Download sample tasks - Deep Curriculum Alignment Project for Mathematics

Common Core Learning Standards
GRADE 7 Mathematics
STATISTICS & PROBABILITY
Common Core Learning
Standards
Use random sampling to draw
inferences about a population.
7.SP.1.
Understand that statistics can be used to gain
information about a population by examining a
sample of the population; generalizations
about a population from a sample are valid
only if the sample is representative of that
population. Understand that random sampling
tends to produce representative samples and
support valid inferences.
Concepts
random
sampling
Embedded Skills
Explain how statistics is used to gain information
about a population.
Evaluate the validity of a statistical sample from a
population.
Explain why random sampling produces a sample
representative of a population.
Vocabulary
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Population
Sample
representative
sample
biased sample
random
sampling
inferences
validity
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Use random sampling to draw
inferences about a population.
7.SP.2.
Use data from a random sample to draw
inferences about a population with an
unknown characteristic of interest. Generate
multiple samples (or simulated samples) of the
same size to gauge the variation in estimates
or predictions. For example, estimate the mean
word length in a book by randomly sampling
words from the book; predict the winner of a
school election based on randomly sampled
survey data. Gauge how far off the estimate or
prediction might be.
Concepts
Embedded Skills
drawing
inferences
Draw inferences about a population with a certain
characteristic from data gathered from a random
sample.
Gather data from multiple random samples of the
same size in reference to a certain characteristic.
Read and draw conclusions from statistical data and
representations (box-and-whisker plot, line/dot
plot)
Vocabulary
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Inference
random
sampling
population
characteristic
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Concepts
Draw informal comparative
inferences about two populations.
variability of
data
distributions
7.SP.3.
Informally assess the degree of visual overlap
of two numerical data distributions with similar
variabilities, measuring the difference between
the centers by expressing it as a multiple of a
measure of variability. For example, the mean
height of players on the basketball team is 10
cm greater than the mean height of players on
the soccer team, about twice the variability
(mean absolute deviation) on either team; on a
dot plot, the separation between the two
distributions of heights is noticeable.
Embedded Skills
Describe the variability of two numerical data sets.
Compute the mean absolute deviation, range, and
interquartile range.
Describe how many times larger/smaller the
variability of one data set is to another.
Read and interpret data from statistical
representations (box-and-whisker plot, line/dot
plot).
Vocabulary
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variability
(how far away
from the
mean)
mean
absolute
deviation
range
outlier
interquartile
range
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Draw informal comparative
inferences about two populations.
7.SP.4.
Use measures of center and measures of
variability for numerical data from random
samples to draw informal comparative
inferences about two populations. For
example, decide whether the words in a
chapter of a seventh grade science book are
generally longer than the words in a chapter of
a fourth-grade science book.
Concepts
Embedded Skills
measures of
central
tendency and
variability to
make
inferences
Compare/contrast measures of central tendency to
draw conclusions about two random samples.
Compare/contrast variability of two data sets to
draw conclusions about two random samples.
Read and interpret data from statistical
representations (box-and-whisker plot, line/dot
plot).
Vocabulary
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measures of
central
tendency
(mean,
median,
mode)
variability
range
outlier
interquartile
range
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
Concepts
Probability
Embedded Skills
Define probability as number between 0 and 1.
Describe a situation in which the event is unlikely.
Identify the probability of an unlikely event as a
number near 0.
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.
Vocabulary
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Probability
Event
likely event
unlikely event
Describe a situation in which the event is likely.
Identify the probability of a likely event as a number
near 1.
Describe a situation in which the event is neither
likely nor unlikely.
Identify the probability of an event that is neither
likely nor unlikely as a number near ½.
SAMPLE TASKS
I.
Sara has box that holds 7 blue marbles, 5 purple marbles, 3 white marbles, and 15 red marbles. She pulls one marble out of the
box without looking.
a. Is it more likely, less likely, or equally likely that Sara will pick a blue marble than a purple marble from the box? Explain why
you chose your answer.
b. Describe an event in which the outcome has a probability of 0.
c. Describe an event in which the outcome has a probability of 1.
d. Describe an event in which the outcome has a probability of 1/2.
II.
The 7th grade math class has a number cube and a fair coin. Order the following probabilities from least likely to most likely:
flipping a tail, flipping a head or a tail, rolling a number that is not 1, and rolling a 1.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.6.
