1. Splash Screen

2. Five-Minute Check (over Chapter 12) CCSS Then/Now New Vocabulary
Example 1: Represent a Sample Space
Example 2: Real-World Example: Multi-Stage Tree Diagrams
Key Concept: Fundamental Counting Principle
Example 3: Real-World Example: Use the Fundamental Counting Principle
Lesson Menu

3. Find the surface area of a rectangular prism with length of 6 inches, width of 5 inches, and height of 4.5 inches.
A. 159 in2
B. 145 in2
C. 135 in2
D. 120 in2
5-Minute Check 1

4. Find the volume of a cone with slant height of 4
Find the volume of a cone with slant height of 4.3 centimeters and radius of 3.5 centimeters.
A cm3
B cm3
C cm3
D cm3
5-Minute Check 2

5. Find the volume of a hemisphere with radius of 6 meters.
A m3
B m3
C m3
D m3
5-Minute Check 3

6. Find the lateral area of a cylinder with radius of 8 feet and height of 12 feet.
A. 84 ft2
B ft2
C ft2
D ft2
5-Minute Check 4

7. Find the surface area of a cone with slant height of 8
Find the surface area of a cone with slant height of 8.5 yards and radius of 3.5 yards.
A yd2
B yd2
C yd2
D yd2
5-Minute Check 5

8. The volume of a sphere is 24,429 cubic inches
The volume of a sphere is 24,429 cubic inches. What is the radius of the sphere?
A. 8.7 in.
B in.
C in.
D in.
5-Minute Check 6

9. Mathematical Practices
Content Standards
Preparation for S.CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
CCSS

10. You calculated experimental probability.
Use lists, tables, and tree diagrams to represent sample spaces.
Use the Fundamental Counting Principle to count outcomes.
Then/Now

11. multi-stage experiment Fundamental Counting Principle
sample space
tree diagram
two-stage experiment
multi-stage experiment
Fundamental Counting Principle
Vocabulary

12. Represent a Sample Space
One red token and one black token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Represent the sample space for this experiment by making an organized list a table, and a tree diagram.
Organized List
Pair each possible outcome from the first drawing with the possible outcomes from the second drawing.
R, R B, B R, B B, R
Example 1

13. Represent a Sample Space
Table
List the outcomes of the first drawing in the left column and those of the second drawing in the top row.
Example 1

14. Represent a Sample Space
Tree Diagram
Example 1

15. One yellow token and one blue token are placed in a bag
One yellow token and one blue token are placed in a bag. A token is drawn and the color is recorded. It is then returned to the bag and a second draw is made. Choose the correct display of this sample space.
A. B.
C. D. Y, Y; B, B; Y, B
Example 1

16. The sample space is the result of 4 stages. ● Dressing (F, R, or BC)
Multi-Stage Tree Diagrams
CHEF’S SALAD A chef’s salad at a local restaurant comes with a choice of French, ranch, or blue cheese dressings and optional toppings of cheese, turkey, and eggs. Draw a tree diagram to represent the sample space for salad orders.
The sample space is the result of 4 stages.
● Dressing (F, R, or BC)
● Cheese (C or NC)
● Turkey (T or NT)
● Eggs (E or NE)
Draw a tree diagram with 4 stages.
Example 2

17. Multi-Stage Tree Diagrams
Answer:
Example 2

18. BASEBALL GAME In the bleachers at a major league game you can purchase a hotdog, bratwurst, or tofu dog. This comes with the optional choices of ketchup, mustard, onions, and/or relish. How many stages are in the sample space?
A. 3
B. 4
C. 5
D. 6
Example 2

19. Concept

20. Use the Fundamental Counting Principle.
CARS New cars are available with a wide selection of options for the consumer. One option is chosen from each category shown. How many different cars could a consumer create in the chosen make and model?
Use the Fundamental Counting Principle.
exterior interior seat engine computer wheels doors possible color color outcomes
,160 × =
Answer: So, a consumer can create 83,160 different possible cars.
Example 3

21. BICYCLES New bicycles are available with a wide selection of options for the rider. One option is chosen from each category shown. How many different bicycles could a consumer create in the chosen model?
A. 3,888
B. 3,912
C. 4,098
D. 4,124
Example 3

22. End of the Lesson