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How can you represent, interpret, and analyze information using data?

Common Core Standards 2017-2018 Print Unit 10
High School - Math - Algebra I - Unit 10
Descriptive Statistics
*How to use measures of central tendency and statistical plots
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Students will use algebra skills to model, organize, and interpret information in order to solve real-life problems.

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-Data Representations include dot plots, histograms, box plots (S.ID.1)
-Compare measures of center & spread based on shape of data distributions (S.ID.2)
-Interpret differences in data sets, extreme outliers (S.ID.3)
-Summarize categorical data in two-way frequency tables. Interpret joint, marginal and conditional relative frequencies (S.ID.5)
-Classify two variable data as linear, exponential, quadratic (scatter plots) (S.ID.6)
-Create best fit line for linear scatter plots; interpret slope and intercept (S.ID.6b,c, S.ID.7)
-Use residual values to informally assess the fit of a function. (S.ID.6b)
-Correlation coefficient (technology) of linear fit (S.ID.8)
-Distinguish between correlation and causation (S.ID.9)

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I can choose the best representation for a set of data.
I can determine whether or not a representation shows all the data values in a set.
I can choose the appropriate measure for spread of data distribution.
I can choose appropriate measure for center and data distribution.
I can choose the box and whisker plot with the greatest interquartile range when several box and whisker plots are shown.
I can identify outliers for a data set.
I can interpret differences in shape, center and spread in the context of data sets.
I can describe the possible effects the presence of outliers in a set of data can have on shape, center and spread in the context of data sets.
I can recognize the differences between joint, marginal and conditional relative frequencies.
I can calculate relative frequencies including joint, marginal and conditional relative frequencies.
I can write clear summaries of data displayed in a two-way frequency table.
I can interpret and explain the meaning of relative frequencies in the context of a problem.
I can make appropriate displays of joint, marginal and conditional distributions.
I can describe patterns observed in data.
I can recognize the association between two variables by comparing conditional and marginal percentages.
I can represent data on a scatter plot.
I can fit a given function class (linear, exponential and quadratic) to data.
I can use given scatter plot data represented on the coordinate plane and describe how the two variables are related.
I can determine which function best models scatter plot data represented on the coordinate plane.
I can use functions fitted to data to solve problems in the context of the data.
I can represent the residuals from a function and the data set it models numerically and graphically.
I can informally assess the fit of a function by analyzing residuals from the residual plot.
I can sketch a line of best fit on a scatter plot that appears linear.
I can write the equation of the line of best fit using technology or by using two points on the scatter plot.
I can interpret the slope and the intercept of a linear model for a data set.
I can use technology to compute the correlation coefficient of a linear line of best fit.
I can define the correlation coefficient.
I can interpret the correlation coefficient of a linear fit as a measure of how well the data fits the relationship.
I can define positive, negative and no correlation.
I can explain why correlation does not imply causation.
I can distinguish between correlation and causation.
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Mean, median, mode, stem-and-leaf plot, measure of central tendency, box-and-whisker plot, quartiles, scatter plot, positive correlation, negative correlation, no correlation, scatter plot, outliers, joint, marginal and conditional, residuals
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Educator Uploaded Plans (These are educators specific templates with included information and specifics)
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Common core standards, textbook, geometry sketchpad, zoom math, TI-84 graphing calculators,
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Thinking Strategies for Readers
Researchers who have studied the thinking processes of proficient readers conclude that if teachers taught the following strategies instead of much of the traditional skills-based reading curriculum, students who use the strategies would be better equipped to deal with a variety of texts independently (Keene and Zimmerman, 1997). These strategies are use­ful for composing meaning at both a text and word level.
