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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:________
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(II) Reading Halves on a Measuring Tape
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(III) Reading Quarters on a Measuring Tape
Answer:________ Answer:________
Answer:________
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(IV) Reading Eights on a Measuring Tape
Answer:________ Answer:________
Answer:________
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(V) Reading Tape Lengths
Ans:________
Ans:________
Ans:________
Ans:________
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Practice Problems:
State the imperial length for each diagram below.
1.
2.
3.
4.
5.
6.
7.
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Use the tape below to determine the indicated length.
Ans:________
Ans:________
Ans:________
Ans:________
Ans:________
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Note: The smallest measurement (in Red) is in the
______________ position.
Practice Problems:
Ans:________
Ans:________
Ans:________
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State the imperial length for each diagram below.
1.
2.
3.
4.
P.62 – P.63 #5 and #6
5.
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Reading Imperial Tape MeasurementsState the indicated tape lengths.
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(I) Quarter Measurements1. Tape measurement = _________
2. Tape Measurement = _________
(II) Eighth Measurements
3. Tape measurement = _________
4. Tape Measurement = _________
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5. Tape Measurement = _________
6. Tape Measurement = _________(III) Sixteenth Measurements
7. Tape Measurement = _________
8. Tape Measurement = _________
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9. Tape Measurement = _________
(IV) Mixture of Measurements
10. Tape Measurement = _________
11. Tape Measurement = _________12. Tape Measurement = _________
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Reading Imperial Tape Measurements
1. Tape
measurement = _________2. Tape Measurement = _________
13. Tape Measurement = ___________
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3. Tape measurement = _________
4. Tape Measurement = _________5. Tape Measurement = _________
6. Tape Measurement = _________
7. Tape Measurement = ___________
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8. Tape Measurement = _______
9. Tape Measurement = _________
10. Tape Measurement = _________
11. Tape Measurement = ___________
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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.
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Using referents for imperial units
Unit ReferentInch (in.) Thumb LengthFoot (ft.) Foot Length
Yard (yd.) Arm spanMile (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.
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Classroom Activity – Using References to Approximate Length
Item Referent Estimated Measurement
Actual Measurement
Desk Width of hand ≈ 4“
Item 1 Length of Pencil
Example 1 Estimating Lengths Using Imperial Units
Describe how you would estimate the width (across) your desk.
SolutionThe 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.
Unit I Measuring Length 22
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.
Item 3 Length of a floor tile
Item Referent Estimated Measurement
Actual Measurement
Pencil Thumb (Tip to first joint) ≈ 1“
Item Referent Estimated Measurement
Actual Measurement
Textbook Width of hand ≈ 4“
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Use the length of your foot to determine the length of one floor tileto 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 anoutstretched 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 thetape to determine the actual measure.
Converting Imperial Units
Item Referent Estimated Measurement
Actual Measurement
Floor Tile Foot (Back of heel to toe) ≈ 1 foot
Item Referent Estimated Measurement
Actual Measurement
Width of Classroom
Arm span ≈ 3 ft.
Goals
Converting Inches to Feet
Converting Feet to Inches
Adding Feet and Inches
Converting Miles to Yards
QUESTION: Why is it necessary to have standardized measurements for length instead of using referents as a means to measuring?
______________________________________________________________
______________________________________________________________
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(I) Converting Inches to Feet
(II) Converting Feet to Inches
1 ft. = 12 in.
1 ft. = 12 in.
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(III) Adding Feet and Inches
(IV)Converting Miles to Yards
1 mi. = 1760 yds
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Practice Sheet for Imperial Measurement
1. Express each of the following in feet and inches:
P.68 - 69 #3, #4, #6, #7
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(a) 9″ + 13″ (b) 4′ 5″ + 3′ 3″
(c) 6′ 5″ + 8′ 11″ (d) (2′ 7″) x 3
(e) 1′ 11″ + 6″
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Reading SI (Metric) Measurements
SI units Abbreviation Relationship between unitsmillimeter mmcentimetre cm 1 cm = 10 mm
metre m 1 m = 100 cmkilometre 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
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(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)
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(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
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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 ofDoor
5. Width of the Textbook
Item SI Measurement(mm)
SI Measurement(cm)
SI Measurement(m)
Width ofTextbook
6. Inside Width of One Window Pane
Item SI Measurement(mm)
SI Measurement(cm)
SI Measurement(m)
Window Pane
Relating SI and Imperial Units
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(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 theunit indicated.
(a)
Goals
Reading SI units
Converting SI units to Imperial units
___mm ___cm
___mm ___cm(b)
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When we use metric measurements for determining length it is based on increments of 10
SI units Abbreviation Relationship between unitsmillimeter mmcentimetre cm 1 cm = 10 mm
metre m 1 m = 100 cmkilometre 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 theindicated SI unit.
(ii) Use the conversion table to determinethe measurement in imperial units.
(iii) Measure the object in imperial units.
Item SI Measurement(m)
Converted ImperialMeasurement(nearest ft.)
Recorded ImperialMeasurement
(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
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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 ImperialMeasurement(nearest ft.)
Recorded ImperialMeasurement
(ft. & in.)Width of
SmartboardLength 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 SIMeasurement
(m)
Recorded SIMeasurement
(m)
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Your Height
Converting SI and Imperial Measurement
(I) Converting SI Measurement to Imperial Measurement
Ex. Convert to the imperial measurement indicated.
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
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
Unit I Measuring Length 37
(a) 42 cm to inches
(b) 50 km/h to mph
(c) 100 m to yards
(d) 6 km to miles(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
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
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(c) 20 yd. to meters
(d) 202 miles to km
P.90 #1d, f #2c, e #4d, e #5 #6a #7 #8a, b
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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
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
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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
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.
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
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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?
Section 2.4 Working With Length
Applications of Measured Length
(I) PerimeterWhen carpenters are building homes (as in the floor plan below) they have to installtrim such as baseboard within each room. How do they determine how much baseboardto order before installing?
Goals
Solving problems that involve length, perimeter or circumference of a circle
Unit I Measuring Length 42
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 arounda circle is known as the _______________
10 cm
4 cmANSWER:______________________________________________________________
______________________________________________________________
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Formula is C = _____ or C = _____
Example: Determine the circumference for each circle to the nearest hundredthof a unit.
(a) (b)
Example: To ship with Canada Post the
length + girth (distance around an object)
must be less than 3 m.
76 cm18 in.
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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
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Section 2.4 Working With Lengthcontinued
(I) Application of Midpoint
A midpoint is a number half way between 2 numbers.
Goals
Application problems that involve length and midpoint
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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)
Example: Hanging Pictures
You purchase a picture that will be hung in the center of a wall thatis 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
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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 whichmeasures 15 feet.
(a) Determine the midpoint of the foundation.
(b) How far from the corner of the foundation willthe flowerbed start?
P. 102 – 103 #1c, d, e #7, #8 a #9 a, b P. 104 #1, #2, #3
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