measuring length - qerhs math · pdf fileunit i measuring length 38 comparing si units to...

Unit I Measuring Length 1

Section 2.1 Imperial Length Measurements

(I) Reading Fractions

Goals

Reading Fractions

Reading Halves on a Measuring Tape

Reading Quarters on a Measuring Tape

Reading Eights on a Measuring Tape

Reading Tape Measurements

Answer:________

Answer:________


(II) Reading Halves on a Measuring Tape


(III) Reading Quarters on a Measuring Tape

Answer:________ Answer:________

Answer:________


(IV) Reading Eights on a Measuring Tape

Answer:________ Answer:________

Answer:________


(V) Reading Tape Lengths

Ans:________

Ans:________

Ans:________

Ans:________


Practice Problems:

State the imperial length for each diagram below.

1.

2.

3.

4.

5.

6.

7.


Ans:________

Ans:________

Ans:________

Ans:________

Ans:________


Use the tape below to determine the indicated length.

Note: The smallest measurement (in Red) is in the

______________ position.

Ans:________

Ans:________

Ans:________


Practice Problems:

State the imperial length for each diagram below.

1.

2.

3.

4.

5.


P.62 – P.63 #5 and #6


Reading Imperial Tape Measurements State the indicated tape lengths.

(I) Quarter Measurements

1. Tape measurement = _________

2. Tape Measurement = _________

(II) Eighth Measurements



(III) Sixteenth Measurements





(IV) Mixture of Measurements




13. Tape Measurement = ___________


Reading Imperial Tape Measurements





8. Tape Measurement = _______





Estimating Length Using References

Review Reading an actual imperial measurement

1.

2.

Goals

Review Reading Imperial Tape

Measurement

What is a Referent ?

Using References to Estimate Length in

Imperial Measurements

Ans:________

Ans:________

Ans:________

3.


Using referents for imperial units

Unit Referent

Inch (in.) Thumb Length

Foot (ft.) Foot Length

Yard (yd.) Arm span

Mile (mi.) Distance walked in

20 minutes

Note: The distance between the tip of the thumb to the

knuckle is approximately 1 inch. This is called

a referent measurement.

The thumb length, foot length, and arm span are referents.

Each referent is an approximate measure for an imperial unit.


Classroom Activity – Using References to Approximate Length

Item Referent Estimated

Measurement

Actual Measurement

Desk Width of hand ≈ 4“

Example 1 Estimating Lengths Using Imperial Units

Describe how you would estimate the width (across) your desk.

Solution The most appropriate imperial unit is the inch.

Use the width of your hand as a referent. It is about 4 in. across.

Line up one hand with one edge of the desk.

Count how many times you place your hands, one next to the other, to go from

one edge of the desk to the other.

Multiply the number of hands by 4, to get the approximate width of the desk in

inches.

Use a tape to determine

the actual measurement.

Using Referents to Estimate Length

(i) Get in groups (3 to 4) where you will have items to measure using the

referent measurement indicated to determine an estimated length.

(ii) Use the measuring device (ruler or tape) to determine the actual length of that

item.


Item 1 Length of Pencil

Determine how many thumb lengths to measure from one end of the

pencil to the other to attain an estimated measure then use the ruler or

tape to determine the actual measure.

Item 2 Length of course textbook

Determine how many hand widths to measure from one end of the

cover to the other end of the cover along the longest edge. Then use

the ruler or tape to determine the actual measure.


Measurement

Actual Measurement

Pencil Thumb (Tip to first

joint) ≈ 1“


Measurement

Actual Measurement

Textbook Width of hand ≈ 4“


Item 3 Length of a floor tile

Use the length of your foot to determine the length of one floor tile

to attain an estimated measure then use the ruler or tape to determine

the actual measure.

Item 4 Width of the classroom

Hold a piece of string from your nose to the longest finger of an

outstretched arm. Have your partner cut the string to this length.

Use this string to estimate then record the width of the classroom,

in arm spans to calculate the estimated measurement. Then use the

tape to determine the actual measure.


