Transcript 6th_MA_SDP_3.3_PROBABILITY_DW

Name ___________________________
Learning Objective
Today, we will represent1 probability as ratios and percentages.
1
show
CFU
What are we going to do today?
What are we going to represent?
What does represent mean?
Today, we will represent probability as ratios and percentages.
We are going to represent probabilities as ratios and percentages.
Represent means to show.
Activate (or provide) Prior Knowledge
A ratio compares two numbers using a fraction.
98
For example, 98 out of 100 or
people wear
100
seatbelts.
A percent is a fraction or ratio with 100 understood
as the denominator.
98
For example, 0.98 equals
and 98%.
100
There are 30 kids in a class. Eighteen of them are girls and twelve of them are boys.
1). a. What is the ratio of girls to the total number of students?
b. What is the reduced form of the ratio?
c. What is the percentage of girls to the total number of students?
18
30

3
5
.6
5 3.0
30
0
.6  60%
2). a. What is the ratio of boys to the total number of students?
b. What is the reduced form of the ratio?
c. What is the percentage of boys to the total number of students?
12
30

2
5
.4
5 2.0
20
0
.4  40%
CFU
Teacher completes example 1. Students complete example 2. Students, you already know how to compare two numbers using ratios and
percentages. Today, we will use our knowledge of ratios and percentages to represent probabilities.
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6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Concept Development
Probability is the likelihood or chance that an event will occur2.
• Probability can be represented as a ratio 2 or 2:5, and as a percentage 40%.
5
An event is one or more outcomes of an experiment3.
An outcome is each result. They are what could happen in an experiment.
2
3
happen
an activity involving chance
Example:
Jennifer has 16 shirts.
The number of each color is
shown in the table.
Color
Number of Shirts
White
8
Black
4
Pink
2
Total
16
If Jennifer chooses a shirt without looking, what is the probability that she will choose a white shirt?
The formula for probability of an event when all outcomes of an experiment are likely to happen is:
Probability=
number of ways the event can occur
total number of all possible outcomes
Number of ways the event or white shirt can occur is: 8
Total number of all possible outcomes is: 16 (total amount of shirts)
The probability of choosing a white shirt is 8 , 8:16, or 50%.
16
In its simplest (reduced) form, the probability would be 1 or 1:2.
2
CFU
In your own words, explain what probability is. Probability is __________________________.
How can probability be represented?
What is the difference between outcomes and events?
What is the formula for finding the probability of an event?
In a bag, there are 5 blue marbles, 3 yellow marbles, and 2 red marbles. What is the total number of outcomes?
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10
b. 5
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Skill Development/Guided Practice
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
The table shows how many types of fruit are in a bowl.
Fruit
Amount
Orange
6
Pear
2
Apple
3
Banana
1
Total
12
1. What is the probability, that without looking, Marcos
will choose an apple?
.25
4
1.00
Event: ____
Total Outcomes: ____
3
12
8
20
20
0
3
1

25%
Ratio: __________________
Percent: __________
4
12
2. What is the probability, that without looking, Marcos
will choose an orange?
.5
Event: _____
Total Outcomes: _____
12
6
2 1.0
10
0
6
1

50%
Ratio: ___________________
Percent: __________
12 2
CFU
How did I know the number of ways the event could occur? How did I determine the number of total outcomes? How did I know
how to write the probability as a ratio? How did I know if I had to reduce? What did I do to write the probability as a percentage? Do Step
#2 and show. How did you know the number of ways the event could occur? Do Step #3… How did you determine the number of total
outcomes? Do Step #4… How did you know how to write the probability as a ratio? How did you know if you had to reduce? Do Step #5…
What did you do to write the probability as a percentage?
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6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Skill Development/Guided Practice (continued)
number of ways the event can occur
Probability=
Probability is the likelihood or chance that an event will occur.
total number of all possible outcomes
Represent probability as ratios and percentages.
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
3. A glass jar contains 9 red, 8 green, 3 blue, and 5 yellow marbles. If a single marble is chosen at random2
from the jar, what is the probability of choosing a blue marble?
2 without planning
9+8+3+5 = 25
.12
Event: _____
Total Outcomes: _____
25
3
3
Ratio: ________________________
25
25 3.00
25
50
50
12%
0 Percent: __________
4. A gumball machine has 9 white, 6 blue, 3 red, and 2 green gumballs. If one gumball is chosen at random
from the machine, what is the probability of choosing a red gumball?
9+6+3+2 = 20
3
Event: _____
Total Outcomes: _____
20
3
20
Ratio: ________________________
.15
20 3.00
20
100
100
15%
0 Percent: __________
CFU
How did I know the number of ways the event could occur? How did I determine the number of total outcomes? How did I know
how to write the probability as a ratio? What did I do to write the probability as a percentage? Do Step #2 and show. How did you the
number of ways the event could occur? Do Step #3… How did you determine the number of total outcomes? Do Step #4… How did you
know how to write the probability as a ratio? Do Step #5…What did you do to write the probability as a percentage? What is the difference
between Step #2 and Step #3? Which step is the hardest for you? Why? Which step is the easiest for you? Why?
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6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Importance
Probability is the likelihood or chance that an event will occur.
1. Representing probability as ratios and percentages will help you show and
understand data for research.
Jane conducted a survey about favorite foods in her class. Of the twenty five
students, eleven chose pizza, four chose hamburgers, six chose chicken, and
four chose spaghetti.
2. Represent probability as ratios and percentages will help you determine your
chances of winning a prize; for example, a raffle or lottery.
1 tickets sold and you bought two. The probability of you
There have been 112
winning a prize is 56 .
3. Represent probability as ratios and percentages will help you do well on tests.
CFU
Does anyone else have another reason why it is important to represent probability as ratios and percentages? (pair-share) Why is it
important to represent probability as ratios and percentages? You may give me one of my reasons or one of your own. Which reason is
most important to you? Why?
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
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Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
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0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Closure
1. In your own words, what is probability? number of ways the event can occur
2. What is the formula for probability?
total number of all possible outcomes
3. Represent probability as ratios and percentages below.
4. What did you learn today about representing probability as ratios and percentages? Why is that important to you? (pair-share)
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
Sarah has a collection of bracelets.
The table shows the amount of each type.
Bracelet Type
Number of Bracelets
Silver
3
Gold
5
Beaded
7
Total
15
1. What is the probability if a bracelet is chosen at random, that Sarah will get a silver bracelet?
.2
Event: _____
Total Outcomes: _____
15
3
5
1.0
3
1

