts e. 35 gal 3. a. 2 qts b. 2 lbs c. 2 oz d. 5 000 gal 4. (Answers may vary but should be in this range) a. ¼ qt b. 225 lbs c. 1 gal d. 6 oz Lesson Twelve

1. a. 2 x 1760 = 3520 yds b. 12 x 3 = 36 ft c. 27 x 12 = 324” d. 144 ÷ 3 = 48 yds e. 144 x 12 = 1728” f. 12 x 3 = 36 ft x 12 = 432” g. 7040 ÷ 1760 = 4 miles h. 3 x 1760 = 5280 yds x 3 = 15 840 ft

i. 1 x 1760 = 1760 yds x 3 = 5280 ft x 12 = 63 360 inches 2. a. 8 ÷ 4 = 2 gal b. 3 x 4 = 12 qts c. 12 x 16 = 192 oz d. 160 ÷ 16 = 10 lbs e. 0.5 x 16 = 8 oz f. 0.5 x 4 = 2 qts g. 24 ÷ 16 = 1.5 = 1 lb + (.5 x 16) = 1 lb 8 oz h. 2 ÷ 4 = .5 gal

Lesson Thirteen 1. a. 2 x 1.6093 = 3.2186 km b. 12 x 2.54 = 30.48 cm c. 27 x 0.3048 = 8.2296 m d. 144 x 2.54 = 365.76 cm e. 144 x 1.0936 = 157.4784 yds f. 100 x 0.3937 = 39.37 in g. 7040 x 0.6214 = 4374.656 miles h. 3 x 1.6093 = 4.8279 km i. 100 x 0.03937 = 3.937 in j. 250 x 0.9144 = 228.6 m k. 8 x 0.2642 = 2.1136 gal l. 3 x 3.785 = 11.355 L m. 12 x 0.4536 = 5.4432 kg n. 160 x 2.2046 = 352.736 lbs o. 2 x 28.35 = 56.7 g p. 100 x 0.0353 = 3.53 oz Lesson Fourteen 1. a. 5 + 5 + 5 + 2 = 17 cm; 7 + 3 + 2 + 3 = 15 cm b. 5 + 5 + 5 + 5 = 20 cm; 4 + 5 + 4 + 5 = 18 cm

c. 10 + 5 + 10 + 5 = 30 cm; 8.25 + 3 + 8.25 + 3 = 22.5 cm d. 5 + 5 + 3 = 13 cm; 6 + 6 + 2.5 = 14.5 cm e. 10 + 10 + 15 = 35’; 11 + 12 + 16.28 = 39.28’



f. 10 + 10 + 10 + 10 = 40 cm; 11 + 11 + 11 + 11 = 44 cm g. 20 + 10 + 5 + 5 + 5 + 10 = 55 m; 18 + 6 + 6 + 6 + 12 + 12 = 60 m h. 10 + 10 + 10 + 10 + 10 + 10 = 60 mm; 12.2 + 8.6 + 8.4 + 7.9 + 9.1 + 9 =

55.2 mm Lesson Fifteen 1. a.

2cm64

8 8 WLarea estimated

=

×=×=

2cm68.89 8.3 8.3

WLArea

=

×=×=

b.

2m50 5 10

WLarea estimated

=

×=×=

2

Area L W 9.7 4.8 46.56 m

= ×= ×

=

c.

2

1

cm60 4 15

WL Aestimated

=

×=×=

2

2

cm60 6 10

WL Aestimated

=

×=×=

2

21

cm120 60 60

A A AreaTotal Estimated

=

+=+=

2

1

cm 56.24 3.8 14.8

WL A

=

×=×=

2

2

cm61.11 6.3 9.7

WL A

=

×=×=

2

21

cm 117.35 61.11 56.24

A A AreaTotal

=

+=+=

2.

2cm 47.04

5.68.4 WLA

=

×=×=

3. a. 26 b. 27 2cm 2cm



4. Area in Smaller Units Area in Larger Units 900 cm x 650 cm = 585 000 cm 2 9 m x 6.5 m = 58.5 m 2

120 mm x 150 mm = 18 000 mm 2 12 cm x 15 cm = 180 cm 2

250 mm x 120 mm = 30 000 mm 2 25 cm x 12 cm = 300 cm 2

12 000 m x 1 100 m = 13 200 000 m 2 12 km x 1.1 km = 13.2 km 2 72 in x 12 in = 864 in 2 8 ft x 1 ft = 8 ft 2

5.

Length Height Area 100 ÷ 4 = 25 cm 36 ÷ 9 = 4 m 225 ÷ 15 = 15 km


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Imperial Units: Mass and Capacity - · PDF fileImperial Units: Mass and Capacity Lesson 11. Mathematics – MAT1L Unit 3 ... Convert each measurement to the imperial unit given. a