Transcript Measurement Powerpoint

Measurement
Year 7 & 8
missburkerocks.wordpress.com
missburkerocks.wordpress.com
Length
A
length is a distance.
 In Australia we use the metric system for
measurement and the base unit is the metre.
 The length of an object is commonly measured
in:




millimetres (mm)
centimetres (cm)
metres (m)
kilometres (km).
missburkerocks.wordpress.com
 1km
= 1000m (km
m = x1000)
 1m = 100cm (m
cm = x100)
 1cm = 10mm (cm
mm = x10)
From this information you can create a
Length conversion chart:
1000
100
10
km
m
cm
mm
1000
100
10
missburkerocks.wordpress.com
Length Conversions
1. Write the question.
2. Use the conversion chart to identify
conversion factor.
3. Multiply or divide original measurement.
4. Put correct units.
Eg/ Complete the following metric
conversions.
a) 756m=__________ km
b) 0.034km (m)
c) 374cm=_________m
d) 54cm (mm)
e) 380mm (cm)
f) 374cm (km)
missburkerocks.wordpress.com
Length Conversions
missburkerocks.wordpress.com
Length Conversions
missburkerocks.wordpress.com
Classwork
Year 7
Text: Cambridge Essential
Maths 7: Chapter 11
 Ex 11B Q4a-f, 5a-c, 6g-h,
7a-f, 10a, b, 12, 13, 17, 19
missburkerocks.wordpress.com
Length Conversion: Exit questions
Complete the following metric conversions.
a)
b)
c)
d)
38m=__________ km
24cm=_________mm
49cm (m)
380m (mm)
missburkerocks.wordpress.com
Geometric symbols
 Similarly
marked
segments are
congruent (the same
length)
A
box in the corner of
an angle denotes a
right angle
missburkerocks.wordpress.com
Perimeter
 Perimeter
is the measurement of the
distance (length) around the outside of a
2D shape.
8cm
5cm
 To
calculate the perimeter of an object
we add the length of all of the sides
together once they are in common units.
missburkerocks.wordpress.com
Calculating Perimeter
1.
2.
3.
4.
Convert all dimensions (measurements) to the same units (mm,
cm, m, km).
Calculate and record any missing lengths.
Add all lengths together.
Put correct units.
5m
Examples:
1.
3.
8cm
5c
m
2.
9m
m
8mm
98cm
4m
4m
4cm
4.
9cm
10m
missburkerocks.wordpress.com
Calculating Perimeter
missburkerocks.wordpress.com
Calculating Perimeter
missburkerocks.wordpress.com
Calculating Perimeter
missburkerocks.wordpress.com
Classwork
Year 7
Text: Cambridge
Essential Maths 7:
Chapter 11
 Ex 11C Q1, 3, 4, 5,
6, 8, 11
Remember to show
all working
Year 8
Text: Cambridge
Essential Maths 8:
Chapter 4
Ex 4A Q3, 5a,b,e,f,I,j,m,n,
6, 7c-f, 8a-d, 10
Remember to show all
working
missburkerocks.wordpress.com
Perimeter: Exit questions
missburkerocks.wordpress.com
Area