10
Ratio: ________________________
20%
15 5
0 Percent: __________
2. A car has 2 tall clowns and 6 short clowns in it. Find the probability that a short clown will get out of the car
.75
first.
8
6.00
6
Event: _____
Total Outcomes: _____
8
6 3

Ratio: ________________________
8 4
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56
40
40
0 Percent: __________
75%
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Independent Practice
Name ___________________________
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
The table shows how many pairs of socks Jaime has in a drawer.
Color
Number of Socks
Black
8
White
6
Brown
1
Grey
5
Total
20
1. What is the probability, that without looking, Jaime
will pick a white pair of socks?
Event: ____
Total Outcomes: ____
6
20
2. What is the probability, that without looking, Jaime
will pick a black pair of socks?
Event: _____
Total Outcomes: _____
20
8
6
3

Ratio: __________________
Percent: __________
30%
20 10
8
2

Ratio: __________________
Percent: __________
40%
20 5
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6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Independent Practice (continued)
Name ___________________________
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
3. In a box of donuts, there are 4 chocolate, 5 glazed, 3 maple bars, and 8 sprinkled donuts. If a donut is
chosen at random, what is the probability of getting a glazed donut?
20
Event: _____
Total Outcomes: _____
5
5
1

Ratio: ________________________
20 4
Percent: __________
25%
4. In a desk drawer there are 12 blue pens, 10 black pens, 5 red pens and 3 green pens. Find the probability
that, if a pen is chosen at random, it will be a blue pen.
12
Event: _____
Total Outcomes: _____
30
12 2

30 5
Ratio: ________________________
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40%
Percent: __________
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Periodic Review 1
Name ___________________________
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
The table shows how many vowel-letter tiles are in a
word game.
Vowel Letter
Number of Tiles
A
9
E
12
I
7
O
8
U
4
Total
40
Event: _____
6
1. Randi is playing a word game with his brother. He
needs the letter O. What is the probability, that
without looking, Randi will pick the letter O?
8
Event: ____
Total Outcomes: ____
40
8
1

Ratio: __________________
Percent: __________
20%
40 5
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2. In Julia’s bag of candy, there are 7 lemon, 8 grape,
3 strawberry, and 6 lime flavored Skittles. What is
the probability, that without looking, Julia will
choose a lime flavored Skittle?
Total Outcomes: _____
24
6
1

Ratio: ___________________
Percent: __________
25%
24 4
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Periodic Review 2
Name ___________________________
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
The table shows the eye color of all the students in a
class.
Eye Color
Number of Students
Blue
10
Brown
16
Hazel
2
Green
4
Total
32
Event: _____
3
1. If the teacher chooses a student without looking,
what is the probability that the student will have
brown eyes?
16
Event: ____
Total Outcomes: ____
32
16 1

50%
Ratio: __________________
Percent: __________
32 2
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2. In Ryan’s closet, he has 9 white, 7 black, 6 grey,
and 3 blue T-shirts. If he selects a T-shirt at
random, what is the probability that the T-shirt will
be blue?
Total Outcomes: _____
25
3
Ratio: ___________________
Percent: __________
12%
25
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Periodic Review 3
Name ___________________________
Probability is the likelihood or chance that an event will occur.
Probability=
Represent probability as ratios and percentages.
number of ways the event can occur
total number of all possible outcomes
Step #1: Read the question carefully.
a. Underline what you are finding the probability of.
Step #2: Write the number of ways the event can occur.
Step #3: Determine the number of total outcomes.
Step #4: Write the probability as a ratio and reduce if necessary.
Step #5: Write the probability as a percentage. Hint: Divide the numerator by the denominator then convert the decimal to a
percentage.
The table shows the number of lollipops in a jar.
Lollipop Color
Number of Lollipops
Yellow
14
Purple
9
Red
11
Green
10
Total
44
2. Rosa has 12 pink, 6 purple, 14 red, and 8 green
jelly beans in her pocket. What is the probability,
that without looking, Rosa will pick a purple jelly
bean from her pocket?
Event: _____
6
Total Outcomes: _____
40
1. If a child chooses a lollipop without looking, what is
the probability that the child will choose a red
lollipop?
11
44
Event: ____
Total Outcomes: ____
11 1

Ratio: __________________
Percent: __________
25%
44 4
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6
3

Ratio: ___________________
Percent: __________
15%
40 20
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.
Blank Page
DataWORKS Educational Research
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©2011 All rights reserved.
Comments? [email protected]
6th Grade Math Statistics, Data Analysis, and Probability 3.3 (3Q)
Represent probability using ratios, proportions, decimals between 0 and 1, and percentages between
0 and 100 and verify that the probabilities computed are reasonable; know that if P is the probability
of an event, 1 - P is the probability of an event not occurring.
Lesson to be used by EDI trained teachers only.