Approximate the probability of a chance event
by collecting data on the chance process that
produces it and observing its long-run relative
frequency, and predict the approximate
relative frequency given the probability. For
example, when rolling a number cube 600
times, predict that a 3 or 6 would be rolled
roughly 200 times, but probably not exactly
200 times.
Concepts
Embedded Skills
Approximating Predict the number of times an event occurs by
multiplying the theoretical probability by the
probability
number of trials.
Compute the experimental probability of an event
occurring through repeated trials.
Compare the theoretical probability of an event
occurring and the experimental probability.
Predict future probabilities based on data collected.
Vocabulary
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Probability
Event
Outcomes
possible
outcomes
favorable
outcomes
theoretical
probability
experimental
probability
trials
Compare theoretical and experimental probability.
(delete? Same as 3rd one?)
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
SAMPLE TASKS
I.
a. What is the theoretical probability of rolling a 2 on a number cube?
b. Predict the number of time you will roll a 2 if you roll the die 50 times.
c. Roll a number cube 50 times and record your results in a table.
d. Calculate the experimental probability of rolling a 2.
e. Explain any similarities or differences between your experimental probability and theoretical probability.
II. Keith and his grandfather are counting the types of birds that arrive at a feeder in their backyard. The results of their observations are in
the table below.
Birds at the Feeder
Goldfinch
Robins
21
7
Use the experimental probability to predict how many of the next 20 birds will be goldfinches.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.7a.
Develop a uniform probability model by
assigning equal probability to all outcomes,
and use the model to determine probabilities
of events. For example, if a student is selected
at random from a class, find the probability
that Jane will be selected and the probability
that a girl will be selected.
Concepts
Probability of
equally likely
events
Embedded Skills
Compare and contrast uniform probability with
experimental probability.
Vocabulary
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Calculate simple probabilities of events.
Create a uniform probability model (a situation in
which all outcomes are equally likely)
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Outcomes
Events
simple
probability
equally likely
uniform
probability
model
Create an experimental probability model (or
survey).
SAMPLE TASKS
I.
II.
Define uniform probability.
Explain
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.7b.
Develop a probability model (which may not be
uniform) by observing frequencies in data
generated from a chance process. For example,
find the approximate probability that a
spinning penny will land heads up or that a
tossed paper cup will land open-end down. Do
the outcomes for the spinning penny appear to
be equally likely based on the observed
frequencies?
Concepts
experiments
Embedded Skills
Design an experiment to investigate the likelihood
of an outcome.
Compare the results of a series of trials and draw
conclusions.
Vocabulary
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probability
model (not
uniform)
probability
model
(uniform)
frequencies
data
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.8a.
Understand that, just as with simple events,
the probability of a compound event is the
fraction of outcomes in the sample space for
which the compound event occurs.
Concepts
Compound
probability
Embedded Skills
Calculate compound probabilities.
Determine the total number of possible outcomes
(sample space or Counting Principle).
Define compound probabilities as fractions of the
sample space taken from.
Vocabulary
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Probability
tree diagrams
simulation
sample space
compound
events
simple events
outcomes
Fundamental
Counting
Principle
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.8b.
Represent sample spaces for compound events
using methods such as organized lists, tables
and tree diagrams. For an event described in
everyday language (e.g., “rolling double sixes”),
identify the outcomes in the sample space
which compose the event.
Concepts
compound
sample space
Embedded Skills
Construct a tree diagram, list, or table to illustrate
all possible outcomes of a compound event.
Calculate the probability of a compound event
based on a table, list, or tree diagram.
Vocabulary
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tree diagrams
lists
tables
compound
events
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Common Core Learning
Standards
Investigate chance processes and
develop, use, and evaluate
probability models.
7.SP.8c.
Design and use a simulation to generate
frequencies for compound events. For
example, use random digits as a simulation tool
to approximate the answer to the question: If
40% of donors have type A blood, what is the
probability that it will take at least 4 donors to
find one with type A blood?
Concepts
Embedded Skills
simulation
Design a simulation to generate data for compound
events.
Calculate the probability of a compound event from
data generated in a simulation.
Vocabulary
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Simulation
compound
events
data
SAMPLE TASKS
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.
Copyright (c) 2011 by Erie 1 BOCES- Deep Curriculum Project for Mathematics-- Permission to use (not alter) and reproduce for educational purposes only.