ESSENTIAL QUESTION
Common Core Standards
2017-2018
Print Unit 3

How can we use linear functions to graph and interpret data?

High School - Math - Algebra I - Unit 3

Linear Functions

* Graph linear functions
* Describe the relationship of a graph and its fucntion
* Compare and contrast different forms of linear functions
* Use slopes and intercepts to graph functions and interpret data

OVERVIEW
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Students will graph linear functions using a variety of techniques including a table of values, points, slopes, and intercepts to evaluate, compare, contrast, model, and solve real-life problems.

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COMMON CORE STANDARDS
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* Define, evaluate, and compare functions; describe domain and range (F.IF.1)

*Use function notation and evaluate functions for inputs (F.IF.2)

*Slope and Rate of change (S.ID.7, F.IF.6, F.LE.5)

*Graph linear functions and inequalities (A.REI.10, A.CED.3, F.IF.5, F.IF.7a)

*Create linear equations (F.LE.2)

*Use functions to model relationships between quantities (F.IF.4, F.BF.1, F.LE.5)

*Use functions to model relationships between quantities (F.IF.4, F.BF.1, F.LE.5)

*Find inverse functions (F.BF.4)

*Arithmetic sequences (F.IF.3, F.BF.2)

STUDENT LEARNING TARGETS
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**F.IF.1**

I can identify the domain and range of a function.

I can determine if a relation is a function.

I can determine the value of the function with proper notation (i.e. f(x)=y, the y value is the value of a function at a particular value of x.)

I can evaluate functions for given values of x.

**F.IF.2**

I can identify mathematical relationships and express them using function notation.

I can define a reasonable domain which depends on the situation, for a function focusing on linear functions.

I can evaluate functions at a given input in the domain, focusing on linear functions.

I can interpret statements that use functions in terms of real world situations, focusing on linear functions.

**F.IF.3**

I can recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.

**F.IF.6**

I can recognize slope as an average rate of change.

I can calculate the average rate of change of a function.

I can estimate the rate of change from a linear graph.

I can interpret the average rate of change of a function over a specified interval.

**F.LE.5**

I can recognize the parameters in a linear function.

I can recognize rates of change and intercepts as “parameters” in linear or functions.

I can interpret the parameters in a linear function in terms of context.

**A.REI.10**

I can explain that every point (x,y) on the graph of an equation represents values x and y that makes the equation true.

I can explain why each point on a curve is a solution to its equation.

**A.CED.3**

I can recognize when a modeling context involves constraints.

I can identify the variables and quantities represented in a real-world problem.

I can determine when a problem should be represented by equations, inequalities, systems of equations and/or inequalities.

I can represent constraints by equations or inequalities, and by systems of equations and/or inequalities.

I can interpret all solutions and determine if they are reasonable.

I can draw a coordinate plane and label axes with appropriate labels and scales.

**F.IF.7a**

I can graph linear functions and show/label intercepts of the graph.

I can determine the differences between simple and complicated linear, exponential and quadratic functions and know when the use of technology is appropriate.

**F.LE.2**

I can recognize that arithmetic sequences can be expressed as linear functions.

I can construct linear functions, including arithmetic sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).

**F.IF.4**

I can define and recognize the key features in tables and graphs of linear functions.

I can identify whether the function is linear, given its table or graph.

I can interpret key features of graphs and tables of functions.

I can create a graph that models the description and indicates all of the key features of the function.

**F.BF.2**

I can identify arithmetic patterns in given sequences.

I can generate arithmetic sequences from recursive and explicit formulas.

I can define an arithmetic sequences and its common difference.

I can use given and constructed arithmetic and geometric sequences to model real-life situations.

I can determine the recursive rule given arithmetic sequences.

I can justify the translation between the recursive form and explicit formula for arithmetic sequences.

I can write an explicit formula for an arithmetic sequence.

CRITICAL VOCABULARY
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Coordinate plane, ordered pair, quadrants, graph of an ordered pair, scatter plot, solution of an equation, graph of an equation, x-intercept, y-intercept, slope, rate of change, perpendicular lines, parallel lines, positive and negative correlation, line of best fit, standard form

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LEARNING EXPERIENCES
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Educator Uploaded Plans
(These are educators specific templates with included information and specifics)

E-TOOLS
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Coming Soon.

RESOURCES
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LITERACY STRATEGIES
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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

THOUGHTFUL EDUCATION TOOLS
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**Thoughtful Strategies by Learning Style**

Mastery | Interpersonal | Understanding | 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 Categories Memory Box Write to Learn Building Writing | Reciprocal Learning Think/Pair/Share Give one, Get one Collaborative Summarizing Jeopardy | Anticipation Guides KWL Concept Attainment Compare/Contrast 1,2,3,4 Yes, No, Why | Etch-a-Sketch Mystery | Graduated Difficulty Comprehension Menu Task Rotation Voc Notebook Carousel Brainstorming Boggle Reader’s Theatre Vocabulary Code TGT Jigsaw 4-2-1 Free Write Kindling |

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

**C**onnect – new words to prior knowledge**O**rganize – new words to find relationships**D**eep-processing – internalizing the words, deepen the understanding**E**xercise – 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:

**C**onnect – hook students’ attention**O**rganize – use graphic organizer/note taking procedure to help organize info**D**eep-processing – pause every 5-7 min during lecture to allow students time to process information with questions in the different learning styles**E**xercise – use review questions and have students use notes in a synthesis or application task.

**Activities/Tools**

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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