Monitoring for Meaning
at a text level, readers . . .
pause to reflect on their growing understandings
recognize when they understand the text, and when they don’t
identify when and why the meaning of the text is unclear
identify the ways in which a text becomes gradually more understandable by reading past an unclear portion and by rereading text
decide if clarifying a particular confusion is critical to overall understanding
explore a variety of means to remedy confusion
consider, and sometimes adjust, their purpose for reading
check, evaluate and make revisions to their evolving interpretation(s) of text
at a word level, readers . . .
identify confusing words
employ a range of options for reestablishing meaningful reading (e.g., rereading, reading on, using words around the unknown word, using letters and sounds, using a meaningful substitution)
Activating, Utilizing and Building Background Knowledge (Schema)
at a text level, readers . . .
activate relevant, prior knowledge before, during and after reading
build knowledge by deliberately assimilating new learning with their related prior knowledge
clarify new learning by deleting inaccurate schema
relate texts to their world knowledge, to other texts and to their personal experiences
activate their knowledge of authors, genre, and text structure to enhance understanding
recognize when prior knowledge is inadequate and take steps to build knowledge necessary to understand
at a word level, readers . . .
apply what they know about sounds-letter relationships and word parts to make sense of unknown words
Asking Questions
at a text-level, readers . . .
generate questions before, during and after reading about the text’s content, structure and language
ask questions for different purposes, including clarifying their own developing understandings, making predictions, and wondering about the choices the author made when composing
realize that one question may lead to others
pursue answers to questions
consider rhetorical questions inspired by the text
distinguish between questions that lead to essential/deeper understandings and “just curious” types of questions
allow self-generated questions to propel them through text
contemplate questions posed by others as inspiration for new questions
at a word level, readers . . .
pose self-monitoring questions to help them understand unknown/unfamiliar words (e.g., “What would make good sense?”, “What would sound like language?”, “What would sound right and match the letters?”, “Is this a word I want to use as a writer? If so, how am I going to remember it?”)
Drawing Inferences
at a text level, readers . . .
draw conclusions about their reading by connecting the text with their schema
make, confirm, and/or revise reasonable predictions
know when and how to infer answers to unanswered questions
form unique interpretations to deepen and personalize reading experiences
extend their comprehension beyond literal understandings of the printed page
make judgments and create generalizations about what they read
create a sense of expectation as they read
at the word level, readers . . .
use context clues and their knowledge of language to predict the pronunciation and meaning of unknown/unfamiliar words
Determining Importance
at a text level, readers . . .
identify key ideas, themes and elements as they read
distinguish between important and unimportant information using their own purpose(s), as well as the text structures and word cues the author provides
use text structures and text features to help decide what is essential and what is extraneous
use their knowledge of important and relevant parts of text to prioritize what they commit to long-term memory and what they retell and/or summarize for others
consider the author’s bias/point of view
use the filter of essential/other to clarify usefulness when applying other cognitive strategies to their reading
at a word level, readers . . .
determine which words are essential to the meaning of the text
know when choosing to skip words/phrases of text will or will not impact their overall un­derstanding
make decisions about when unknown/unclear words need clarification immediately and accurately, and when substitutions can be used to maintain meaning and fluency
Creating Sensory Images
at a text level, readers . . .
immerse themselves in rich detail as they read
create images connected to the senses of sight, hearing, taste, touch and smell to enhance and personalize understandings
attend to “heart” images – feelings evoked while reading
revise their images to incorporate new information and new ideas revealed in the text
adapt their images in response to the images shared by other readers
at a word level, readers . . .
use visual, auditory and kinesthetic modes when learning how words work
use what they know about a word’s appearance (e.g., length, spacing above and below the line) to understand unknown words
ask themselves “Does that look right?” and “Does that sound right?” whencross-checking unknown words
Synthesizing Information
at a text level, readers . . .
continually monitor overall meaning, important concepts and themes while reading
recognize ways in which text elements fit together to create larger meaning
create new and personal meaning
develop holistic and/or thematic statements which encapsulate the overall meaning of the text
capitalize on opportunities to share, recommend and criticize books
attend to the evolution of their thoughts across time while reading a text, and while reading many texts
at a word level, readers . . .
