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Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Quarter 3Instructional Strategies
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Chapters 8 and 9GeometryGrade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Vertical Angles
Vertical angles are the angles opposite each other when 2 lines cross.
Vertical angles are congruent.
a°
b°
a = b
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Vertical Angles
Vertical angles are the angles opposite each other when 2 lines cross.
Vertical angles are congruent.
c° d°
c = d
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Adjacent Angles
“Adjacent” means “next to”.
Adjacent angles are next to each other, sharing one side.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Complementary AnglesComplementary angles add up to
90°.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Supplementary Angles
Supplementary angles add up to 180°.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
AREAof a circle
Area = r 2
3.14
Area is the space inside the circle.
r = radius
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Circumference of a Circle
C = d 3.14Circumference is the distance
around a circle or sphere.
d = diameter
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Finding The Volume Any Prism
Volume of a prism = Area of one Base height
V = B hheight
Area of the Base
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Volume of a Rectangular Prism
Volume =
area of the Base
x height
V = B h
V = lw h
h
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Volume of a Triangular Prism
Volume =
area of the Base
x height
V = B h
V =
bh21
h
h
h
b
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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 2: Identify B and h.
Step 3: Substitute 35 for B,and 50 for h.
31,750V ft
10 ft
7 ft50 ft12 ft 12 ft
(35)(50)V
Remember B is thearea of the base. In this
case, the area ofthe triangle!!
Area of atriangle:
1
2A bh
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
Volume of a Cylinder
Volume =
area of the Base
x height
V = B h
V = 2r h h
r
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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 2: Identify B and h.
Step 3: Substitute 25π for B,and 12 for h.
Remember B is thearea of the base. In this
case, the area ofthe circle!!
)12)(25( V
3mm 300V
Area of acircle:
2rA
12 mm
5 mm
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
wlP 22
wlA wlA 4282 P
816Pft24P
48A2ft32A
Perimeter and Area of Rectangles
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
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
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
MAP2D
Chapters 10 and 11Probability and Statistics
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - 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
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?
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
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?
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