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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

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

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. 85.8 cm3 B. 64.5 cm3 C. 32.0 cm3 D. 15.05 cm3 5-Minute Check 2

Find the volume of a hemisphere with radius of 6 meters. A. 339.3 m3 B. 360.4 m3 C. 421.5 m3 D. 452.4 m3 5-Minute Check 3

Find the lateral area of a cylinder with radius of 8 feet and height of 12 feet. A. 84 ft2 B. 603.2 ft2 C. 1005.3 ft2 D. 2412.7 ft2 5-Minute Check 4

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. 93.4 yd2 B. 99.4 yd2 C. 131.9 yd2 D. 142.8 yd2 5-Minute Check 5

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. 18.0 in. C. 19.8 in. D. 76.4 in. 5-Minute Check 6

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

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

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

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

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

Represent a Sample Space Tree Diagram Example 1

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

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

Multi-Stage Tree Diagrams Answer: Example 2

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

Concept

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 11 7 5 3 6 4 3 83,160 × = Answer: So, a consumer can create 83,160 different possible cars. Example 3

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

End of the Lesson