Transcript Gr04_Ch_16 - Etiwanda E

Chapter 16
Probability
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16
Probability
Lesson 16-1
Probability and Outcomes
Lesson 16-2
Probability and Fractions
Lesson 16-3
Problem-Solving Strategy: Make
an Organized List
Lesson 16-4
Find Probability
Lesson 16-5
Problem-Solving Investigation:
Choose a Strategy
Lesson 16-6
Tree Diagrams
16-1
Probability and Outcomes
Five-Minute Check (over Chapter 15)
Main Idea and Vocabulary
California Standards
Example 1: Describe Outcomes
Example 2: Describe Outcomes
16-1
Probability and Outcomes
• I will describe probability.
• outcome
• probability
16-1
Probability and Outcomes
Standard 4SDAP2.2 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).
16-1
Probability and Outcomes
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.
16-1
Probability and Outcomes
Lexie has a bag with 7 blue marbles and 7 red
marbles. Describe how likely it is that Lexie will
choose a red marble.
A. certain
B. likely
C. equally likely
D. not likely
16-1
Probability and Outcomes
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.
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
16-2
Probability and Fractions
Five-Minute Check (over Lesson 16-1)
Main Idea and Vocabulary
California Standards
Key Concepts: Probability as a Fraction
Example 1: Find Probability
Example 2: Find Probability
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
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.
Probability =
favorable outcomes
total possible outcomes
=
roll a 5
roll any number
=
1
6
16-2
Probability and Fractions
Answer: So, the probability of rolling a 5 on a
number cube is 1 out of 6 or 1 , which
6
is unlikely.
16-2
Probability and Fractions
Use words and a fraction to describe the probability
of tossing a coin and getting heads.
2
A. certain;
2
B. equally likely; 1
2
1
C. equally likely;
4
0
D. impossible;
2
16-2
Probability and Fractions
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
Probability =
favorable outcomes
total possible outcomes
purple tennis balls
=
every color of tennis balls
=
4
20
Answer: So, the probability of choosing a purple
4
tennis ball is
, or 4 out of 20.
20
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.
10
A. 17
2
C. 17
5
B. 17
17
D. 10
16-3
Problem-Solving Strategy: Make an Organized List
Five-Minute Check (over Lesson 16-2)
Main Idea
California Standards
Example 1: Problem-Solving Strategy
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).
16-3
Problem-Solving Strategy: Make an Organized List
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?
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
Nikki–Jade
Jade–Terrell
Nikki–Terrell
Jade–Devon
Terrell–Devon
Nikki–Devon
Answer: There are 6 different combinations that
can be in each tent.
16-3
Problem-Solving Strategy: Make an Organized List
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.
16-4
Find Probability
Five-Minute Check (over Lesson 16-3)
Main Idea and Vocabulary
California Standards
Example 1: Use a Grid
Example 2: Make and Use a Grid
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;
).
16-4
Find Probability
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, pink
red, pink
pink, red
red, red
There are four possible color combinations: pink and
pink, pink and red, red and pink, and red and red.
16-4
Find Probability
One of the outcomes is pink and pink.
Probability =
=
favorable outcomes
total possible outcomes
1
4
Answer: So, the probability is 1 out of 4, or
1
.
4
16-4
Find Probability
Use the grid to find the probability of tossing two
coins and getting tails on both.
16-4
Find Probability
1
A.
4
2
B.
4
3
C. 4
D.
4
4
16-4
Find Probability
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.
16-4
Find Probability
H1
T1
H2
T2
H3
T3
H4
T4
H5
T5
H6
T6
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
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.
9
A. 12
3
C. 12
6
B. 12
1
D. 12
16-5
Problem-Solving Investigation: Choose a Strategy
Five-Minute Check (over Lesson 16-4)
Main Idea
California Standards
Example 1: Problem-Solving Investigation
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.
16-5
Problem-Solving Investigation: Choose a Strategy
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.
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 solve the problem.
16-5
Problem-Solving Investigation: Choose a Strategy
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.
