1. Instructional Strategies
MAP2D
Quarter 3
Instructional Strategies
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

2. Chapters 8 and 9 Geometry Grade 6 MAP2D
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

3. Grade 6 MAP2D Quarter 3 Instructional Strategies
Adjacent and Vertical Angles
Adjacent Angles :
angles that are next to each other. 1 2 3
 1 and 2 are adjacent angles.
Vertical Angles :
angles that are opposite of one another.
 1 and 3 are vertical angles.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

4. Vertical Angles a° b° a = b
Vertical angles are the angles opposite each other when 2 lines cross. a° b°
Vertical angles are congruent.
a = b
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

5. Vertical Angles c° d° c = d
Vertical angles are the angles opposite each other when 2 lines cross. c° d°
Vertical angles are congruent.
c = d
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

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

7. Complementary angles add up to 90°.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

8. Supplementary angles add up to 180°.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

9. Triangle Sum Property 1 2 3
For any triangle, the sum of the measures of the interior angles is always 180º. 1 3 2 1 2 3
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

10. Solve for a Missing Angle in a Triangle
73º xº
1. Write the equation:
m1 + m2 + m3 = 180º
m1 + m2 + m3 = 180º
90º
73º x
2. Fill in the angle measures
163º + x = 180º
3. Solve the equation for the missing value.
163º+x –163º= 180º–163º
x = 17º
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

11. Area is the space inside the circle.
of a circle
r = radius
Area = r 2
  3.14
Area is the space inside the circle.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

12. C = d   3.14 Circumference of a Circle
d = diameter
Circumference
  3.14
Circumference is the distance around a circle or sphere.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

13. 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.
C = πd
A = πr 2 8
C = π  2r
A = π  82
C = π  2  8
A = π  64
C = 16π
A = 64π
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

14. Estimating with Pi
π ≈ …
JUST USE 3 
C = πd
A = πr 2 8
C = π  2r
A = π  82
C = π  2  8
A = π  64
C = 16π
A = 64π
C ≈ 16  3
A ≈ 64  3
C ≈ 48
A ≈ 192
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

15. Area vs. Volume
Remember, area is the space inside a flat figure. It is measured using square units.
Volume is the amount of space inside a prism. It is measured using cubic units.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

16. Finding The Volume Any Prism
Volume of a prism = Area of one Base  height
V = B h
height
Area of the Base
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

17. Volume of a Rectangular Prism
area of the Base
Volume = x
height
V = B h h
V = h
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

18. Find the Volume of a Rectangular Prism
Remember B is the
area of the base. In this
case, the area of
the rectangle!!
Step 1: Use the formula for
the volume of a prism
4 m
6 m
11 m
Step 2: Identify B and h.
Step 3: Substitute 24 for B,
and 11 for h.
Area of a
rectangle:
Step 4: Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

19. Volume of a Triangular Prism
area of the Base
Volume = x
height h b
V = B h h
V = h
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

20. Find the Volume of a Triangular Prism
Remember B is the
area of the base. In this
case, the area of
the triangle!!
Step 1: Use the formula for
the volume of a prism
Step 2: Identify B and h.
Step 3: Substitute 35 for B,
and 50 for h.
Area of a
triangle:
Step 4: Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

21. Volume of a Cylinder r h V = B h V = h area of the Base Volume = x
height h
V = B h
V = h
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

22. Find the Volume of a Cylinder
Remember B is the
area of the base. In this
case, the area of
the circle!!
Step 1: Use the formula for
the volume of a cylinder
5 mm
Step 2: Identify B and h.
12 mm
Step 3: Substitute 25π for B,
and 12 for h.
Area of a
circle:
Step 4: Simplify
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

23. Find the Area of a Shaded Region5 2 13 9
Think of putting wallpaper on a wall… 5 2
With a window
Find the area of the wall
And subtract out the window
l  w
l  w
13  9
5  2
117 10
= 107
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

24. Perimeter and Area of Rectangles
8 ft
4 ft
Perimeter is the sum of all sides
Area is the number of square units in a region. 4
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6
3 m

25. Area of a rectangle is bh.
Area of a Triangle
The FORMULA for finding the
area of a triangle is
because a triangle is half of a rectangle.
5 in.
4 in.
Area of a rectangle is bh.
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

26. Probability and Statistics
MAP2D
Chapters 10 and 11
Probability and Statistics
Grade 6
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

27. Probability of an Event
The probability of an event equals:
yellow blocks
(yellow)
blocks in the bag 1
P(Y) = 2
Copyright ©, Long Beach Unified School District. All rights reserved. - Grade 6

28. Representing Outcomes
1st Die
2nd Die
Outcome
You can use a tree diagram, a list, or a table to list the outcomes of compound events. 1 2 3 4 5 6
1, 1
1, 2
1, 3
1, 4
1, 5
1, 6
2, 1
2, 2
2, 3
2, 4
2, 5
2, 6
36 Outcomes 1 1 2 3 4 5 6 2 1 2 3 4 5 6
3, 1
3, 2
3, 3
3, 4
3, 5
3, 6 3 1 2 3 4 5 6
4, 1
4, 2
4, 3
4, 4
4, 5
4, 6
What are all the possible outcomes when 2 dice are rolled? 4 1 2 3 4 5 6
5, 1
5, 2
5, 3
5, 4
5, 5
5, 6 5 1 2 3 4 5 6
6, 1
6, 2
6, 3
6, 4
6, 5
6, 6 6

29. Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events.
36 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)
What are all the possible outcomes when 2 dice are rolled?
(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)

30. Representing Outcomes
You can use a tree diagram, a list, or a table to list the outcomes of compound events.
(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
What are all the possible outcomes when 2 dice are rolled?