# MEASUREMENT by fjhuangjun

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LESSON 1: REVIEW AND PREVIEW

Rounding

Number     One   Ten       Hundred Tenth Hundredth    First  Second
Decimal Decimal
Place   Place
538.5968   539   540        500    538.6   538.60     538.6  538.60

Look at the number after the one trying to round and see if it is 5
or greater, if it is that number will move up one.

Using a graphing calculator to round off (page 2 of workbook)

Rounding feature: Math: 2: round

Example: round(0.95*0.83,2)=0.79

Use a graphing calculator to round off where indicated:

a. 10.6297 to three places __________(pg. 3, Ex. 2a)

b. 1.95 x 4.68 to 2 decimals __________ (pg. 3, Ex. 2d)

Scientific Notation: (pg. 4)

150 000 000 = 1.5 10
8

Find the first number and place a decimal point after it. Count to
the right starting with the first number after the decimal point, and

Ex. 75 300 000 = _____________ (pg. 4, Ex. 3a)
Measurement

Look on page 4 on how to use your graphing calculator for
Scientific Notation.

Substitution:

Find the value of each for the following if x = 2 and y = -3

a.   y2  7x  3   (pg. 6, Ex. 5a)

 3        7  2  3  8
2

b. v = 12, solve for t (pg. 7, Ex. 7a)
60 = vt

Converting a Fraction to Decimal: (pg. 7, Ex. 8ab)

5                                        7
a.   8                               b.      16

Converting a Decimal to a Fraction: (pg. 8)

124   31                                                 45 5
0.124                                                   0.45      
1000 250     (terminating)                               99 11   (repeating)

Assignment: pg. 9-13 #1-13

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Measurement

LESSON 2: ACCURACY AND PRECISION IN
MEASUREMENT

Accuracy: indicates how close a measurement comes to it’s real
value.

Measurement Error: Difference between a measurement and its
real value

Precision: how close a set of measurements are to one another
using the same measuring device.

Uncertainty: acceptable range of the measuring device. The
uncertainty is one-half of the smallest measuring scale on the
measuring device.

Class Ex. 2 ( pg. 16)

A player throws four darts in a game where the goal of the game is
to throw as many darts as possible in the centre. The first three
attempts are shown in the workbook.

a. Determine which diagram best represents the following
phrases:

i) accurate and precise       ii) precise but not accurate

iii)   neither accurate nor precise

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Measurement

Class Ex. 3 (pg. 16)

Rema has security bars installed in a door frame at her new home.
The installer uses a tape measure to measure the door frame at 0.86
m by 2.32m.
a. The precision of the measuring device is:

b. The uncertainty of the measurements are between:

Class Ex. 4 (pg. 17)

Explain whether or not the following measuring instruments are
appropriate for the given situation:

a. a track coach uses a watch with a precision of 1 second to
time runners in a 50m sprint

b. a bathroom scale with a precision of 1 pound to measure a
football players weight.

Assignment: pg. 17-20 #1-10

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Measurement

LESSON 3: MEASURING DEVICES

Units of Measure – Imperial and Metric

**Look over and read pg. 21 – 23

Review Handout

Class Ex. #1 (pg. 25)

a.                        b.

Class Ex. #2 (pg. 25)

63                 3 1 
3       inch           3     
a. Metric: ________, Imperial:       128        inch.    8 128 

b.Metric: __________, Imperial: _________

Homework: pg. 26-29 #1-3, 6, 7, 9

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Measurement

LESSON 4: PERIMETER, AREA, SURFACE AREA AND
VOLUME

Review and define the following:
Perimeter: Distance around a closed figure
Area: value expressed in units squared which is needed to cover a
surface
Surface Area: area needed to cover all surfaces of a solid.
Volume: amount of space in a solid

**Have students review pg. 31 of workbook

Give students the formula sheet to look over.

Class Example #1: (pg. 33)

a. Perimeter is 144
b. Perimeter: need to find circumference of circle first:

C  2 r
C  2 35
 219.8

219.8 + 95 +95 = 409.8

Class Example #3: (pg. 34)
a. A long rectangular garden has an area of 48 m squared. If
the length is 16m, then find the width of the garden:

b. A square driveway has an area of 121 m squared. Find the
lengths of its sides.

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Measurement

Class Example#4 (pg. 34)

a. V = l x w x h = 6 x 3 x 9 = 162/2= 81
SA = 117cm² (2 triangles + 2 rectangles + 1 rectangle)

Class Example #5:
a. The volume of a cone is determined to be 95 m cubed. If the
height of the cone is 5m, then find the radius to the nearest
tenth.

