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Evaluating Student Learning: Preparing to Report:
Unit 7 Data Analysis and Probability
This unit provides an opportunity to report on the Statistics and Probability (Data Analysis) and Statistics
and Probability (Chance and Uncertainty) strands.
Master 7.4: Unit Summary: Data Analysis and Probability provides a comprehensive format for recording and
summarizing evidence collected.
Here is an example of a completed summary chart for this Unit:
Strands: Statistics and
Probability (Data
Analysis), Statistics and
Probability (Chance and
Uncertainty)
Conceptual
Understanding
Procedural
Knowledge
ProblemSolving Skills
Communication
Overall
Ongoing Observations
3
3
3
4
3
Work samples or
portfolios; conferences
2
3
3
3
3
Unit Test
2
3
2
3
2/3
Unit Problem
Promoting Your Cereal
3
3
4
3
3
Achievement Level for reporting*
3
* Use locally or provincially approved levels, symbols, or numeric ratings.
Recording
How to Report
Ongoing Observations
Use Master 7.2 Ongoing Observations: Data Analysis and Probability to determine the most
consistent level achieved in each category. Enter it in the chart. Choose to summarize by
achievement category, or simply to enter an overall level.
Observations from late in the unit should be most heavily weighted.
Portfolios or collections of
work samples; conferences
or interviews
Use Master 7.1 Unit Rubric: Data Analysis and Probability to guide evaluation of collections
of work and information gathered in conferences. Teachers may choose to focus particular
attention on the Assessment Focus questions. Work from later in the unit may be more
heavily weighted.
Teachers may choose to assign some or all of the questions in the Unit Review. Master 7.1
Unit Rubric: Data Analysis and Probability may be helpful in determining levels of
achievement. See Assessment for Learning at the end of each lesson for specific data.
Unit Test
Master 7.1 Unit Rubric: Data Analysis and Probability may be helpful in determining levels of
achievement. #2 provides evidence of Conceptual Understanding; #4 provides evidence of
Procedural Knowledge; #3 provides evidence of Problem-Solving Skills; #5 provides
evidence of Communication.
Unit Problem
Use Master 7.3 Performance Assessment Rubric: Promoting Your Cereal. The Unit Problem
offers a snapshot of students’ achievement. In particular, it shows their ability to synthesize
and apply what they have learned.
Student Self-Assessment
Note students’ perceptions of their own progress. This may take the form of an oral or
written comment, or a self-rating. Use any of Master 7.5, PM 2, PM 3, PM 4, PM 5, PM 6,
PM 7, and PM 8.
Comments
Analyse the pattern of achievement to identify strengths and needs. In some cases, specific
actions may need to be planned to support the learner.
Learning Skills
Ongoing Records
PM 9: Learning Skills Checklist
PM 11: Observation Record 1
PM 12: Observation Record 2
PM 14: Work Sample Records
Use to record and report evaluations of student achievement over
clusters, a reporting period, or a school year.
These can also be used in place of the Unit Summary.
Use to record and report throughout a reporting period, rather
than for each unit and/or strand.
