Math Gr4 Ch16

Chapter 16Probability

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Lesson 16-1 Probability and OutcomesLesson 16-2 Probability and FractionsLesson 16-3 Problem-Solving Strategy:

Make an Organized ListLesson 16-4 Find ProbabilityLesson 16-5 Problem-Solving

Investigation: Choose a StrategyLesson 16-6 Tree Diagrams

16Probability

Five-Minute Check (over Chapter 15)Main Idea and VocabularyCalifornia StandardsExample 1Example 2

16-1 Probability and Outcomes

16-1 Probability and Outcomes

• I will describe probability.

• outcome• probability

16-1 Probability and Outcomes

Standard 4SDAP1.2 Express outcomes of

experimental probability situations verbally and

numerically (e.g., 3 out of 4; ).

16-1 Probability and Outcomes

Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).

There are 10 marbles and 8 are green.

Kimmela has 8 green and 2 white marbles. Describe how likely it is that Kimmela will choose a green marble.

16-1 Probability and Outcomes

Answer: So, it is likely that Kimmela will choose a green marble.

16-1 Probability and Outcomes

Lexie has a bag with 7 blue marbles and 7 red marbles. Describle how likely it is that Lexie will choose a red marble.

A. certain

B. likely

C. equally likely

D. not likely

Jeremiah has 15 coins in his pocket. 10 are dimes, 5 are nickels. If he drops a coin on the ground, describe the probability that the coin is a penny.

There are 15 coins in Jeremiah’s pocket. Of those coins, none of them are pennies.

Answer: Since there are no pennies, it is impossible that Jeremiah dropped a penny.

16-1 Probability and Outcomes

16-1 Probability and Outcomes

Luna has 12 coins in her pocket. All of them are dimes. If she drops a coin on the ground, describe the probability that the coin is a dime.

A. impossible

B. likely

C. unlikely

D. certain

Five-Minute Check (over Lesson 16-1)Main Idea and VocabularyCalifornia StandardsKey Concepts: Probability as a FractionExample 1Example 2

16-2 Probability and Fractions

16-2 Probability and Fractions

• I will describe probability in words and in numbers.

• favorable outcome

16-2 Probability and Fractions

Standard 4SDAP2.2 Express outcomes of

experimental probability situations verbally and

numerically (e.g., 3 out of 4; ).

16-2 Probability and Fractions

Use words and a fraction to describe the probability of rolling a 5 on a number cube.

One out of six numbers on a number cube is a 5.

16-2 Probability and Fractions

Probability = favorable outcomestotal possible outcomes

= roll a 5roll any number

= 16

16-2 Probability and Fractions

Answer: So, the probability of rolling a 5 on a

number cube is 1 out of 6 or , which

is unlikely.

16

16-2 Probability and Fractions

Use words and a fraction to describe the probability of tossing a coin and getting heads.

A. certain; 22

B. equally likely; 12

C. equally likely; 14

D. impossible; 02

In a bucket of tennis balls, there are 10 yellow, 6 green, and 4 purple balls. Ms. Gorman reaches in without looking and chooses one. Use words and a fraction to describe the probability of choosing a purple tennis ball.

Four out of twenty tennis balls are purple.

16-2 Probability and Fractions

16-2 Probability and Fractions

Probability = favorable outcomestotal possible outcomes

= purple tennis ballsevery color of tennis balls

= 420

Answer: So, the probability of choosing a purple

tennis ball is , or 4 out of 20.420

16-2 Probability and Fractions

Tammy has a jar in her room with 5 nickels, 10 pennies, and 2 dimes. She reaches into her jar without looking and chooses one. Use words and a fraction to describe the probability of choosing a penny.

A. likely; 1017

B. likely; 517

C. unlikely; 217

D. unlikely; 1017

Five-Minute Check (over Lesson 16-2)Main IdeaCalifornia StandardsExample 1: Problem-Solving Strategy

16-3 Problem-Solving Strategy: Make an Organized List

16-3 Problem-Solving Strategy: Make an Organized List

• I will make an organized list to solve problems.

16-3 Problem-Solving Strategy: Make an Organized List

Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing and prioritizing information, and observing patterns.

16-3 Problem-Solving Strategy: Make an Organized List

Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g. tables, grids, tree diagrams).

The Burke family is going camping for the weekend. There are four children in the Burke family, Zane, Nora, Olga, and Peter. They will sleep in two tents, with two children in each tent. How many different combinations are possible?

16-3 Problem-Solving Strategy: Make an Organized List

Understand

What facts do you know?• There are 4 children.• Two children will sleep in each tent.

What do you need to find?• Find how many combinations are possible.

16-3 Problem-Solving Strategy: Make an Organized List

Plan

You can make a list of all the possible combinations. Then count the total number of different combinations.

16-3 Problem-Solving Strategy: Make an Organized List

Solve

First, write the name of one of the children. Then, write the name of another child by the first child’s name. Continue to do this with each child. Do not repeat pairs.

16-3 Problem-Solving Strategy: Make an Organized List

Solve

Nora–Olga

Nora–Peter

Nora–Zane

Answer: There are 6 different combinations who can be in each tent.