Measurement

Actual Measurement

Floor Tile Foot (Back of heel to

toe) ≈ 1 foot


Measurement

Actual Measurement

Width of

Classroom

Arm span ≈ 3 ft.

QUESTION: Why is it necessary to have standardized measurements for

length instead of using referents as a means to measuring?

______________________________________________________________

______________________________________________________________


Converting Imperial Units

(I) Converting Inches to Feet

1 ft. = 12 in.

Goals

Converting Inches to Feet

Converting Feet to Inches

Adding Feet and Inches

Converting Miles to Yards


(II) Converting Feet to Inches

(III) Adding Feet and Inches

1 ft. = 12 in.


(IV) Converting Miles to Yards

1 mi. = 1760 yds

P.68 - 69 #3, #4, #6, #7


Practice Sheet for Imperial Measurement

1. Express each of the following in feet and inches:

(a) 9″ + 13″ (b) 4′ 5″ + 3′ 3″

(c) 6′ 5″ + 8′ 11″ (d) (2′ 7″) x 3

(e) 1′ 11″ + 6″


Reading SI (Metric) Measurements

SI units Abbreviation Relationship between units

millimeter mm

centimetre cm 1 cm = 10 mm

metre m 1 m = 100 cm

kilometre km 1 km = 1000 m

(I) Reading Metric Measurement

Remember: On each ruler (or tape) 1 cm = 10 mm

Goals

Reading Metric Measurement

Determining length in SI units

Converting between SI units for length


(II) Determining Length in SI Units

Ex. State the length of each line in millimeters and centimeters.

(a)

(b)

___mm ___cm

___mm ___cm

___mm ___cm (c)


(III) Converting Between SI Units for Length

Example: Determine the width of the door in the indicated SI unit.

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Width of Door

Determine the measurement of each item in the indicated SI unit.

1. Your desk

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Width of Desk

2. Your Height

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Height


3. Width of the classroom

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Width of Room

4. Height of the Classroom Door

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Height of

Door

5. Width of the Textbook

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Width of

Textbook

6. Inside Width of One Window Pane

Item SI Measurement

(mm)

SI Measurement

(cm)

SI Measurement

(m)

Window Pane


Relating SI and Imperial Units

(I) Reading SI (metric) units

The smallest metric measurement on the ruler below is the _____________.

How many divisions make up 1 cm? Answer:_______________

Examples: For each ruler determine the length of the line based on the

unit indicated.

(a)

Goals

Reading SI units

Converting SI units to Imperial units

___mm ___cm

___mm ___cm

(b)


When we use metric measurements for determining length it is based on

increments of 10

SI units Abbreviation Relationship between units

millimeter mm

centimetre cm 1 cm = 10 mm

metre m 1 m = 100 cm

kilometre km 1 km = 1000 m

(II) Comparing Imperial Units to SI Units & SI Units to Imperial Units

Example: (i) Determine the height of the door in the

indicated SI unit.

(ii) Use the conversion table to determine

the measurement in imperial units.

(iii) Measure the object in imperial units.

Item SI Measurement

(m)

Converted Imperial

Measurement

(nearest ft.)

Recorded Imperial

Measurement

(ft & in.)

Height of Door

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


Comparing SI Units to Imperial Units

(i) Determine the measurement of the identified item in SI units.

(ii) Use the conversion table to determine the measurement in

imperial units.

(iii) Measure the item in imperial units.

Item SI Measurement

(m)

Converted Imperial

Measurement

(nearest ft.)

Recorded Imperial

Measurement

(ft. & in.)

Width of

Smartboard

Length of Room

Comparing Imperial Units to SI Units

(i) Determine the measurement of the identified item in Imperial

units.

(ii) Use the conversion table to determine the measurement in SI

units.

(iii) Measure the item in SI units.

Item Imperial

Measurement

(ft. & in.)

