Download - Name:_______________________________ 6 th Grade Math- Unit 7 Measurement: Two-Dimensional
Name:_______________________________
6th Grade Math- Unit 7
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:
A=______________ B=______________ C=______________
1 2 3 4 56 7 8 9 10
111213141516171819202122232425
1 2 3 4 5 67 8 9 10 11 1213 14 15 16 17 1819 20 21 22 23 2425 26 27 2829 30 31 3233 34 35 36
12 3
4 5 67 8 9 10
11 12 13 14 15
16 17 18 19 20 21
22
23
24
24.5
25 units2 36 units2 24.5 units2
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 = bh
A area A area l length
b base w or h w width
h height
l or bFormula for area of a Parallelogram: A = bh (Area = base x height)
h Formula for area of a Trapezoid: A =
A Areab1 base 1b1 base 2h height
Formula for area of a Triangle: A = (Area = base x height ÷ 2)
h
b
h
b1
b2
h
b
Area ExamplesSquare: A = s2
A = (4)2
A = 4 x 4 4 cm A = 16 cm2
------------------------------------------------------------------------------------------------------------------------------------------------------Rectangle: A = lw OR A = bh 8 yd A = (17)(8) A = (17)(8)
A = 136 yd2 A = 136 yd2
17 yd------------------------------------------------------------------------------------------------------------------------------------------------------Parallelogram:
6m 5 m A = bhA = (9)(5)
9 m 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)
2A = 24 2
6 km A = 12 km2
6 in
.
4 k
m
Area Practice
36 cm2
99 yd2
71.5 ft2
14 m2 22.5 m2
21 m2
72 yd2
105 m2
110 ft2
Parts of a Circle Definition for Radius: a straight line that is the distance from the center to the edge of a circle Memory Aid for Radius:
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 diameterThe diameter ÷ 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
center
radius
center
chord
chord
radius
chord
diameter
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 = 2r OR C = dC Circumference C Circumference Pi = ~3 Pi = ~3r radius d diameter
Formula for Area of a Circle:A = r2
Area = 3 x radius x radius
Circumference and Area Practice
1) AB = 13 cm XY = 11 cm
Circumference=___________________ Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
2) ZX = 10 in. WK = 4 in.YW = 6 in. Circumference=___________________
Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
3) XM = 2 mYX = 8 mNL = 5 m
Circumference=___________________Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
4) WY = 16 ftRX = 14 ft
Circumference=___________________Area=____________________
-----------------------------------------------------------------------------------------------------------------------------------
5) BA = 21 miXC = 18 mi
Circumference=___________________Area=____________________
66 cm 363 cm2
30 in. 75 in.2
30 m 75 m2
48 ft 192 ft2
108 mi 972 mi2
Table Practice
Table Practice
Volume Definition for Volume: The amount of 3-dimensional space an object occupies.
Formulas for Volume:
Cube: V = s3
Volume = side x side x side
s s sRectangular Prism: V = lwhVolume = length x width x height
h
l w
Volume Practice
24 mi3 512 cm3
360 km3
44,268 ft3
64 cm31,386 in.3
Perimeter units 1
Area units 2
Volume units3