54 Unit 7: Evaluating Student Learning
Name
Date
Unit Rubric: Data Analysis and Probability
Master 7.1
Not Yet
Adequate
Adequate
Proficient
Excellent
Conceptual Understanding
 Demonstrates and
explains:
– strengths and limitations
of various types of
graphs
– choice of graph for a
given data set and
context/ purpose
– how format and
formatting choices affect
interpretation
– conclusions that can
(and cannot) be
supported by a given
data set or graph
– a rule for determining the
probability of
independent events
little understanding;
may be unable to
demonstrate or
explain:
– strengths and
limitations of various
types of graphs
– choice of graph
– effect of format and
formatting choices
– conclusions that can
(and cannot) be
supported by a
given data set or
graph
– a rule for probability
of independent
events
some understanding;
partially able to
demonstrate or
explain:
– strengths and
limitations of various
types of graphs
– choice of graph
– effect of format and
formatting choices
– conclusions that can
(and cannot) be
supported by a
given data set or
graph
– a rule for probability
of independent
events
shows understanding;
able to demonstrate
and explain:
– strengths and
limitations of various
types of graphs
– choice of graph
– effect of format and
formatting choices
– conclusions that can
(and cannot) be
supported by a
given data set or
graph
– a rule for probability
of independent
events
shows depth of
understanding; in
various contexts,
demonstrates and
explains:
– strengths and
limitations of various
types of graphs
– choice of graph
– effect of format and
formatting choices
– conclusions that can
(and cannot) be
supported by a
given data set or
graph
– a rule for probability
of independent
events
limited accuracy; often
makes major errors/
omissions in:
– comparing
information in
different graphs
– identifying
misrepresentations
– identifying
misinterpretations
– determining
probability
partially accurate;
makes frequent minor
errors/omissions in:
– comparing
information in
different graphs
– identifying
misrepresentations
– identifying
misinterpretations
– determining
probability
generally accurate;
makes few errors/
omissions in:
– comparing
information in
different graphs
– identifying
misrepresentations
– identifying
misinterpretations
– determining
probability
accurate and precise;
rarely makes errors/
omissions in:
– comparing
information in
different graphs
– identifying
misrepresentations
– identifying
misinterpretations
– determining
probability
does not use
appropriate strategies
to solve probability
problems
uses some appropriate
strategies with partial
success to solve
probability problems
uses appropriate
strategies to
successfully solve
probability problems
consistently uses
effective, and often
innovative, strategies
to solve probability
problems
does not record and
explain reasoning and
procedures clearly and
completely
records and explains
reasoning and
procedures with partial
clarity; may be
incomplete
records and explains
reasoning and
procedures clearly and
completely
records and explains
reasoning and
procedures with
precision and
thoroughness
Procedural Knowledge
 Accurately:
– compares information
provided by different
graphs for the same data
set
– identifies
misrepresentations and
misinterpretations
– determines and verifies
the probability of two
independent events
Problem-Solving Skills
 Uses appropriate
strategies to solve
problems involving the
probability of independent
events
Communication
 Records and explains
reasoning and procedures
clearly and completely,
including appropriate
terminology (e.g., scale of
a graph; outcome)
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Master 7.2
Date
Ongoing Observations:
Data Analysis and Probability
The behaviours described under each heading are examples; they are not intended to be an exhaustive list of all
that might be observed. More detailed descriptions are provided in each lesson under Assessment for Learning.
STUDENT ACHIEVEMENT: Data Analysis and Probability*
Student
Conceptual
Understanding
Procedural
Knowledge
Problem-Solving
Skills
Communication
• Explains and
demonstrates strengths
and limitations,
misrepresentation and
misinterpretation of
graphs
• Compares graphs;
identifies
misrepresentations;
misinterpretations.
Determines
probability of
independent events.
• Solves problems that
involve the probability
of independent events
• Records and explains
reasoning and
procedures clearly and
completely, including
appropriate terminology
* Use locally or provincially approved levels, symbols, or numeric ratings.