16-3 Problem-Solving Strategy: Make an Organized List

Olga–Peter

Olga–Zane

Peter–Zane

Check

Look back at the problem. There are 4 children. They can each pair up with three other children. Each child’s name does appear 3 times on the list. So, the answer is correct.

16-3 Problem-Solving Strategy: Make an Organized List

Five-Minute Check (over Lesson 16-3)Main Idea and VocabularyCalifornia StandardsExample 1Example 2

16-4 Find Probability

16-4 Find Probability

• I will find the probability of outcomes using a grid.

• grid

16-4 Find Probability

Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).

16-4 Find Probability

Standard 4SDAP2.2 Express outcomes of

experimental probability situations verbally and

numerically (e.g., 3 out of 4; ).

Sari chose two flowers from the bucket of half pink, half red flowers without looking. Use the grid to find the probability she chose two pink flowers.

16-4 Find Probability

There are four possible color combinations. Red and red, red and pink, pink and red, and pink and pink.

One of the outcomes is pink and pink.

16-4 Find Probability

Probability = favorable outcomestotal possible outcomes

= 14

Answer: So, the probability is 1 out of 4, or .14

16-4 Find Probability

Use the grid to find the probability of tossing two coins and getting tails on both.

A. 14

16-4 Find Probability

Use the grid to find the probability of tossing two coins and getting tails on both.

B. 24

C. 34

D. 44

Create a grid to show all possible outcomes of flipping a coin and rolling a number cube. Then use the grid to find the probability of getting heads and a number greater than 2.

16-4 Find Probability

Step 1 Write the possible outcomes for a coin on the side of the grid and the outcomes for a number cube on the top of the grid.

Step 2 Write the possible outcomes for tossing a coin and rolling a die in the squares where each row and column intersect.

16-4 Find Probability

16-4 Find Probability

Answer: There are 12 possible outcomes. Four of the

outcomes are getting a heads and rolling a

number greater than 2. So, the probability is

4 out of 12 or .4

12

16-4 Find Probability

Use the grid to find the probability of getting tails and an even number.

A. 9

12

B. 6

12

C. 3

12

D. 1

12

Five-Minute Check (over Lesson 16-4)Main IdeaCalifornia StandardsExample 1: Problem-Solving Investigation

16-5 Problem-Solving Investigation: Choose a Strategy

16-5 Problem-Solving Investigation: Choose a Strategy

• I will choose the best strategy to solve a problem.

16-5 Problem-Solving Investigation: Choose a Strategy

Standard 4MR1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, sequencing, and prioritizing information, and observing patterns.

16-5 Problem-Solving Investigation: Choose a Strategy

Standard 4NS3.0 Students solve problems involving addition, subtraction, of whole numbers and understand the relationships among the operations.

CARMEN: My family ate dinner at a restaurant. We ordered salads for $6 each, steaks for $15 each, and chicken sandwiches for $8 each. The total cost was $43.

YOUR MISSION: Find how many of each item was ordered.

16-5 Problem-Solving Investigation: Choose a Strategy

Understand

What facts do you know?• You know the cost of each item.• You know the total cost of the meal.

What do you need to find?

• You need to find how many of each item was ordered.

16-5 Problem-Solving Investigation: Choose a Strategy

Plan

Use logical reasoning to find how many of each item was ordered.

16-5 Problem-Solving Investigation: Choose a Strategy

Solve

At least one of each item was ordered. Add the costs.

16-5 Problem-Solving Investigation: Choose a Strategy

$15 + $6 + $8 = $21 + $8

= $29

So, the cost of the other items ordered must be $43 – $29, or $14.

Solve

Since $8 + $6 is the only combination of costs that equal $14, you know that another salad and chicken sandwich were ordered.

16-5 Problem-Solving Investigation: Choose a Strategy

Answer: So, Carmen’s family ordered 1 steak, 2 salads, and 2 chicken sandwiches.

Check

You can check your answer with addition.

16-5 Problem-Solving Investigation: Choose a Strategy

$6 + $6 + $8 + $8 + $15 = $43

So, the answer is correct.

Five-Minute Check (over Lesson 16-5)Main Idea and VocabularyCalifornia StandardsExample 1Example 2

16-6 Tree Diagrams

16-6 Tree Diagrams

• I will use a tree diagram to show outcomes.

• tree diagram

16-6 Tree Diagrams

Standard 4SDAP2.1 Represent all possible outcomes for a simple probability situation in an organized way (e.g., tables, grids, tree diagrams).

16-6 Tree Diagrams

Standard 4SDAP2.2 Express outcomes of

experimental probability situations verbally and

numerically (e.g., 3 out of 4; ).

How many outcomes are possible when both spinners are spun?

16-6 Tree Diagrams

Use a tree diagram to find the possible outcomes.

List each color on each of the spinners. Then pair each color choice from one spinner to each color choice on the other spinner.

