Estimating Probability using a Number Line (7.SP.5)
Domain:
Statistics and Probability
Big Idea (Cluster):
Investigate chance processes and develop, use, and evaluate probability models
Common Core Standards:
7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that expresses the
likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0
indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely,
and a probability near 1 indicates a likely event.
Mathematical Practice(s):
MP 1: Make sense of problems and persevere in solving them
MP 2: Reason abstractly and quantitatively
MP 3: Construct viable arguments and critique the reasoning of others
MP 7: Look for and make sure of structure
Content Objectives:
Language Objectives:
Students will be able to understand the probability
of a chance event is a number between 0 and 1
Talk with your group about what each card means
Students will be able to explain the probability of
an event as likely, unlikely, or equally likely based
on event occurring
Talk with your group about where each card might
go along the number line between 0 and 1
Write a number to describe unlikely, equally likely,
and likely
Students will be able to express the likelihood of
an event occurring as a number between 0 and 1
Students will be able to describe values closer to 1
as having a greater likelihood of occurring and
values closer to 0 as unlikely
Vocabulary:
Chance
Equally Likely
Event
Likelihood
Prior Knowledge: Concepts students need to
know
Likely
Outcome
Probability
Unlikely
In Grade 7, students write the same value represented
as a fraction, decimal or percent.
Beginning the 2014-2015 school year, Grade 7 will
be the only K-8 grade level where probability is
taught. Deep understanding will need to be the focus
of instruction.
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Estimating Probability using a Number Line (7.SP.5)
Questions to Develop Mathematical Thinking:
Common Misconceptions/Challenges:

Challenge: Students often struggle when converting
forms of probability from fractions to percent and
vice versa.

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What are the possible outcomes for the event
in this situation?
How do the outcomes help you identify
probability?
How should a spinner look if all outcomes are
equally likely?
What is an example of an equal chance on a
number cube?
What does it mean for the probability of
is close to 0, ½, or 1?
Strategy: To help students with the discussion of
probability, don’t allow the conversions to detract
from the meaning of the probability model. By
having students use technology such as a calculator,
the focus is on the interpretation of the probability
model.
Challenge: Students may also attempt to give a
probability as a number greater than one rather than
representing the probability as a number between
zero and one.
Strategy: Check for student understanding of how
percentage can be used to represent the number of
times an outcome would likely occur if an event took
place 100 times. Also, revisit prior connections of one
whole equal to 100% of the outcomes.
ASSESSMENT:
Observe student work and listen to student discussions for:
 Explanations of vocabulary or probability scenario card as closer to 0, ½ or 1
 Descriptions of the likelihood of the probability scenario or vocabulary card
 Students making sense of similar vocabulary words such as “unlikely,” “small chance,” and “hardly
ever”
 Strategies to decide the placement of the card from 0 to 1
You might use problem F as a formative assessment. Students should identify that likely is a chance of an
event occurring that is closer to 1, equally likely is a ½ chance, and unlikely is a chance closer to 0.
MATERIALS:
One set of vocabulary cards per group
Masking tape strip per group
Scissors
Marker
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Estimating Probability using a Number Line (7.SP.5)
Launch: (5-10 minutes)
Have the students work on the warm-up question with their group. Students should justify their reasoning
with numbers and words. While students are working on the launch, listen for understanding of
“likelihood” and prior knowledge of accurate placement of values on a number line.
When students finish the warm-up, ask students what is meant by “likelihood.” As of 2015-2016, this will
likely be the first time students use this vocabulary in a math class. Students should understand that
likelihood is the chance an event will occur. In addition, have students identify key words in the statement
that might help identify the likelihood of the event occurring. For example, “it will rain today” versus “it
will rain today at 3pm.” With a more specific description, the likelihood might actually increase or
decrease based on the additional description. When students begin the task today, they will have to pay
attention to the words and probability models that relate to benchmark fractions and their numerical
conversions.
Possible solution:
A. Since the chance of rain today is 80%, it is very likely it will rain during the day. There is a really
good chance of rain since the percent is close to 100%.
B.
0
Chance of rain
1
Explore: (20 minutes)
Hand out the task and have students read task in their groups. Have students share out to the class or group
student actions the teacher and students should see and hear during the task. For example, we should see
all students cutting the probability cards, leaning in to work together, and placing the cards on, above, or
below the number line between 0 and 1. We should hear all students discussing each vocabulary or
probability card, explaining their reasoning, and asking questions of each other when they disagree on the
placement of a card.
When I observe students:
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Look at student work for estimation of card placement based on the meaning of the card and its
approximate value on the number line (MP 6)
Listen for student disagreement around placement of cards as closer to 0, ½ or 1 (MP 2 and MP 3)
When students disagree, encourage students to ask clarifying questions of each other in order to
come to a consensus. Encourage students to use mathematical or real-world evidence to reason
through the card being closer to 0, ½, or 1.
Listen for students making sense of similar words or phrases such as “unlikely,” “small chance,”
and “hardly ever” (MP 6)
When students struggle to make sense of the vocabulary words, ask students to look up the word,
use it in a sentence, or make use of the word in a real-world scenario to determine if they all have
the same meaning or if one word is closer to zero than another.
Listen and read student responses for strategies to decide the placement of card from 0 to 1 (MP 1)
Listen for students describing likelihood of events and using probability related vocabulary (MP 1
and MP 6)
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Estimating Probability using a Number Line (7.SP.5)
Questions to Develop Mathematical Thinking as you observe:
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What are the possible outcomes for the event in this situation?
How do the outcomes help you estimate probability?
How are the numbers zero, half, and one used to classify probability events?
How should a spinner look if all outcomes are equally likely?
What is an example of an equal chance on a number cube?
What does it mean for the probability of
is close to 0, ½, or 1?
Summarize: (10 minutes)
Have students complete a gallery walk around the room to look for similarities and differences between
each other’s placement of the cards between 0 and 1. Have students take note on where groups placed
cards such as, “hardly ever,” “almost always,” “you will watch TV sometime today,” and cards that are
less obvious to place between 0 and 1. Did the students place them in similar positions along the number
line? Also, use the student disagreements from Problem D to help summarize with the class how to make
decisions about probability estimations.
Ask the students:
 How did your group determine accuracy of the card placement?
 What were the strategies used by your group when placing a card from 0 to 1 along the number
line?
Have students share out their numerical descriptions for likely, equally likely, and unlikely. Students
should identify that likely is a chance closer to 1, equally likely is a ½ chance, and unlikely is a chance
closer to 0. Emphasize that very few events have a probability of 0 or 1. This would also be an
opportunity to introduce outcomes for a probability model and how outcomes are used to identify an
event’s likelihood.
Solutions:
C. See sample at end of solutions.
D. Have groups share out strategies observed during the task. One strategy students might share is
placing the numerical values cards based on their understanding of benchmark fractions or
conversions. A second strategy for students might be writing out the possible outcomes that could
occur for a probability scenario. Another strategy might be using the words that describe
probability in a sentence to better understand the chance being closer to 0, ½, or 1.
E. Have groups share out the cards that were challenging to place and the evidence they used to come
to an agreement.
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Estimating Probability using a Number Line (7.SP.5)
F. Students should identify that likely is a chance closer to 1, equally likely is a ½ chance, and
unlikely is a chance closer to 0.
Feedback for lesson improvement:
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