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Chapter 2
Measuring Length
Math 1202
2.1 Imperial Length Measurements
Reading a ruler/measuring tape
· A ruler has both inches and centimeters.
· The imperial unit of measuring is inches and uses fractions, not decimals.
· There are 16 marks between 0 and 1 inch (symbol ").
· The first mark represents ".
Ex) A partial ruler is shown. Fill in the measurements between 0 and 1.
When measuring in imperial units, remember to give your answer in fractional form.
Ex) Give the length of each line:
1) 2)
3) 4)
5) 6)
Try “The RULER Game” http://www.globalclassroom.org/rulergame200/index.html
Assign pages 62-63 #’s 5 & 6
Imperial Lengths
Inch
· smallest imperial unit of measurement.
· can be broken into halves, quarters, eighths and sixteenths.
1 Foot = 12 inches
1 Yard = 3 Feet
Or 36 inches
1 Mile = 1760 yards
Or 5280 Feet
Or 63360 inches
Adding Imperial Units
1) Add units in same measure (ie inches & inches, feet & feet, etc)
2) Regroup 1 foot for every 12 inches
3) Regroup 1 yard for every 3 feet
4) Regroup 1 mile for every 1760 yards.
Ex) Add the following
1) 10 in. + 6 in. 2) 8 in. + 11 in.
3) 10 " + 8 " 4) 7" + 7"
5) 6 ft. 8 in. 6) 10 ft. 7 in.
+ 7 ft. 10 in. + 12 ft. 9 in.
7) 10 ft. 11 in. 8) 14 ft. 5 in.
+ 9 ft. 4 in. + 3 ft. 9 in.
Using Referents to estimate Imperial measurements
A referent is an object that can be used to estimate a measurement. Many units in the imperial system can be estimated using referents based on measurements on your body.
Do Activity on page 65 (See handout)
Some common referents for linear measurement include:
Imperial Unit / ReferentInch (in.) / Length from thumb to first knuckle
Thickness of hockey puck
Foot (ft.) / Length from elbow to wrist
Length of average foot
Length of standard floor tile
Length of a sub sandwich
Yard (yd.) / Length from tip of nose to outstretched fingers
Average length of guitar
Mile (mi.) / Distance you can walk in 20 minutes
Questions
When might you use a referent for measuring?
Why is a referent not always a good measurement?
Give some situations where exact measurements are important.
Do pages 66- 67 #’s 1 , 3, 10, 11 & pages 68-69 #’s 3-7
2.2 SI Length Measurements
Metric Lengths
· Common linear measures in increasing order include millimeter, centimeter, meter, and kilometer
· Conversion is easier since you multiply or divide by powers of 10, which means you move the decimal left or right.
· A ruler or measuring tape usually has metric units on one side and imperial units on the other.
1 cm = 10 mm 1 m = 100 cm 1 km = 1000
When measuring in metric units, you give your answer in decimal form.
Ex) Give the distance in cm and mm from the end of the ruler to the arrow:
1)
cm:______
mm:______
2)
cm:______
mm:______
3)
cm:______
mm:______
4)
cm:______
mm:______
Do pages 74 - 75
2.3 Length Conversions
Length conversions may be necessary between imperial and metric measurements
Equivalent Lengths / Converting from____ to ____ / What to do1 in. ≈ 2.5cm / inches (in) to centimetres (cm)
centimetres (cm) to inches (in) / × in by 2.5
÷ cm by 2.5
1ft. ≈ 30 cm / feet (ft) to centimetres (cm)
centimetres (cm) to feet (ft) / × ft by 30
÷ cm by 30
1 m ≈ 3 ft. / meters (m) to feet (ft)
feet (ft) to metres (m) / × m by 3
÷ ft by 3
1 km ≈ 0.6 mi. / kilometers (km) to mile (mi) / × km by 0.6
1 mi. ≈ 1.6 km / miles (mi) to kilometers (km) / × mi by 1.6
Ex) Convert each of the following:
1) 11 in. = ______cm 2) 18 cm = ______in.
3) 12 ft. = ______cm 4) 45 cm = ______ft.
5) 2.5 m = ______ft 6) 35 ft = ______m
7) 85 km = ______mi. 8) 125 mi. = ______km
2.4 Working with Length
Circumference is the distance around a circle.
Circumference Formula: or
Ex) Find the circumference of each circle:
Perimeter of a rectangle is the sum of all its sides
Perimeter of rectangle formula:
Ex) Find the perimeter of each rectangle
Girth is the distance around an object at a 90˚ angle to the length.
Many shipping companies and mail services use measurements like length+girth to determine the cost of shipping a package.
Ex) What is the length + girth measurements of each object?
Assign pages 98-99 #’s 1-10
Finding Midpoints
Midpoint: is the halfway point between two values.
Instances where you may need to find the midpoints include:
· hanging pictures
· finding the centre of a ceiling to install a light fixture
· finding the centre of a floor to install ceramic tile
· finding the centre of a sheet of plywood to create a circular table
Some strategies for determining the midpoint of a linear measurement include:
· dividing the given or measured total length by 2
· using a string to cover the full distance, fold it in half and use this distance to locate the middle
· constructing diagonals, where the point of intersection is the middle
Ex 1) You want to hang the mirror below. A hanger needs to be places 6 cm from the top and centered. Where should you put the hanger?
Ex 2) You want to hang the picture below. A hanger needs to be places 3 cm from the top and centered. Where should you put the hanger?
Assign pages 102-105