16-6 Tree Diagrams

Spinner 1

16-6 Tree Diagrams

Red (R)Red (R2)Blue (B2)Purple (P)

R, R2R, B2R, P

Orange (O)Red (R2)Blue (B2)Purple (P)

O, R2O, B2O, P

Spinner 2 Outcome

16-6 Tree Diagrams

Yellow (Y)Red (R2)Blue (B2)Purple (P)

Y, R2Y, B2Y, P

Light blue (L)Red (R2)Blue (B2)Purple (P)

L, R2L, B2L, P

Blue (B)Red (R2)Blue (B2)Purple (P)

B, R2B, B2B, P

16-6 Tree Diagrams

Answer: So, there are 15 possible outcomes.

16-6 Tree Diagrams

Michelle has a coin and bag of marbles with 1 yellow, 1 blue, 1 red, 1 green, and 1 purple. How many outcomes are possible when the coin is tossed and one marble is drawn?

A. 6

B. 8

C. 10

D. 12

Kasim is flipping three coins. Make a tree diagram and use it to find the probability of flipping at least two heads.

16-6 Tree Diagrams

16-6 Tree Diagrams

Coin 1 Coin 2 Coin 3

Heads

HeadsHeads

Tails

Tails

Heads

Tails

Tails

HeadsHeads

Tails

Tails

Heads

Tails

16-6 Tree Diagrams

There are eight possible outcomes. Four of these outcomes has at least two heads: HHH, HHT, HTH, and THH.

=at least 2 heads

total possible outcomes

Answer: So, the probability is 4 out of 8, or .48

16-6 Tree Diagrams

Noel is flipping two coins and spinning the spinner below. Find the probability of getting heads on one coin, tails on the other, and landing on red.

B. 26

C. 46

A. 412

D. 2

12

16Probability

Five-Minute Checks

16Probability

Lesson 16-1 (over Chapter 15)

Lesson 16-2 (over Lesson 16-1)

Lesson 16-3 (over Lesson 16-2)

Lesson 16-4 (over Lesson 16-3)

Lesson 16-5 (over Lesson 16-4)

Lesson 16-6 (over Lesson 16-5)

16Probability

(over Chapter 15)

Subtract.

A. 0.1

B. 1.9

C. 1.1

D. 11

1.5 – 0.4

16Probability

(over Chapter 15)

A. 8.46

B. 5.04

C. 7.46

D. 6.04

Subtract.

6.75 – 1.71

16Probability

(over Chapter 15)

A. $10.19

B. $11.21

C. $11.11

D. $11.19

Subtract.

$22.38 – $11.19

16Probability

(over Chapter 15)

A. 3.7

B. 4.6

C. 3.6

D. 4.4

Subtract.

9.1 – 5.5

16Probability

(over Lesson 16-1)

Describe the probability of spinning a green.

A. impossible

B. certain

C. likely

D. unlikely

16Probability

(over Lesson 16-1)

Describe the probability of spinning a yellow.

A. impossible

B. certain

C. likely

D. unlikely

16Probability

(over Lesson 16-1)

Describe the probability of spinning a white.

A. impossible

B. certain

C. likely

D. unlikely

16Probability

(over Lesson 16-1)

Describe the probability of spinning a green, blue or yellow.

A. impossible

B. certain

C. likely

D. unlikely

16Probability

(over Lesson 16-2)

Use words or a fraction to describe the probability of spinning a green.

B. 4 out of 12

D. 4 out of 16

A. 415

C. 164

16Probability

Use words or a fraction to describe the probability of spinning a yellow.

(over Lesson 16-2)

D. 16 out of 10

A. 10 out of 6

B. 110

C. 1016

16Probability

Use words or a fraction to describe the probability of spinning a red.

(over Lesson 16-2)

B. 2 out of 14

D. 2 out of 15

A. 216

C. 162

16Probability

Use words or a fraction to describe the probability of spinning a blue.

(over Lesson 16-2)

B. unable to describe probability

D. 16 out of 0

A. 116

C. 0

16Probability

(over Lesson 16-3)

Solve. Use the Make an Organized List strategy. Lunch choices include ham, turkey, or cheese sandwiches and one of the following: carrots, an apple, chips, or a cookie. How many different lunch combinations are possible?

A. 7

B. 9

C. 12

D. 18

16Probability

(over Lesson 16-4)

Use the grid to find the probability of spinning vanilla with berries.

16Probability

(over Lesson 16-4)

Use the grid to find the probability of spinning vanilla with berries.

A. The probability of spinning vanilla with

berries is 2 out of 12.

B. The probability of spinning vanilla

with berries is .412

16Probability

(over Lesson 16-4)

Use the grid to find the probability of spinning vanilla with berries.

C. The probability of spinning vanilla

with berries is 0.

D. The probability of spinning vanilla

with berries is .112

16Probability

(over Lesson 16-4)

Use the grid to find the probability of spinning vanilla with berries.

D. The probability of spinning vanilla

with berries is .112

16Probability

(over Lesson 16-5)

Solve. Gabriela has four different plants but only has room in the garden to plant three of them. She needs to decide which three to plant. How many ways can she choose 3 of the 4 plants?

A. 3

B. 4

D. 12

C. 34

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