Mafs 912 g co 2.8 answers

Graduate Education Assistance

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

~ Introduction to Online Learning

I. Transformations and Congruence

A. Tools of Geometry B. Transformations and Symmetry C. Congruent Figures

II. Lines, Angles, and Triangles - Part A

A. Lines and Angles B. Triangle Congruence Criteria

III. Lines, Angles, and Triangles – Part B A. Applications of Triangle

Congruence B. Properties of Triangles C. Special Segments in Triangles

IV. Quadrilaterals and Coordinate Proof A. Properties of Quadrilaterals B. Coordinate Proof Using Slope and

Distance

V. Similarity and Trigonometry – Part A A. Similarity and Transformations

VI. Similarity and Trigonometry – Part B A. Using Similar Triangles B. Trigonometry with right triangles

VII. Properties of Circles A. Angles and Segments in Circles B. Arc Length and Sector Area C. Equations of Circles

VIII. Measurement and Modeling in Two and Three Dimensions

A. Volume Formulas B. Visualizing Solids C. Modeling and Problem Solving

STEM Lessons - Model Eliciting Activities

• Yogurt Land Container

• Interchangeable Wristwatch Band

• NASA Space Shuttle Mission Patches

• Turning Tires Model Eliciting Activity

• It’s Not Waste—It’s Matter!

• Olympic Snowboard Design

IX. Geometry EOC Review

X. Getting Ready for Algebra II – Functions

A. Analyzing Functions B. Absolute Value Functions,

Equations, and Inequalities

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 22 11 09/08-10/08

Topic II 10 5 10/09-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic III 18 9 10/26-11/20

Topic IV 22 11 11/23-01/08

Topic V 9 4 01/11-01/22

Total 49 24

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VI 20 10 01/25-02/22

Topic VII 23 11 02/23-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VIII 10 5 04/05-04/16

Topic IX 10 5 04/19-04/30

Topic X 27 13 05/03-06/09

Total 47 23

Social Emotional Learning Resources Are Available for All Topics

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

I. Transformations and Congruence MAFS.912.G-CO.1.1 MAFS.912.G-CO.1.2 MAFS.912.G-CO.1.3 MAFS.912.G-CO.1.4 MAFS.912.G-CO.1.5 MAFS.912.G-CO.2.6 MAFS.912.G-CO.2.7

II. Lines, Angles, and Triangles – Part A MAFS.912.G-CO.2.7 MAFS.912.G-CO.2.8 MAFS.912.G-CO.3.9 MAFS.912.G-CO.3.10 MAFS. 912.G-CO.4.12 MAFS.912.G-CO.4.13 MAFS.912.G-GPE.2.5

III. Lines, Angles, and Triangles – Part B MAFS.912.G-C.1.3 MAFS.912.G-CO.3.10 MAFS.912.G-SRT.2.5

IV. Quadrilaterals and Coordinate Proof MAFS.912.G-CO.3.11 MAFS.912.G-GPE.2.4 MAFS.912.G-GPE.2.5 MAFS.912.G-GPE.2.7 MAFS.912.G-SRT.2.5

V. Similarity and Trigonometry – Part A MAFS.912.G-SRT.1.1 MAFS.912.G-SRT.1.2 MAFS.912.G-SRT.1.3

VI. Similarity and Trigonometry – Part B MAFS.912.G-SRT.2.4 MAFS.912.G-SRT.2.5 MAFS.912.G-GPE.2.6 MAFS.912.G-SRT.3.6 MAFS.912.G-SRT.3.7 MAFS.912.G-SRT.3.8

VII. Properties of Circles MAFS.912.G-C.1.1 MAFS.912.G-C.1.2 MAFS.912.G-C.1.3 MAFS.912.G-C.2.5 MAFS.912.G-GPE.1.1 MAFS.912.G-GMD.1.1

VIII. Measurement and Modeling in Two and Three Dimensions MAFS.912.G-GMD.1.1 MAFS.912.G-GMD.1.3 MAFS.912.G-GMD.2.4 MAFS.912.G-MG.1.1 MAFS.912.G-MG.1.2 MAFS.912.G-MG.1.3

IX. Geometry EOC Review

X. Getting Ready for Algebra II - Probability MAFS.912.S-CP.1.1 MAFS.912.S-CP.1.2 MAFS.912.S-CP.1.4 MAFS.912.S-CP.2.8

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 22 11 09/08-10/08

Topic II 10 5 10/09-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic III 18 9 10/26-11/20

Topic IV 22 11 11/23-01/08

Topic V 9 4 01/11-01/22

Total 49 24

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VI 20 10 01/25-02/22

Topic VII 23 11 02/23-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-Up” days:

T B Dates

Topic VIII 10 5 04/05-04/16

Topic IX 10 5 04/19-04/30

Topic X 27 13 05/03-06/09

Total 47 23

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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Geometry Core – H.M.H. Resources Geometry Intensive Math – H.M.H. Resources

Unit Resources Unit Resources

Unit Tests – A, B, and C Math in Careers Video

Performance Assessment Assessment Readiness (Mixed Review)