Converted SI

Measurement

(m)

Recorded SI

Measurement

(m)

Your Height

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


Converting SI and Imperial Measurement

(I) Converting SI Measurement to Imperial Measurement

Ex. Convert to the imperial measurement indicated.

(a) 42 cm to inches

(b) 50 km/h to mph

(c) 100 m to yards

(d) 6 km to miles

Goals

Converting SI measurement to Imperial measurement

Converting Imperial measurement to SI measurement

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


(II) Converting Imperial Measurement to SI Measurement

Ex. Convert to the SI measurement indicated.

(a) 18 inches to cm

(b) 45 mph to km/h

(c) 20 yd. to meters

(d) 202 miles to km

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


P.90 #1d, f #2c, e #4d, e #5 #6a #7 #8a, b


Practice Sheet:

Converting SI and Imperial Measurement

1. Convert each length to centimetres. Round to the nearest tenth.

a) 9 inches b) 11 inches

2. Convert each SI length to the closest inch.

a) 5 cm b) 35 cm

4. Convert each to the nearest centimetre.

a) 5 feet b) 7 feet

5. Convert each SI distance to miles. Round each answer to the nearest 0.1 of a unit.

a) 5 km b) 15 km

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


6. Convert each imperial distance to SI units. Round each answer to the nearest tenth of a unit.

a) 5 mi b) 300 mi

7. A conservation officer is measuring the length of young salmon, or fry.

The average length is 2.54 in. What is this length in centimetres?

8. Brian’s driver’s licence lists his height as 181 cm. How tall is Brian in feet and inches?

9. Melissa is making blinds for her windows. In order to raise the blinds, she needs 80 yards

of string. How many metres of string are needed?

1 in = 25.4 mm

1 in = 2.54 cm

1 ft = 0.3048 m

1 yd = 0.9144 m

1 mi = 1.6093 km


Section 2.4 Working With Length

Applications of Measured Length

(I) Perimeter

When carpenters are building homes (as in the floor plan below) they have to install

trim such as baseboard within each room. How do they determine how much baseboard

to order before installing?

Goals

Solving problems that involve length,

perimeter or circumference of a circle

ANSWER:

______________________________________________________________

______________________________________________________________


Example: Calculate the perimeter of each rectangle.

(a) (b) length = 7 in. and width =

(II) Shipping Packages by Courier

A courier sometimes has to measure packages to determine shipping charges.

Review: Some shapes are circular and the distance around

a circle is known as the _______________

Formula is C = _____ or C = _____

Example: Determine the circumference for each circle to the nearest hundredth

of a unit.

(a) (b)

10 cm

4 cm

76 cm

18 in.


Example: To ship with Canada Post the

length + girth (distance around an object)

must be less than 3 m.

Example: Determine the length + girth measurement for each package below.

(a) (b)

5 cm

91 cm


P.98 – P.99 #1, #2a, b #6 #7 #8 #9 #10


Section 2.4 Working With Length

continued

(I) Application of Midpoint

A midpoint is a number half way between 2 numbers.

Example: Determine the number that represents the midpoint between

(a) 0 and 10 (b) 1 and 8

Example: Determine the midpoint distance (or half) of the given measurements:

(a) 28″ (b) (c)

Goals

Application problems that involve length

and midpoint


Example: Hanging Pictures

You purchase a picture that will be hung in the center of a wall that

is 1200 inches wide. There are 2 hooks on the back of the picture

that are 24 inches apart.

(a) Where is the midpoint of the wall?

(b) How far to the left and right of the midpoint will

you have to insert nails into the wall?

Example: Landscaping

You are going to build a semicircular flowerbed that will have a diameter of 9 feet

along the front foundation from the corner of the house to the main entrance which

measures 15 feet.

(a) Determine the midpoint of the foundation.

(b) How far from the corner of the foundation will

the flowerbed start?


P. 102 – 103 #1c, d, e #7, #8 a #9 a, b P. 104 #1, #2, #3

measuring length - qerhs math · pdf fileunit i measuring length 38 comparing si units to...

Documents