Homework: pg. 35-42 #1-16

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Measurement

LESSON 5: SURFACE AREA AND VOLUME OF SPHERES
AND OTHER SOLIDS

Recall Formula sheet:

Need:
Volume of a Sphere, Surface area of a cylinder and sphere

Class Example #1 (pg. 47)
The Shape of the planet Mars is approximately that of a sphere
with a diameter of about 6786km.

a. Calculate the surface area.

SA  4 r 2
1.46 108

b. Calculate the volume.
4
V   r3
3
1.6 1011

Class Example #2: (pg. 48)
Germain uses a rope to wrap the outer edge of a beach ball exactly
once. She then measured the distance the rope wrapped around the
ball by stretching it out straight and using a ruler to measure its
length. She determined the length to be 88.2cm.

What is the volume of the beach ball?

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Measurement

Class Example #4: (pg. 48)
The surface area of a sphere is 452.4 mm squared. Find the radius
to the nearest mm of the sphere.

Class Example #5: (pg. 48)
The volume of a basketball is 14 137 cm cubed. Find the radius of

Homework: pg. 49-52 #1-11

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Measurement

LESSON 6: CONVERSION

Look over conversion chart on page 54

Class Example#1: (pg. 55)

Use the charts to convert the following:

a. 60 in = 5ft (60/12)            b. 60ml = 2 US fl. Oz

c. 1 lb = ________ grains

d. 1 stone = ________ g

e. 5 yd = ______ in.

f. 2.5L = ________Tsp

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Measurement

g. 2.0573 m = ______ft. _______in

Homework: pg. 56-59 #1-11

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Measurement

LESSON 7: CONVERSION METRIC TO METRIC

Look over chart on page 61

Class Example#1: (pg. 61)
a. 75cm = _______m
b. 35g = ________ mg

Class Example #2: (pg. 61)
a. 12 megametres = _________cm
12 megametres = 12 000 000 m
1 m = 100 cm
12 000 000 x 100 = 1 200 000 000

To convert measurements in area with the chart, multiply the
number of places moved on the chart by two to determine the
number of decimal places moved in the conversion

Prefix   Kilo   Hecta-     Deca-   Metre    Deci-   Centi-      Milli
2       2          2      2        2        2          2
Symbol    km      hm        dam      m       dm       cm         mm

Class Example #3: (pg. 62)

a. 12m 2 = _____________mm 2

Move 3 places on the chart
3x2 = 6 place values to the right
12 000 000

b. 0.775km 2 = ____________________cm 2

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Measurement

To convert measurements in volume with the chart, multiply the
number of places moved on the chart by three to determine the
number of decimal places moved in the conversion

Class Example #4: (pg. 63)
a. 26m 3 = ____________mm 3

3 places on the chart (9 place values)
26 000 000 000

b. 389 275 cm 3 = ________________hm 3

Other common conversion in the metric system involve units of
litres to units of cubes:

1mL = 1 cm 3     1L = 1000cm 3 1L = 0.001m 3 1kL = 1m 3

Class Example #5:

a. 85 765cm 3 = __________ L

85765/1000= 85.765L

Homework: pg. 66-69 #1-5, 7,8,10-13

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Measurement

LESSON 8: LINEAR SCALE FACTORS AND PERIMETER

A linear scale factor describes the enlargement or reduction of
length and width of objects as a ratio.

A scale factor value greater than 1 describes an enlargement
A scale factor value between 0 and 1 describes a reduction

Class Example #1: (pg. 73)
Jordan increased the length and width of a rectangular 8’’ x 10’’
picture by a scale factor of 5:2

a. What is the linear scale factor value?

2.5

b. Is this an enlargement or reduction?

Enlargement

c. Calculate the new dimensions of the picture.

20’’ x 25’’

d. Show how the original perimeter and linear scale factor value
can be used to calculate the new perimeter.

Original perimeter = 36
New perimeter = 36 x 2.5 = 90

e. Verify this by calculating the perimeter using the new
dimensions.

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Measurement

Class Example #2 (pg. 73)
Kylie from Abstract Renovations designs a plan for a candy store
to be renovated. The scale drawing on the plan of the candy store
is 1cm: 50cm.

a. What are the actual dimensions of the storage room if the
scale drawing dimensions are 8cm x 12cm.

b. What are the dimensions on the plan if the dimensions of the
chocolate section of the store are to be expanded to be 3.5m x
4.75m?