16-5
Problem-Solving Investigation: Choose a Strategy
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.
16-5
Problem-Solving Investigation: Choose a Strategy
Check
You can check your answer with addition.
$6 + $6 + $8 + $8 + $15 = $43
So, the answer is correct.
16-6
Tree Diagrams
Five-Minute Check (over Lesson 16-5)
Main Idea and Vocabulary
California Standards
Example 1: Use a Tree Diagram
Example 2: Use a Tree Diagram
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;
).
16-6
Tree Diagrams
How many outcomes are possible when both
spinners are spun?
Use a tree diagram to find the possible outcomes.
16-6
Tree Diagrams
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
Spinner 2
Outcome
Red (R)
Red (R2)
Blue (B2)
Purple (P)
R, R2
R, B2
R, P
Red (R2)
O, R2
Blue (B2)
O, B2
Purple (P)
O, P
Orange (O)
16-6
Tree Diagrams
Yellow (Y)
Green (G)
Blue (B)
Red (R2)
Blue (B2)
Purple (P)
Y, R2
Y, B2
Y, P
Red (R2)
G, R2
Blue (B2)
G, B2
Purple (P)
G, P
Red (R2)
B, R2
Blue (B2)
B, B2
Purple (P)
B, 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
16-6
Tree Diagrams
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
Coin 1
Coin 2
Heads
Heads
Tails
Heads
Tails
Tails
Coin 3
Heads
Tails
Heads
Tails
Heads
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
4
Answer: So, the probability is 4 out of 8, or 8 .
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.
4
A.
12
2
B.
6
4
C. 6
2
D. 12
16
Probability
Five-Minute Checks
Math Tool Chest
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16
Probability
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16
Probability
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Probability
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Probability
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Probability
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Probability
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)
16
Probability
(over Chapter 15)
Subtract.
1.5 – 0.4
A. 0.1
B. 1.9
C. 1.1
D. 11
16
Probability
(over Chapter 15)
Subtract.
6.75 – 1.71
A. 8.46
B. 5.04
C. 7.46
D. 6.04
16
Probability
(over Chapter 15)
Subtract.
$22.38 – $11.19
A. $10.19
B. $11.21
C. $11.11
D. $11.19
16
Probability
(over Chapter 15)
Subtract.
9.1 – 5.5
A. 3.7
B. 4.6
C. 3.6
D. 4.4
16
Probability
(over Lesson 16-1)
Describe the probability of spinning a green.
A. impossible
B. certain
C. likely
D. unlikely
16
Probability
(over Lesson 16-1)
Describe the probability of spinning a yellow.
A. impossible
B. certain
C. likely
D. unlikely
16
Probability
(over Lesson 16-1)
Describe the probability of spinning a white.
A. impossible
B. certain
C. likely
D. unlikely
16
Probability
(over Lesson 16-1)
Describe the probability of spinning a green, blue
or yellow.
A. impossible
B. certain
C. likely
D. unlikely
16
Probability
(over Lesson 16-2)
Use a fraction to describe the probability of
spinning a green.
4
A. 15
B. 4 out of 12
16
C. 4
D. 4 out of 16
16
Probability
(over Lesson 16-2)
Use a fraction to describe the probability of
spinning a yellow.
A. 10 out of 6
1
B. 10
10
C. 16
D. 16 out of 10
16
Probability
(over Lesson 16-2)
Use a fraction to describe the probability of
spinning a red.
2
A. 16
B. 2 out of 14
16
C. 2
D. 2 out of 15
16
Probability
(over Lesson 16-2)
Use a fraction to describe the probability of
spinning a blue.
1
A. 16
B. unable to describe
probability
C. 0
D. 16 out of 0
16
Probability
(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
16
Probability
(over Lesson 16-4)
Use the grid to find the probability of choosing
vanilla with berries.
16
Probability
(over Lesson 16-4)
A. 2 out of 12
B.
4
12
C. 0
D.
1
12
16
Probability
(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
3
C.
4
D. 12
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