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