1c
m
Area is the amount of space inside a 2D shape.
The area is measured in squared units (mm2, cm2, m2 or km2).
Units are squared units as you are calculating how many 1x1
squares would fit inside the shape!
if 1cm = 10mm
then 1cm x 1cm = 10mmx10mm
=102 mm2
=100mm2
 1km2=1
000 000m2 (km2
 1m2=10 000cm2 (m2
 1cm2=100mm2 (cm2
10mm
m2= x10002)
cm2= x1002)
mm2= x102)
missburkerocks.wordpress.com
Calculating Areas of 2D shapes
1. Convert all dimensions (measurements)
to the same units (mm, cm, m, km).
2. Write formula and dimensions.
3. Substitute values into formula.
4. Solve.
5. Put correct units.
missburkerocks.wordpress.com
Area (Year 7&8)
missburkerocks.wordpress.com
Area (Year 7&8)
missburkerocks.wordpress.com
Area (Year 7&8)
missburkerocks.wordpress.com
Area (Year 7&8)
Area (Year 8)
missburkerocks.wordpress.com
Area (Year 8)
missburkerocks.wordpress.com
Area (Year 8)
missburkerocks.wordpress.com
missburkerocks.wordpress.com
Classwork
Year 7
Text: Cambridge
Essential Maths 7:
Chapter 11
 Ex 11D 6a-f
 Ex 11E 4a-e
 Ex 11F 3a-d
Remember to show all
working
Extension
 Ex 11D 7, 10, 12
 Ex 11E 3, 6, 10, 11
 Ex 11F 6, 8
Year 8
Text: Cambridge
Essential Maths 8:
Chapter 4
 Ex 4C 5a-f
 Ex 4D 3a,b,d,e,g,h,j,k
Remember to show all
working
Extension
 Ex 4C 1a,b, 2, 6
 Ex 4D 6, 7, 8
missburkerocks.wordpress.com
Area: Year 7 exit questions
Write the formulae for the following shapes
a)
b)
c)
d)
e)
f)
missburkerocks.wordpress.com
Area Conversions

1c
m
Remember: Area is the amount of space inside a 2D
object. Units are squared units as you are calculating
how many 1x1 squares would fit inside the shape!
if 1cm = 10mm
then 1cm x 1cm = 10mmx10mm
=102 mm2
=100mm2
 1km2=1
000 000m2 (km2
 1m2=10 000cm2 (m2
 1cm2=100mm2 (cm2
10mm
m2= x10002)
cm2= x1002)
mm2= x102)
missburkerocks.wordpress.com
Area continued
 From
this you can create an area
conversion chart:
km2
10002
10002
m2
1002
1002
cm2
102
102
mm2
missburkerocks.wordpress.com
Area conversion
missburkerocks.wordpress.com
Area conversion
missburkerocks.wordpress.com
Circles


Diameter (D): The distance across a circle from one side
to the other, passing through the centre.
Radius (r): The distance from the side of a circle to the
centre.
D


r
Calculations for measurements involving circles involve
a special number called π (pi pronounced pie).
The value of πis close to 3.14159… However, you should
always use the πbutton on your calculator when
calculating with πunless told otherwise.
missburkerocks.wordpress.com
Circumference of a circle
 The
circumference of a circle is the
distance around the outside (perimeter)
of a circle.
The formula for the circumference of a circle
is:
Circumference =πx Diameter
=πD
or
C=2πr
Circumference = 2xπxradius
=2πr
To remember:
Twinkle, Twinkle little star
Circumference of a circle is
2πr
missburkerocks.wordpress.com
Area of a circle
 The
formula for the area of a circle is:
Area = πx radius x radius
=πr2
Area =πx r x r
=πr2
missburkerocks.wordpress.com
Circumference and Area of a circle: Examples
Calculate the circumferences and areas of the
following circles.
a)
b)
8cm
20mm
c)
d)
52km
13m
missburkerocks.wordpress.com
Area of a circle
missburkerocks.wordpress.com
Area of a circle
missburkerocks.wordpress.com
Classwork
Year 8
Text: Cambridge Essential
Maths 8: Chapter 4
 Ex 4B Q5a,b,d,e
 Ex 4E Q3, Q5a,d,e, Q6a,d,f
Remember to show all working
Extension:
 Ex 4B Q6
 Ex 4E Q
missburkerocks.wordpress.com
Circles: Exit questions
Calculate the circumferences and areas of
two circles below.
a)
b)
25cm
5km
missburkerocks.wordpress.com
Area of a circle
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas of composite shapes
missburkerocks.wordpress.com
Areas and perimeters of
sectors
A
sector is a portion of a circle enclosed
by two radii.