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Lesson 1 MI/Vocab

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Probability and Outcomes

16-1

- I will describe probability.

- outcome
- probability

Probability and Outcomes

16-1

Standard 4SDAP2.2Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; ).

Probability and Outcomes

16-1

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

Probability and Outcomes

16-1

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

There are 10 marbles and 8 are green. More than half the marbles are green.

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

Probability and Outcomes

16-1

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

- certain
- likely
- equally likely
- not likely

Probability and Outcomes

16-1

Jeremiah has 15 coins in his pocket. 10 are dimes and 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.

Probability and Outcomes

16-1

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.

- impossible
- likely
- unlikely
- certain

Probability and Fractions

16-2

- I will describe probability in words and in numbers.

- favorable outcome

Probability and Fractions

16-2

Standard 4SDAP2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; ).

Probability and Fractions

16-2

Probability and Fractions

16-2

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.

favorable outcomes

Probability =

total possible outcomes

roll a 5

=

roll any number

1

=

6

Probability and Fractions

16-2

Answer: So, the probability of rolling a 5 on a number cube is 1 out of 6 or , which is unlikely.

1

6

Probability and Fractions

16-2

2

1

1

0

A. certain;

2

2

4

2

B. equally likely;

C. equally likely;

D. impossible;

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

Probability and Fractions

16-2

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.

Probability and Fractions

16-2

Answer: So, the probability of choosing a purple tennis ball is , or 4 out of 20.

4

20

favorable outcomes

Probability =

total possible outcomes

purple tennis balls

=

every color of tennis balls

4

=

20

Probability and Fractions

16-2

10

17

5

2

A.

C.

17

17

10

17

B.

D.

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.

Problem-Solving Strategy: Make an Organized List

16-3

- I will make an organized list to solve problems.

Problem-Solving Strategy: Make an Organized List

16-3

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

Problem-Solving Strategy: Make an Organized List

16-3

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

Problem-Solving Strategy: Make an Organized List

16-3

The Burke family is going camping for the weekend. There are four children in the Burke family, Devon, Nikki, Jade, and Terrell. They will sleep in two tents, with two children in each tent. How many different combinations are possible?

Problem-Solving Strategy: Make an Organized List

16-3

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.

Problem-Solving Strategy: Make an Organized List

16-3

Plan

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

Problem-Solving Strategy: Make an Organized List

16-3

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.

Problem-Solving Strategy: Make an Organized List

16-3

Solve

Terrell–Devon

Jade–Terrell

Jade–Devon

Nikki–Jade

Nikki–Terrell

Nikki–Devon

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

Problem-Solving Strategy: Make an Organized List

16-3

Check

Look back at the problem. There are 4 children. They can each pair up with three other children. The list shows each child’s name paired with 3 other children. So, the answer is correct.

Find Probability

16-4

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

- grid

Find Probability

16-4

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

Find Probability

16-4

Standard 4SDAP2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; ).

Find Probability

16-4

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.

pink, red

pink, pink

red, red

red, pink

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

Find Probability

16-4

1

4

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

One of the outcomes is pink and pink.

favorable outcomes

Probability =

total possible outcomes

1

=

4

Find Probability

16-4

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

Find Probability

16-4

1

2

3

4

A.

4

4

4

4

B.

C.

D.

Find Probability

16-4

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.

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.

Find Probability

16-4

H1

H2

H3

H4

H5

H6

T1

T2

T3

T4

T5

T6

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

Find Probability

16-4

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

Find Probability

16-4

9

6

3

1

12

12

12

12

A.

B.

C.

D.

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

Problem-Solving Investigation: Choose a Strategy

16-5

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

Problem-Solving Investigation: Choose a Strategy

16-5

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

Problem-Solving Investigation: Choose a Strategy

16-5

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

Problem-Solving Investigation: Choose a Strategy

16-5

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

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

Problem-Solving Investigation: Choose a Strategy

16-5

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.

Problem-Solving Investigation: Choose a Strategy

16-5

Plan

Use logical reasoning to solve the problem.

Problem-Solving Investigation: Choose a Strategy

16-5

Solve

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

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

= $29

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

Problem-Solving Investigation: Choose a Strategy

16-5

Solve

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

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

Problem-Solving Investigation: Choose a Strategy

16-5

Check

You can check your answer with addition.

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

So, the answer is correct.

Tree Diagrams

16-6

- I will use a tree diagram to show outcomes.

- tree diagram

Tree Diagrams

16-6

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

Tree Diagrams

16-6

Standard 4SDAP2.2 Express outcomes of experimental probability situations verbally and numerically (e.g., 3 out of 4; ).

Tree Diagrams

16-6

How many outcomes are possible when both spinners are spun?

Use a tree diagram to find the possible outcomes.

Tree Diagrams

16-6

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

Tree Diagrams

16-6

Spinner 1

Spinner 2

Outcome

Red (R2)

R, R2

Red (R)

Blue (B2)

R, B2

Purple (P)

R, P

Red (R2)

O, R2

Orange (O)

Blue (B2)

O, B2

Purple (P)

O, P

Tree Diagrams

16-6

Red (R2)

Y, R2

Yellow (Y)

Blue (B2)

Y, B2

Purple (P)

Y, P

Red (R2)

G, R2

Green (G)

Blue (B2)

G, B2

Purple (P)

G, P

Red (R2)

B, R2

Blue (B)

Blue (B2)

B, B2

Purple (P)

B, P

Tree Diagrams

16-6

Answer:So, there are 15 possible outcomes.

Tree Diagrams

16-6

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?

- 6
- 8
- 10
- 12

Tree Diagrams

16-6

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

Tree Diagrams

16-6

Coin 1

Coin 2

Coin 3

Heads

Heads

Tails

Heads

Heads

Tails

Tails

Heads

Heads

Tails

Tails

Heads

Tails

Tails

Tree Diagrams

16-6

4

8

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

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

Tree Diagrams

16-6

4

2

2

4

A.

12

12

6

6

B.

C.

D.

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.

(over Lesson 16-1)

Describe the probability of spinning a green.

- impossible
- certain
- likely
- unlikely

(over Lesson 16-1)

Describe the probability of spinning a yellow.

- impossible
- certain
- likely
- unlikely

(over Lesson 16-1)

Describe the probability of spinning a white.

- impossible
- certain
- likely
- unlikely

(over Lesson 16-1)

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

- impossible
- certain
- likely
- unlikely

16

4

15

4

A.

C.

(over Lesson 16-2)

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

B. 4 out of 12

D. 4 out of 16

10

1

10

16

B.

C.

(over Lesson 16-2)

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

A. 10 out of 6

D. 16 out of 10

16

2

16

2

A.

C.

(over Lesson 16-2)

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

B. 2 out of 14

D. 2 out of 15

1

16

A.

(over Lesson 16-2)

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

B. unable to describe probability

C. 0

D. 16 out of 0

(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?

- 7
- 9
- 12
- 18

(over Lesson 16-4)

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

B.

4

1

12

12

D.

(over Lesson 16-4)

A. 2 out of 12

C. 0

3

4

C.

(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