Homework: pg. 74-76 #1-11

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Measurement

LESSON 9: LINEAR SCALE FACTORS AND AREA

Complete the chart:

Original     Original    Linear      New     New Area       Area
Area        Scale   Dimensions                Scale
Factor                            Factor
A         3x5                 2     2:1      6x10             2       4:1
15cm                            60cm
B         2x6                2      3:1      6x18           2         9:1
12 cm                          108cm
C          8x2                2    1:2        4x1             2       1:4
16cm                             4cm
2
D          9x6         54cm        1:3        3x2         6           1:9

Class Example #1: (pg. 80)
Maggie has scanned an 8’’ x 10’’ photograph to her computer to
enlarge and reduce.

a. Maggie would like to increase the size by 40%. Determine
the linear scale factor and the area scale factor.

Scale factor of 1.4 is 7:5 or 1:1.4
Area scale factor is 49:25 or 1:1.96

b. Explain why these scale factors are different.

One is the linear scale and the other is the area scale (squared)

c. Determine the new dimensions of the photograph.

d. Calculate the area the printer must cover by the following
two methods.

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Measurement

i)    Using the dimensions of the enlargement:

ii)   Using the original area and the area scale factor
value:

e. Maggie must also produce a print which will be reduced by
25% . What will the new dimensions and area of the
photograph be?

Leave 75% of the original.
3:4
8 x 0.75 = 6
10 x 0.75 = 7.5
New Area is 6 x 7.5 = 45
(9:16 = 0.5625 x 80 = 45)

Homework: pg. 81 #1-7

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Measurement

LESSON 10: LINEAR SCALE FACTORS, SURFACE ARE
AND VOLUME

Complete page 85 of workbook

Linear Scale Factor is a ratio in the form a:b which describes an
enlargement or reduction of 1 dimensional figures.

Linear Scale Factor Value is a number which describes how
many times to enlarge or reduce a 1-D figure. To calculate the
linear scale factor value (new dimension / original dimension)

Area Scale Factor is a ratio in the form c:d which describes the
area of an enlargement or reduction of a 2-D figure.

Area Scale Factor Value is a number which describes how many
times to enlarge or reduce the area of a 2-D figure. To calculate
the scale factor value use (new area / original area)
The area scale factor value = (linear scale factor value) 2

Surface Area scale factor is a ratio in the form c:d which
describes the surface area of an enlargement or reduction of a 3-D
figure. When c is greater than d, it is an enlargement

Surface Area Scale Factor Value is a number which describes
how many times to enlarge or reduce the surface area of a 3-D
figure. To calculate the area scale factor value use (new area /
original area).
The area scale factor value = (linear scale factor value) 2

Volume Scale Factor is a ratio in the form e:f which describes the
surface area of an enlargement or reduction of a 3-D figure.

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Measurement

Volume Scale Factor Value is a number which describes how
many times to enlarge or reduce the surface are of a 3-D figure.
To calculate the area scale factor value use (new volume / original
volume).
The volume scale factor value = (linear scale factor value) 3

Complete the chart on pg. 86 and 87 of the workbook

Class Example #2: (pg. 89)
Sllab Ltd. Produces beach balls with a diameter of 30cm. To
increase the profile of the company in the market place the
company hires Jen from Word of Mouth Advertising. She
suggests to produce large beach balls with a diameter of 1.5m.

a. The surface area and volume of the beach balls with a
diameter of 30cm have been calculated below. Calculate the
surface area and volume of the beach ball with a diameter of
1.5m to the nearest tenth.

SA of 30 cm ball = 2827.4cm 2
V of 30 cm ball = 14 137.2cm 3
SA of 150cm ball = ____________
V of 150 cm ball = _____________

b. Determine the following:

i)     linear scale factor: 30:150 = 1: 5
ii)    Surface Area Scale Factor: 1:25
iii)   Volume Scale Factor: 1:125

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Measurement

c. Show how to use the volume scale factor to determine the
linear scale factor value.

d. Show how to use the volume scale factor value to determine
the area scale factor value.

e. Sllab. Ltd decides to produce a beach ball with a volume
scale factor of 216:64 from the original. Determine the new
surface area of the ball to the nearest tenth.
3
216 : 64  6 : 4  3 : 2 = linear scale factor

Surface area scale factor = 
3: 2   9 : 4
2

9
SAnew  2827.4    6361.7cm 2
4

Homework: pg. 90-92 #1-7

Lesson 11: Quiz
Lesson 12: Review
Lesson 13: Exam
Lesson 14: Project (2-3 days)

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