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Master 7.3
Date
Performance Assessment Rubric:
Promoting Your Cereal
Not Yet
Adequate
Adequate
Proficient
Excellent
Conceptual Understanding
• Shows understanding of
data presentation by
choosing graphs that:
– misrepresent a data set
– accurately represent a
data set
Choice of graphs
shows very limited
understanding of data
presentation
Choice of graphs
shows partial
understanding of data
presentation
Choice of graphs
shows understanding
of data presentation
Choice of graphs
shows thorough
understanding; may
introduce complexity or
subtleties (e.g.,
misrepresentation may
be hard to detect)
limited accuracy; major
errors or omissions in:
– constructing chosen
graphs
– representing and
misrepresents data
as required
– determining
probability of
winning
Partially accurate;
some errors or
omissions in:
– constructing chosen
graphs
– representing and
misrepresents data
as required
– determining
probability of
winning
generally accurate; few
errors or omissions in:
– constructing chosen
graphs
– representing and
misrepresents data
as required
– determining
probability of
winning
accurate and precise;
very few or no errors
in:
– constructing chosen
graphs
– representing and
misrepresents data
as required
– determining
probability of
winning
uses few effective
strategies; does not
construct the game
successfully
uses some appropriate
strategies with partial
success; game may
have some flaws
uses appropriate
strategies to
successfully construct
a game to given
specifications
uses effective
strategies to
successfully constructs
a relatively complex or
innovative game
does not present work
and explanations
clearly, uses few
appropriate
mathematical terms
presents work and
explanations with
some clarity, using
some appropriate
mathematical terms
presents work and
explanations clearly,
using appropriate
mathematical terms
presents work and
explanations precisely,
using a range of
appropriate
mathematical terms
Procedural Knowledge
• Accurately:
– constructs chosen
graphs
– represents and
misrepresents data as
required
– determines the
probability of winning the
game
Problem-Solving Skills
• Uses appropriate
strategies to construct a
game that involves the
probability of two
independent events
Communication
• Presents work and
explanations clearly, using
appropriate mathematical
terminology
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Master 7.4
Date
Unit Summary: Data Analysis and Probability
Review assessment records to determine the most consistent achievement levels for the assessments conducted.
Some cells may be blank. Overall achievement levels may be recorded in each row, rather than identifying
levels for each achievement category.
Most Consistent Level of Achievement*
Strands: Statistics and
Probability (Data Analysis),
Statistics and Probability
(Chance and Uncertainty)
Conceptual
Understanding
Procedural
Knowledge
ProblemSolving Skills
Communication
Ongoing Observations
Work samples or portfolios;
conferences
Unit Test
Unit Problem
Promoting Your Cereal
Achievement Level for reporting
*Use locally or provincially approved levels, symbols, or numeric ratings.
Self-Assessment:
Comments: (Strengths, Needs, Next Steps)
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Name
Master 7.5
1.
Date
Reflecting on Learning: Unit 7
Read each of the Learning Goals for data analysis and probability. Think about your learning.
Rate your learning for each goal using these symbols.
+ = I can understand and do this very well.
√ = I can understand and do this all right.
– = I am still having trouble with this.
× = This is a big problem for me.
Learning goal
Critique ways in which data are presented
My rating
In my own words, this means I am able to
Solve problems that involve the probability of
independent events
In my own words, this means I am able to
2.
Which of the following activities is usually most helpful to you in math:
– listening to explanations
– talking to your classmates or working in a group
– working with concrete objects
– using real-life examples
– doing practice work (pencil and paper)
Choose one and explain how it helps you learn.
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
_______________________________________________________________________________
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Master 7.6a
Date
Additional Activity 1:
Scenario Graphs
Work in groups of 3 or 4.
You will need Scenario Cards (Master 7.6b), a die, 0.5-cm grid paper (PM 22), and percent circles
(Master 7.10) or a compass and protractor.
How to Play:
 Choose a scenario card.
 Fill in each blank on the card by rolling the die and recording the number shown.
 Display the data using the graph that best represents the data.
 Present your graph to the rest of the group and describe a scenario when your graph would be
the best choice to display the data.
 Other members of the group may “challenge” you. To do this, they must choose a different
type of graph that they think would better display the data for your scenario and explain their
reasoning to the group. The group decides which type of graph is best or whether more than
one graph is best.
 You win 5 points if your type of graph is best.
Challengers win 2 points if their type of graph is best.
 Continue playing until each group member has used 2 scenario cards to create a graph.
Take It Further: Create your own scenario cards.
