Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6 MAP 2 D Quarter 3...

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

MAP2D

Quarter 3Instructional Strategies

Grade 6


MAP2D

Chapters 8 and 9GeometryGrade 6


Adjacent and Vertical Angles

1

23

Vertical Angles :

angles that are opposite of one another.

1 and 2 are adjacent angles.

Adjacent Angles :

angles that are next to each other.

1 and 3 are vertical angles.


Vertical Angles

Vertical angles are the angles opposite each other when 2 lines cross.

Vertical angles are congruent.

a°

b°

a = b


Vertical Angles

Vertical angles are the angles opposite each other when 2 lines cross.

Vertical angles are congruent.

c° d°

c = d


Adjacent Angles

“Adjacent” means “next to”.

Adjacent angles are next to each other, sharing one side.


Complementary AnglesComplementary angles add up to

90°.


Supplementary Angles

Supplementary angles add up to 180°.


Triangle Sum Property1

2 3

1

32

For any triangle, the sum of the

measures of the interior angles is

always 180º.

1

2

3


m1 + m2 + m3 = 180º

1. Write the equation:

2. Fill in the angle measures

3. Solve the equation for the missing value.

73º

xº

m1 + m2 + m3 = 180º90º 73

ºx

163º + x = 180º

163º+x –163º= 180º–163º

x = 17º

Solve for a Missing Angle in a Triangle


AREAof a circle

Area = r 2

3.14

Area is the space inside the circle.

r = radius


Circumference of a Circle

C = d 3.14Circumference is the distance

around a circle or sphere.

d = diameter


Leaving Answers in Terms of Pi

Instead of multiplying by 3.14, leave the π symbol.

Like a variable, it should appear after a coefficient.

8

C = πd

C = π 2r C = π 2 8

C = 16π

A = πr 2

A = π 82 A = π 64

A = 64π


Estimating with Piπ ≈

3.141592653589793238462643383279502884197169399375105820974944592307816

4062862089986280348253421170679…

JUST USE 3

8

C = πd C = π 2r C = π 2 8 C = 16π

A = πr 2 A = π 82 A = π 64 A = 64π

C ≈ 16 3 C ≈ 48

A ≈ 64 3 A ≈ 192


Area vs. VolumeVolume is the amount of space inside a prism. It is

measured using cubic units.

Remember, area is the space inside a flat figure. It is

measured using square units.


Finding The Volume Any Prism

Volume of a prism = Area of one Base height

V = B hheight

Area of the Base


Volume of a Rectangular Prism

Volume =

area of the Base

x height

V = B h

V = lw h

h


Find the Volume of a Rectangular Prism

m 11

m 24 2

h

B

V Bh

Step 1: Use the formula forthe volume of a prism

Step 4: Simplify

Step 2: Identify B and h.

Step 3: Substitute 24 for B,and 11 for h.

Remember B is thearea of the base. In this

case, the area ofthe rectangle!!

4 m6 m

11 m

)11)(24(V

3m 264V

Area of arectangle:

wA


Volume of a Triangular Prism

Volume =

area of the Base

x height

V = B h

V =

bh21

h

h

h

b


Find the Volume of a Triangular Prism

V Bh235

50

B ft

h ft

Step 1: Use the formula forthe volume of a prism

Step 4: Simplify


Step 3: Substitute 35 for B,and 50 for h.

31,750V ft

10 ft

7 ft50 ft12 ft 12 ft

(35)(50)V


case, the area ofthe triangle!!

Area of atriangle:

1

2A bh


Volume of a Cylinder

Volume =

area of the Base

x height

V = B h

V = 2r h h

r


Find the Volume of a Cylinder

mm 12

mm 25 2

h

B

V Bh

Step 1: Use the formula forthe volume of a cylinder

Step 4: Simplify


Step 3: Substitute 25π for B,and 12 for h.


case, the area ofthe circle!!

)12)(25( V

3mm 300V

Area of acircle:

2rA

12 mm

5 mm


Find the Area of a Shaded Region

Think of putting wallpaper on a wall…

52

13

9

With a window

Find the area of the wall

And subtract out the windowl w

13 9

l w

117

5 2

10 = 107

52


wlP 22

wlA wlA 4282 P

816Pft24P

48A2ft32A

Perimeter and Area of Rectangles


The FORMULA for finding the

area of a triangle is

because a triangle is half of a

rectangle.

bhA21

Area of a rectangle is bh.

5 in.

4 in

.

Area of a Triangle


MAP2D

Chapters 10 and 11Probability and Statistics

Grade 6


Probability of an Event

=12P(Y)

outcomes possible of numberoutcomes favorable of number

P(event)

The probability of an event equals:

outcomes possible of numberoutcomes favorable of number

P(event)

(yellow)

yellow blocks

blocks in the bag

Representing Outcomes

You can use a tree diagram, a list, or a table

to list the outcomes of compound

events.

What are all the possible outcomes

when 2 dice are rolled?

1st Die 2nd Die Outcome

1

2

3

4

5

6

123456

123456

123456

123456

123456

123456

1, 11, 21, 31, 41, 51, 6

2, 12, 22, 32, 42, 52, 6

3, 13, 23, 33, 43, 53, 6

4, 14, 24, 34, 44, 54, 6

5, 15, 25, 35, 45, 55, 6

6, 16, 26, 36, 46, 56, 6

36

Outco

mes




events.



Outcomes

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36

Outco

mes




events.



Outcomes

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

1 2 3 4 5 6

1

2

3

4

5

6

Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6 MAP 2 D Quarter 3...

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