Module Resources

Module Test B

Common Core Assessment Readiness

Advanced Learners – Challenge Worksheets

Lesson Resources

Lessons – Work text/Interactive Student Edition

Practice and Problem Solving: A/B

Advanced Learners - Practice and Problem Solving: C

PMT Preferences Auto-assign for intervention and enrichment: NO

PMT Preferences Auto-assign for intervention and enrichment: YES

Test and Quizzes Daily Intervention

Homework Standard-Based Intervention

Course Intervention

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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Technology Integration: The SAMR Model

Video Link: Introduction to the SAMR Model

Link: Other Examples of Transformed Lessons/Tasks

Stages of the SAMR Model:

Examples of Tasks at each Stage:

https://youtu.be/9aJsmWzCRaw
https://www.dropbox.com/s/t915wmn1nwvd5y2/SAMR%20Transformed%20Lesson%20Examples-2.pdf?dl=0
MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-CO.1.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

MAFS.4.MD.3.5 MAFS.4.G.1.1 MAFS.4.G.1.2

Topic I

MAFS.912.G-CO.1.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

MAFS.8.G.1.1 MAFS.8.G.1.2 MAFS.8.G.1.3 MAFS.8.G.1.4 MAFS.912.F-BF.2.3 Topic I

MAFS.912.G-CO.1.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

MAFS.8.G.1.1 MAFS.8.G.1.3

MAFS.912.G-CO.1.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

MAFS.8.G.1.2 MAFS.8.G.1.3 Topic I

MAFS.912.G-CO.1.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

MAFS.912.G-CO.2.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent

MAFS.8.G.1.2

Topic I

MAFS.912.G-CO.2.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.

Topic I Topic II

MAFS.912.G-CO.2.8 Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid motions.

Topic II

MAFS.912.G-CO.3.9 Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.

MAFS.4.MD.3.7 MAFS.7.G.2.5 MAFS.8.G.1.5

Topic II

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

Division of Academics – Department of Mathematics Page 8 of 17 Year-at-a-Glance

GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-CO.3.10 Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.

MAFS.7.G.1.2 MAFS.8.G.1.5

Topic II Topic III

MAFS.912.G-CO.3.11 Prove theorems about parallelograms; use theorems about parallelograms to solve problems. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals

MAFS.5.G.2.3 Topic IV

MAFS.912.G-CO.4.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line.

MAFS.7.G.1.2

Topic II

MAFS.912.G-CO.4.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

MAFS.4.MD.3.6 MAFS.7.G.1.2

Topic II

MAFS.912.G-SRT.1.1 Verify experimentally the properties of dilations given by a center and a scale factor:

a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the

center unchanged.

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

MAFS.8.G.1.4 Topic V

MAFS.912.G-SRT.1.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

MAFS.8.G.1.4 Topic V

MAFS.912.G-SRT.1.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. MAFS.8.G.1.4 Topic V

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Congruency, Similarity, Right Triangles, and Trigonometry % of Test: 46% 2019 Average % Correct: 44%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-SRT.2.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.

MAFS.8.G.2.6

MAFS.912.G-SRT.2.5 Use congruence and similarity criteria for triangles to solve problems & to prove relationships in geometric figures

Topic II Topic V

MAFS.912.G-SRT.3.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. ★ MAFS.8.G.2.6 MAFS.912.N-RN.2.3

Topic VI MAFS.912.G-SRT.3.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

MAFS.912.G-SRT.3.7 Explain and use the relationship between the sine and cosine of complementary angles. MAFS.7.G.2.5 Topic V

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Circles, Geometric Measurement, and Geometric Properties with Equations % of Test: 38% 2019 Average % Correct: 38%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-C.1.1 Prove that all circles are similar. Topic VII

MAFS.912.G-C.1.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.

Topic III Topic VII

MAFS.912.G-C.1.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. Topic VII

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide YEAR AT A GLANCE

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GEOMETRY 2020– 2021 Course Code: 120631001

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YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: Circles, Geometric Measurement, and Geometric Properties with Equations % of Test: 38% 2019 Average % Correct: 38%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-C.2.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Topic VII

MAFS.912.G-GMD.1.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.

MAFS.7.G.2.4 Topic VII Topic VIII

MAFS.912.G-GMD.1.3

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems. ★ MAFS.8.G.3.9 Topic VIII

MAFS.912.G-GMD.2.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

MAFS.7.G.1.3 Topic VIII

MAFS.912.G-GPE.1.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

MAFS.8.G.2.8 MAFS.912.A-REI.2.4

Topic VII

MAFS.912.G-GPE.2.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).

MAFS.8.G.2.8 Topic IV

MAFS.912.G-GPE.2.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).