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Master 7.6b
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Scenario Cards
Ujarak collected these data
about the colours of socks
students in his class wore on
Monday:
No socks: ____ students
White: ____ students
Grey: ____ students
Black: ____ students
Other: ____ students
The number of hours Maurice
spent doing extracurricular
activities after school are:
Monday: ____ h
Tuesday: ____ h
Wednesday: ____ h
Thursday: ____ h
Friday: ____ h
The final marks for the students
in Mrs. Van Ee’s class were:
A: ____ students
B: ____ students
C: ____ students
D: ____ students
F: ____ students
The number of people in the
families of the students in
Nathan’s class are:
2: ____ students
3: ____ students
4: ____ students
5: ____ students
6 or more: ____ students
A band purchases T-shirts for
all of its members. The sizes it
orders are:
XS: ____ band members
S: ____ band members
M: ____ band members
L: ____ band members
XL: ____ band members
The ocean temperature near
Prince Rupert, BC on
5 consecutive days was:
Day 1: ____°C
Day 2: ____°C
Day 3: ____°C
Day 4: ____°C
Day 5: ____°C
The number of times Annika
went to the movie theatre each
month was:
Jan.: ____ times
Feb.: ____ times
Mar.: ____ times
Apr.: ____ times
Haruna collected these data
about how often her father
napped for 4 weeks:
Week 1: ____ times
Week 2: ____ times
Week 3: ____ times
Week 4: ____ times
The favourite seasons of the
students in Mikayla’s class are:
Autumn: ____ students
Winter: ____ students
Summer: ____ students
Spring: ____ students
Maurice recorded how often
each of his sisters said “like” in
an hour:
Mandisa: ____ times
Keira: ____ times
Jayda : ____ times
Latasha: ____ times
Tony collected these data about
the weekly allowance students
in his class received:
None: ____ students
Less than $5: ____ students
$5–$9.99: ____ students
$10–$14.99: ____ students
$15 or more: ____ students
The number of hours Malik
spent watching television each
week was:
Week 1: ____ h
Week 2: ____ h
Week 3: ____ h
Week 4: ____ h
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Master 7.7
Date
Additional Activity 2:
Misleading Graphs Scavenger Hunt
Work with a partner.
You will need newspapers, magazines, or access to the Internet.
How to Play:
 To complete this scavenger hunt, look through newspapers, magazines, or the Internet with
your partner for different types of misleading graphs. Record where you found each graph in
the reference column of the table below.
Look for these misleading graphs:
 Reference
Pictograph
Bar Graph
Line Graph
Circle Graph
Other:
Other:
Other:
Other:
 Stop searching for graphs after 30 minutes. Compare graphs with another pair of students.
Explain why each graph is misleading and why it may have been displayed in that way.
Whichever pair finds the most types of misleading graphs wins.
Take It Further: Draw an accurate representation of the data in each graph, if possible.
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Master 7.8a
Date
Additional Activity 3:
Spinner Winner
Play in pairs.
You will need a copy of Spinners for Spinner Winner (Master 7.8b).
How to Play:
 Choose one of the spinners.
Colour or shade it to create different sectors.
 Suppose you spin the pointer once.
Which events are possible?
What is the probability of each event?
Suppose you spin the pointer twice.
Which events are possible?
What is the probability of each event?
Continue to find as many events and their probabilities as you can for up to 5 spins.
 For example, if you choose a spinner with congruent red and blue sectors, you might find the
probabilities of these events:
Landing on red or blue: 1
1
2
1
8
: Landing on red once
: Landing on red, then blue, then blue
1
32
: Landing on blue 5 times in a row
 After 3 minutes, play stops.
With your partner, compare the possible events you found.
Cross out all the events you have in common.
If one person has an event the other person does not have, the other player draws a probability
tree or uses the rule to check that the probability of the event is correct.
Each correct probability is worth 1 point.
 Whoever has more points wins.
Take It Further: Use two or more spinners.