select specific vocabulary from the text(s) to include in their synthesis because they know that specific language is highly meaning-laden
know when certain vocabulary is critical to the text’s overall meaning, and therefore, must be understood if comprehension is to be achieved
Problem Solving
at a text level, readers . . .
know that once meaning has broken down, that any of the other cognitive behaviors can be employed to repair understanding
use information from the three deep surface structure systems to repair text meaning
at a word level, readers . . .
use information from the three surface structure systems to solve word issues
select from a wide range of word strategies (e.g., skip and read on, reread, use context clues, use the letters and sounds, speak to a peer reader) to help make sense of unknown words
develop reading fluency
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Thoughtful Strategies by Learning Style
Self – Expressive
Utility (Can be used in multiple styles)
Fact or Fiction
Spider/Fist List
Word Association
Word Wall
Reading for Meaning
Interactive Lecture
Group & Labeling
Memory Box
Write to Learn
Building Writing
Reciprocal Learning
Give one, Get one
Collaborative Summarizing
Anticipation Guides
Concept Attainment
Yes, No, Why
Graduated Difficulty
Comprehension Menu
Task Rotation
Voc Notebook
Carousel Brainstorming
Reader’s Theatre
Vocabulary Code
4-2-1 Free Write
The biggies…. The following strategies require a little more planning to use. They are all very effective. Your school has folders and materials that specifically explain these strategies.
Word Works-Cracking Vocabulary’s CODE – 4 phases of vocabulary learning
  • Connect – new words to prior knowledge
  • Organize – new words to find relationships
  • Deep-processing – internalizing the words, deepen the understanding
  • Exercise – or rehearse their knowledge of new words
Reading for Meaning – strategy that helps students become proficient at making claims, finding main ideas, and using reasoning and details to support their ideas.
· Students are presented with a series of statements before they read the text, they need to either agree/disagree with the statement.
· After reviewing the statements, the students read the text and collect evidence either for or against the statements.
Task Rotation – creating activities that fit students’ learning styles:
· Mastery
· Interpersonal
· Understanding
· Self-expressive
Interactive Lecture – strategy that increases the students’ ability to remember, comprehend, and think actively about a lectures’ content. It engages the students by moving them through the four phases:
  • Connect – hook students’ attention
  • Organize – use graphic organizer/note taking procedure to help organize info
  • Deep-processing – pause every 5-7 min during lecture to allow students time to process information with questions in the different learning styles
  • Exercise – use review questions and have students use notes in a synthesis or application task.
These activities or tools are easy to slip in anywhere within your unit plan. They can be used for the CODE strategies, class openers, to brainstorm, to review, or as energizers for those “glazed over” moments. They are categorized somewhat, but several of these activities can be used in more than one category. Many of the strategies are referenced (in parenthesis) if you want more information on each of these activities.
Class Openers
Fact or Fiction/ Three’s a Crowd – Students decide which word/fact of three doesn’t belong and explain why. (Tool book p.10)
Anticipation Guides – Teacher prepares 3-5 statements based on the content that the students will be reading. Students are asked to decide which statements they believe the text will support. Teacher develops a class tally for each statement and discusses opinions. Students then read text. (Tool book p. 40)
Give one, Get one- students generate ideas from a question posed by the teacher, then have to collect a predetermined number of ideas from their classmates. (Tool book, p.11)
KWL- Tool to assess students’ prior knowledge, help generate questions about what they want to learn, and encourage reflection about what they have learned. (Tool book, p.28)
Spider List/Fist list/Fishbone- teacher provides a category in palm of hand/belly of spider and the students brainstorm ideas to fill in the fingers/legs/bones of hand print, spider, or fish sketch or vice versa.
