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Big Idea Data Analysis: Reading,
understanding, interpreting, and communicating data are critical in
modeling a variety of real-world situations, drawing appropriate
inferences, making informed decisions, and justifying those
decisions.
Big Idea Probability: Probability quantifies the
likelihood that something will happen and enables us to make
predictions and informed decisions.
Big Idea Discrete Mathematics: Discrete mathematics
consists of tools and strategies for representing, organizing, and
interpreting non-continuous data. |
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4.4 A.
Data Analysis |
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Descriptive Statement: In today's information-based world,
students need to be able to read, understand, and interpret data in
order to make informed decisions. In the early grades, students
should be involved in collecting and organizing data, and in
presenting it using tables, charts, and graphs. As they progress,
they should gather data using sampling, and should increasingly be
expected to analyze and make inferences from data, as well as to
analyze data and inferences made by others. |
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Essential Questions |
Enduring Understandings |
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- How can the collection, organization,
interpretation, and display of data be used to answer questions?
(4.5A4; 4.5A6; 4.5E1; 4.5E2; 4.5F1; 4.5F6) |
- The message conveyed by the data depends on how
the data is collected, represented, and summarized. (4.5A6; 4.5D6;
4.5E1; 4.5E2; 4.5E3)
- The results of a statistical investigation can be used to support
or refute an argument. (4.5D1; 4.5D3; 4.5D5; 4.5E2; 4.5E3; 4.5F6) |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Collect, generate,
record, and organize data in response to questions, claims, or curiosity.
·
Data collected
from students’ everyday experiences
·
Data generated
from chance devices, such as spinners and dice
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2.
Read, interpret,
construct, and analyze displays of data.
·
Pictures, tally
chart, pictograph, bar graph, Venn diagram
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Smallest to
largest, most frequent (mode)
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4.4
B. Probability |
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Descriptive Statement: Students need to understand the
fundamental concepts of probability so that they can interpret
weather forecasts, avoid unfair games of chance, and make informed
decisions about medical treatments whose success rate is provided in
terms of percentages. They should regularly be engaged in predicting
and determining probabilities, often based on experiments (like
flipping a coin 100 times), but eventually based on theoretical
discussions of probability that make use of systematic counting
strategies. High school students should use probability models and
solve problems involving compound events and sampling. |
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Essential Questions |
Enduring Understandings |
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- How can experimental and theoretical
probabilities be used to make predictions or draw conclusions?
(4.5D5; 4.5D6) |
- Experimental results tend to approach
theoretical probabilities after a large number of trials. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Use chance devices
like spinners and dice to explore concepts of probability.
·
Certain,
impossible
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More likely, less
likely, equally likely |
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2.
Provide
probability of specific outcomes.
·
Probability of
getting specific outcome when coin is tossed, when die is rolled, when spinner
is spun (e.g., if spinner has five equal sectors, then probability of getting a
particular sector is one out of five)
·
When picking a
marble from a bag with three red marbles and four blue marbles, the probability
of getting a red marble is three out of seven |
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4.4
C. Discrete Mathematics - Systematic Listing And Counting |
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Descriptive Statement: Development of strategies for
listing and counting can progress through all grade levels, with
middle and high school students using the strategies to solve
problems in probability. Primary students, for example, might find
all outfits that can be worn using two coats and three hats; middle
school students might systematically list and count the number of
routes from one site on a map to another; and high school students
might determine the number of three-person delegations that can be
selected from their class to visit the mayor. |
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Essential Questions |
Enduring Understandings |
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- How can attributes be used to classify
data/objects?
- What is the best way to solve this? What counting strategy works
best here? |
- Grouping by attributes (classification) can be
used to answer mathematical questions. (4.5E1; 4.5E3)
- Algorithms can effectively and efficiently be used to quantify and
interpret discrete information. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Sort and classify
objects according to attributes.
·
Venn diagrams
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2.
Generate all
possibilities in simple counting situations (e.g., all outfits involving two
shirts and three pants). |
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4.4 D. Discrete Mathematics - Vertex-Edge Graphs And Algorithms |
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Descriptive Statement: Vertex-edge graphs, consisting of
dots (vertices) and lines joining them (edges), can be used to
represent and solve problems based on real-world situations.
Students should learn to follow and devise lists of instructions,
called "algorithms," and use algorithmic thinking to find the best
solution to problems like those involving vertex-edge graphs, but
also to solve other problems. |
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Essential Questions |
Enduring Understandings |
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- How can visual tools such as networks
(vertex-edge graphs) be used to answer questions? (4.5E1; 4.5E3)
- How can algorithmic thinking be used to solve problems? |
- Optimization is finding the best solution
within given constraints.
- Algorithms can effectively and efficiently be used to quantify and
interpret discrete information. |
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Areas of Focus/Cumulative Progress Indicators |
Comments and Examples |
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By the end of Grade 2: |
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1.
Follow simple sets
of directions (e.g., from one location to another, or from a recipe). |
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2.
Color simple maps
with a small number of colors. |
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3.
Play simple two-person games
(e.g., tic-tac-toe) and informally explore the idea of what the outcome should
be. |
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4.
Explore concrete
models of vertex-edge graphs (e.g. vertices as
“islands” and edges as “bridges”).
·
Paths from one vertex to another |
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