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Spinners for Spinner Winner
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Master 7.9
Date
Additional Activity 4:
Probability Maze
Work alone.
How to Play:
 Find a path through this maze. Your path will go through several dots.
 Suppose an ant walks through the maze.
At each circle, it has the option of going in 2 directions (it cannot go back the way it came).
So, the probability of it going in either direction is
1
2
.
Find the probability that the ant walks along your path.
Take It Further: Find a path through the maze with probability less than 0.05%.
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Master 7.10
Date
Percent Circles
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Date
Step-by-Step 1
Master 7.11
Lesson 7.1, Question 8
Table A
Table B
Sizes of Shoes Sold in May
Step 1
Yearly Sales
Size
Number of Pairs Sold
Year
Sales ($)
6
60
2000
579 000
7
239
2001
621 000
8
217
2002
598 000
9
156
2003
634 000
10
61
2004
657 000
11
43
2005
642 000
12
36
2006
675 000
A line graph displays data that change over ________________
Which table contains this type of data? ____________________
Step 2
Look at the data in the other table. Check off each characteristic that is true for the data.

Characteristics
The data are discrete
The data change over time
The data might be compared
There is a clear part-to-whole relationship
The data are large numbers
The data are small numbers
Which types of graph could you use to display the data? ______________________
Which type of graph would best display the data? Explain. ____________________
___________________________________________________________________
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Master 7.12
Date
Step-by-Step 2
Lesson 7.2, Question 10
Step 1
When you first look at the graphs, does it seem like more boys or
more girls participate in sports?________________________________________
Why do you think so? _______________________________________________
_________________________________________________________________
Step 2
Use the 2 graphs to complete the table.
Swimming
Soccer
Baseball
Cross-Country
Running
Total
Number
of Boys
Number
of Girls
Do more boys or more girls participate in sports? _______________________
Step 3
Complete this chart.
Graph A
Each bar is
Graph B
squares wide
The vertical scale starts at
1 square represents
.
participants
How could the graphs be changed to present the data accurately?_____________
_________________________________________________________________
Step 4
What other graph could you use to accurately represent the data?
double bar graph
line graph
circle graph
pictograph
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Master 7.13
Date
Step-by-Step 3
Lesson 7.3, Question 12
Step 1
A bag contains 6 red (R), 4 blue (B), 2 yellow (Y) marbles.
The total number of marbles is: _____________
On the back of this page, draw a table to show all the possible
outcomes of choosing a marble out of the bag 2 times.
Step 2
Find each probability.
P(red) =
P(yellow) =
P(red then yellow) =
Step 3
Find each probability.
P(blue) =
P(blue 2 times in a row) =
Step 4
Find each probability.
P(not blue) =
P(yellow) =
P(not blue then yellow) =
Step 5
Suppose the marble is not returned to the bag after the first draw.
How many marbles are left? _________
Does removing one marble affect the possible outcomes of the next draw? __________
Explain. _______________________________________________________________
______________________________________________________________________
Are the events independent? _________
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Master 7.14
Date
Step-by-Step 4
Lesson 7.4, Question 9
Step 1
In a deck of cards, there are:
• an equal number of cards of each suit (♥, ♦, ♠, ♣)
The number of suits are: _______
• an equal number of cards of each colour (red and black)
The number of card colours are: _______
• an equal number of cards of each value (A, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K)
The number of card values are: _______
Nadine (N), Joshua (J), and Shirley (S) each have a complete deck of cards.
Step 2
Find each probability.
P(N:♥) =
P(J:♥) =
P(S:♥) =
P(J:♠) =
P(S:red) =
P(J:black) =
P(S:A) =
P(N:♥ and J:♥ and S:♥) =
Step 3
Find each probability.
P(N:♠) =
P(N:♠ and J:♠ and S:red) =
Step 4
Find each probability.
P(N:not ♥) =
P(N:not ♥ and J:black and S:A) =
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Master 7.15a
1.
