# Unit 7 - Cloudfront.net ```Name:_______________________________
Measurement:
Two-Dimensional
This unit bundles student expectations that address length and area in order to investigate
measurement relationships.
Prior to this unit, in Grade 5 Unit 06, students connected the area model used to represent
multiplication with the concept of area as a measure. During this unit, students explore measurement
relationships within formulas for length, including perimeter, circumference, and area. In addition,
students investigate pi to describe the relationships between the diameter, radius, and circumference of
a circle. After this unit, in Grade 6 Unit 08, students will continue to explore measurement concepts to
include standard measurement conversions, capacity, weight, time, temperature, and volume. In Grade
7 Unit 08, students will estimate measurements and solve application problems involving the length and
area of polygons and other shapes as well as the volume of prisms and cylinders.
--------------------------------------------------------------------------------------------------------------------------6.4B: The student uses letters as variables in mathematical expressions to describe how
one quantity changes when a related quantity changes. The student is expected to: Use
tables of data to generate formulas representing relationships involving perimeter and
area.
-----------------------------------------------------------------------------------------------------------------------------------------------------6.6C: The student uses geometric vocabulary to describe angles, polygons, and circles.
The student is expected to: Describe the relationship between radius, diameter, and
circumference of a circle.
-----------------------------------------------------------------------------------------------------------------------------------------------------6.8A: The student solves application problems involving estimation and measurement of
length, and area. The student is expected to: Estimate measurements (including
circumference) and evaluate reasonableness of results.
-----------------------------------------------------------------------------------------------------------------------------------------------------6.8B: The student solves application problems involving estimation and measurement of
length, and area. The student is expected to: Select and use appropriate units, tools, or
formulas to measure and to solve problems involving length (including perimeter), and
area.
Perimeter
Definition for Perimeter: the distance around a
two-dimensional shape.
Memory Aid for Perimeter:
Formulas for Perimeter:
Square: P = 4s
P  Perimeter
s  side length
Rectangle: P = 2l + 2w
P  Perimeter
l  length
w  width
*You can also find the perimeter by adding all of
the side lengths together.*
Perimeter Practice
14 ft
86 in.
16 in.
48 yd
39 mi
24.2 km
32 km
154 cm
Area
Definition for Area: the amount of space inside the
boundary of a flat (2-dimensional) object
Memory Aid for Area:
Different Ways to Find the Area:
1) Counting the Square Units:
1
6
11
16
21
2
7
12
17
3 4
8 9
13 14
18 19
22 23 24
5
10
15
20
25
2
25 units
A=______________
22
1 2 3 4 5 6
1
7 8 9 10 11 12
13 14 15 16 17 18
23 2 3
19 20 21 22 23 24
4 5 6
25 26 27 28
24 7 8 9 10
29 30 31 32
11 12 13 14 15
24.5
33 34 35 36
16 17 18 19 20 21
2
36 units
B=______________
2
24.5 units
C=______________
2) Using a formula:
Formula for area of a Square: A = s2
(Area = side squared)
s
Formula for area of a Rectangle: A = lw
OR
A  area
l  length
w or h
w  width
A = bh
A  area
b  base
h  height
l or b
Formula for area of a Parallelogram: A = bh (Area = base x height)
h
h
b
𝒃𝟏+𝒃𝟐 𝒉
Formula for area of a Trapezoid: A =
𝟐
b1
A Area
b1  base 1
b1  base 2
h  height
h
b2
Formula for area of a Triangle: A =
h
b
𝒃𝒉
𝟐
(Area = base x height &divide; 2)
Area Examples
Square:
A = s2
A = (4)2
A=4x4
4 cm
A = 16 cm2
-----------------------------------------------------------------------------------------------------------------------------------------------------Rectangle:
A = lw
OR
A = bh
8 yd
A = (17)(8)
A = (17)(8)
2
A = 136 yd
A = 136 yd2
17 yd
-----------------------------------------------------------------------------------------------------------------------------------------------------Parallelogram:
6m
5m
6 in.
A = bh
A = (9)(5)
9m
A = 45 m2
-----------------------------------------------------------------------------------------------------------------------------------------------------Trapezoid:
8 in.
A = (b1 + b2)h
2
7 in.
7 in.
A = (8 + 10)6
2
A = (18)6
10 in.
2
A = 108
2
A = 54 in.2
-----------------------------------------------------------------------------------------------------------------------------------------------------Triangle:
A = bh
2
5 km
5 km
A = (6)(4)
2
A = 24
2
6 km
A = 12 km2
4 km
Area Practice
36
2
cm
14 m2
72
2
yd
99
2
yd
71.5
2
ft
22.5 m2 21 m2
105
2
m
110
2
ft
Parts of a Circle
Definition for Radius: a straight line that is the distance from
the center to the edge of a circle
Definition for Diameter: a straight line going through the center
of a circle connecting 2 points on the cirlcle
Memory Aid for Diameter:
Relationship between the Radius and the Diameter:
The radius x 2 = the diameter
The diameter &divide; 2 = the raidus
Definition for Chord: a straight line connecting 2 points on the
circle
Memory Aid for Chord:
Parts of a Circle Practice
diameter
chord
center
chord
center
diameter
chord
center
Circles
Definition for Circumference: the distance
around the edge of a circle. The perimeter
of a circle.
Memory Aid for Circumference and Area of a Circle:
Formula for Circumference:
C = 2𝝅r
OR
C = 𝝅d
C  Circumference
C  Circumference
𝝅  Pi = ~3
𝝅  Pi = ~3
d  diameter
Formula for Area of a Circle:
A = 𝝅 r2
Circumference and Area Practice
1)
AB = 13 cm
XY = 11 cm
66 cm
Circumference=___________________
363 cm2
Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
2)
ZX = 10 in.
WK = 4 in.
YW = 6 in.
30 in.
Circumference=___________________
75 in.2
Area=____________________
----------------------------------------------------------------------------------------------------------------------------------3)
XM = 2 m
YX = 8 m
NL = 5 m
30 m
Circumference=___________________
75 m2
Area=____________________
----------------------------------------------------------------------------------------------------------------------------------4)
WY = 16 ft
RX = 14 ft
48 ft
Circumference=___________________
192 ft2
Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
5)
BA = 21 mi
XC = 18 mi
108 mi
Circumference=___________________
972 mi2
Area=____________________
Table Practice
Table Practice
Volume
Definition for Volume: The amount of 3dimensional space an object occupies.
Formulas for Volume:
Cube: V = s3
Volume = side x side x side
s
Rectangular Prism: V = lwh
Volume = length x width x height
s
s
h
l
w
Volume Practice
24 mi3
512 cm3 360 km3
44,268 ft3
64 cm3 1,386 in.3
Perimeter  units
Area  units
Volume 
2
3
units
1
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