Word Association/3-way tie- students select 3 words from a unit vocabulary and arrange them in a triangle. They then connect the words with lines then write a sentence that describes the relationship between the words that are connected. (binder)
Content Teaching
Word Wall – Collection of words on the wall for students to use during their reading and writing (Binder)
Reciprocal Learning/Peer Practice Strategy- students work in pairs (player and coach) to review or read & summarize concepts.
Think/pair/share-teacher poses a question, the students think and construct a response, then share their ideas with a neighbor, teacher records/collects their ideas. (Tool book, p.10)
Vocabulary Notebook- Where students collect critical vocabulary In the notebook students can write their initial “educated” definitions, then they can write the dictionary definition, and maybe a visual image as well. There is a lot of variations to this one. (Tool book, p. 92; binder)
Group & Labeling – students examine a list of vocabulary words and place them into groups based on common characteristics. For each group that students create, they devise a label that describes
Etch-a-sketch – students draw pictures, symbols, or icons to represent ideas presented in a lecture, reading, or other form of presentation (Tool book, p. 60)
Collaborative Summarizing – After lecture or reading, the students are asked to identify the 3-6 most important ideas. Students then pair up and compare their lists and come up with a consensus of the most important ideas with their partner. They (the group of two) pair up with another group of two and compare lists and once again come with an agreed upon list of 3-6 important ideas. These four use their list to create a collaborative summary. (Tool book, p.78)
Jigsaw- students work cooperatively with each student having an assigned task within the group to accomplish/perform.
Carousel Brainstorming – teacher generates different styles of questions & posts them around the room. The students work in groups of 3-5, rotates around the room to reading the question, the other responses, and either expands on existing ideas or develops a new idea. (Tool book, p.19)
4-2-1 Free Write – students identify 4 important ideas previously presented in the lesson. Each student meets with another student to compare ideas and decide on the two most important from their lists of four. This pair meets with another pair. They compare their ideas, then come to a consensus on the most important idea. The students then take this and do a free write, explaining all they know about the big idea. (Tool book, p. 82)
Concept Attainment – teacher presents examples and non-examples of a concept in a class discussion, the students use these to brainstorm the key attributes/characteristics of the concept.
Compare/Contrast – comparing likenesses and differences. The Georgia website I sent you has several different variations on this that are interesting.
Kindling – F - Find a question that can be explored
I - Internalize the question
R - Record your thoughts (sketch, write…)
E - Exchange ideas with a neighbor
S - Select and record your ideas in public (Tool Book p.74)
Comprehension Menu – an abbreviated version of Task Rotation. Teacher creates at least four questions in the four learning styles about the content. (Tool book, 162)
Review Activities/Tools
1,2,3,4 – teacher stops 5 minutes before end of class period to allow the students to reflect upon what was presented by writing in this format:
1 – What was the big idea
2 – Important details discussed
3 – Personal connections discovered
4 – Questions students have about the content
Boggle – students review notes for 2 minutes, then list as many ideas or details they can remember for 2-5 minutes, then students share their ideas with 1 or 2 other students and can add to their lists. Lastly, students pair up and compete with another student using the Boggle technique (They earn a point for every idea that their Boggle partner doesn’t have). Then the students go back to their study teams and compute the team score. (Tool book p.134)
Memory Box – a box usually put on a test where students can take the first five minutes to list as many things they can remember(formulas, definitions, etc…)
TGT – (Teams Game Tournament) teacher creates vocabulary/fact cards. The teacher divides the students heterogeneously by academic ability. This is the study group. After they have studied for a while, they then move to homogenous groups established by the teacher and compete against each other. They follow the points system to see how many points they take back to their study teams. This is a great review activity, it takes some time to prepare it, but it is well worth it.
Jeopardy - This follows the same format as the game show. It is great to use on the active board. There are many already developed on the Ashland Schools website.
Categories – technique for forming groups and reviewing content. (Tool book,
p. 138)
Tool Book refers to: Silver & Strong, 2001 Tools for Promoting Active, In-Depth Learning, Thoughtful Education Press.
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