Date
Unit Test: Unit 7 Data Analysis and Probability
Each graph displays the number of students who were late for class at A.R.C. High School in one
week.
a) What is an advantage of each graph?
b) What is a disadvantage of each graph?
c) Which graph would you choose to show how the number of late students
changed throughout the week?
d) Which graph would you choose to show that the number of late students
was about the same each day?
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Master 7.15b
2.
Date
Unit Test continued
These graphs show the number of sport cards Robbie and Spencer have each collected.
a) What impression does each graph give?
b) Who do you think drew the graphs, Robbie or Spencer? Why?
c) What would you change about the graphs to present the data accurately?
3.
These tables show data about movie ticket sales at Clear View Theatre.
Table A
Table B
Number of Tickets Sold Last Week
Total Number of Tickets Sold
Ticket Type
Number of
Tickets
Week
Number of
Tickets
Child
553
1
3558
Student
780
2
3459
Adult
1434
3
3010
Senior
312
4
2780
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Master 7.15c
Date
Unit Test continued
a) Graph the data in a misleading way.
b) What impression does your graph give?
________________________________________________________________________
________________________________________________________________________
c) Describe how you created that impression.
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
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Master 7.15d
4.
Date
Unit Test continued
A spinner has three congruent sectors coloured orange, green, and purple.
a) Use the rule to find the probability of each event:
i) Landing on orange, then landing on purple.
ii) Landing on the same colour 2 times in a row.
b) Use a tree diagram to verify your answers to part a.
5.
A bag contains 2 red marbles, 1 white marble, and 3 blue marbles. A marble is removed without
looking, its color is recorded, and it is returned to the bag. Find the probability of each event:
a) Removing a red marble, then a white marble, then a blue marble.
b) Removing a marble that is not red 3 times in a row.
c) Removing a blue marble, then a black marble, then a red marble.
d) Removing a blue marble, then a white marble, then 3 red marbles.
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Master 7.16
1.
2.
3.
Date
Unit 7 Test Sample Answers
Answers may vary. For example:
a) Line graph: Shows the actual number of
students who are late, and the trend over time:
more students were late just after or just before
the weekend.
Circle graph: Shows how the number of late
students for each day compares to the total
number of late students for the week.
b) Line graph: Since the graph uses the zigzag
symbol on the vertical axis, it is difficult to
compare the total number of late students for
different days. It is a bit difficult to read data
values not on horizontal lines.
Circle graph: The actual number of late students
isn’t given, so you can’t tell whether there were
about 100 late students each day or about 5.
c) Line graph
d) Circle graph
b) Ticket sales are about the same—they are all
low.
c) I made the vertical scale very large and extended
the graph a long way above the largest data
value.
4.
1
×
3
1
=
3
ii) 1 ×
1
9
=
3
1
3
b)
First
Spin
Second
Spin
Possible
Outcomes
orange
orange/orange
green
orange/green
purple
orange/purple
orange
green/orange
green
green/green
purple
green/purple
orange
purple/orange
green
purple/green
purple
purple/purple
orange
Answers may vary. For example:
a) The left graph gives the impression that Spencer
doesn’t have many sport cards. The right graph
gives the impression that Robbie has a lot of
hockey and basketball cards.
b) Robbie; It looks like he has more cards.
c) Graph the data on a double bar graph so I could
make sure the vertical scales were the same.
Make each bar have the same width.
Answers may vary. For example:
a)
1
a) i)
green
purple
5.
a)
2
6
×
1
6
×
3
6
=
b)
4
6
×
4
6
×
4
6
=
1
3
1
6
×
2
2
×
3
1
2
×
×
3
=
2
=
3
1
36
8
27
c) 0
d)
3
6
×
1
6
×
2
6
×
2
6
=
1
2
×
1
6
×
1
3
×
×
1
3
2
6
×
1
3
=
1
324
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