MAFS.8.EE.2.6 MAFS.8.F.1.3

Topic II Topic IV

MAFS.912.G-GPE.2.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio. Topic V

MAFS.912.G-GPE.2.7

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. ★ MAFS.8.G.2.8 Topic IV

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REPORTING CATEGORY: Modeling with Geometry % of Test: 16% 2019 Average % Correct: 31%

Standards Previous Grade

Standards Geometry Topic(s)

MAFS.912.G-MG.1.1 Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a

cylinder). ★

MAFS.6.G.1.4 MAFS.7.G.2.6

Topic VIII

MAFS.912.G-MG.1.2

Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). ★ MAFS.7.G.2.6 MAFS.8.G.3.9

Topic VIII

MAFS.912.G-MG.1.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost;

working with typographic grid systems based on ratios). ★

MAFS.7.G.1.1 MAFS.7.G.2.6 MAFS.8.G.3.9

Topic VIII

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CAN DO Descriptors: Grade Level Cluster 9-12

Level 1 Entering Level 2 Emerging Level 3 Developing Level 4 Expanding Level 5 Bridging

L IS

T E

N IN

G

• Point to or show basic parts, components, features, characteristics, and properties of objects, organisms, or persons named orally

• Match everyday oral information to pictures, diagrams, or photographs

• Group visuals by common traits named orally (e.g., “These are polygons.”)

• Identify resources, places, products, figures from oral statements, and visuals

• Match or classify oral descriptions to real-life experiences or visually- represented, content- related examples

• Sort oral language statements according to time frames

• Sequence visuals according to oral directions

• Evaluate information in social and academic conversations

• Distinguish main ideas from supporting points in oral, content- related discourse

• Use learning strategies described orally

• Categorize content-based examples described orally

• Distinguish between multiple meanings of oral words or phrases in social and academic contexts

• Analyze content-related tasks or assignments based on oral discourse

• Categorize examples of genres read aloud

• Compare traits based on visuals and oral descriptions using specific and some technical language

• Interpret cause and effect scenarios from oral discourse

• Make inferences from oral discourse containing satire, sarcasm, or humor

• Identify and react to subtle differences in speech and register (e.g., hyperbole, satire, comedy)

• Evaluate intent of speech and act accordingly

S P

E A

K IN

G

• Answer yes/no or choice questions within context of lessons or personal experiences

• Provide identifying information about self

• Name everyday objects and pre- taught vocabulary

• Repeat words, short phrases, memorized chunks of language

• Describe persons, places, events, or objects

• Ask WH- questions to clarify meaning

• Give features of content- based material (e.g., time periods)

• Characterize issues, situations, regions shown in illustrations

• Suggest ways to resolve issues or pose solutions

• Compare/contrast features, traits, characteristics using general and some specific language

• Sequence processes, cycles, procedures, or events

• Conduct interviews or gather information through oral interaction

• Estimate, make predictions or pose hypotheses from models

• Take a stance and use evidence to defend it

• Explain content-related issues and concepts

• Compare and contrast points of view

• Analyze and share pros and cons of choices

• Use and respond to gossip, slang, and idiomatic expressions

• Use speaking strategies (e.g., circumlocution)

• Give multimedia oral presentations on grade-level material

• Engage in debates on content- related issues using technical language

• Explain metacognitive strategies for solving problems (e.g., “Tell me how you know it.”)

• Negotiate meaning in pairs or group discussions

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• Match visual representations to words/phrases

• Read everyday signs, symbols, schedules, and school-related words/phrases

• Respond to WH- questions related to illustrated text

• Use references (e.g., picture dictionaries, bilingual glossaries, technology)

• Match data or information with its source or genre

• Classify or organize information presented in visuals or graphs

• Follow multi-step instructions supported by visuals or data

• Match sentence-level descriptions to visual representations

• Compare content-related features in visuals and graphics

• Locate main ideas in a series of related sentences

• Apply multiple meanings of words/phrases to social and academic contexts

• Identify topic sentences or main ideas and details in paragraphs

• Answer questions about explicit information in texts

• Differentiate between fact and opinion in text

• Order paragraphs or sequence information within paragraphs

• Compare/contrast authors’ points of view, characters, information, or events

• Interpret visually- or graphically- supported information

• Infer meaning from text

• Match cause to effect

• Evaluate usefulness of data or information supported visually or graphically

• Interpret grade-level literature

• Synthesize grade-level expository text

• Draw conclusions from different sources of informational text

• Infer significance of data or information in grade-level material

• Identify evidence of bias and credibility of source

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• Label content-related diagrams, pictures from word/phrase banks

• Provide personal information on forms read orally

• Produce short answer responses to oral questions with visual support

• Supply missing words in short sentences

• Make content-related lists of words, phrases, or expressions

• Take notes using graphic organizers or models

• Formulate yes/no, choice and WH- questions from models

• Correspond for social purposes (e.g., memos, e-mails, notes)

• Complete reports from templates

• Compose short narrative and expository pieces

• Outline ideas and details using graphic organizers

• Compare and reflect on performance against criteria (e.g., rubrics)

• Summarize content-related notes from lectures or text

• Revise work based on narrative or oral feedback

• Compose narrative and expository text for a variety of purposes

• Justify or defend ideas and opinions

• Produce content-related reports

• Produce research reports from multiple sources

• Create original pieces that represent the use of a variety of genres and discourses

• Critique, peer-edit and make recommendations on others’ writing from rubrics

• Explain, with details, phenomena, processes, procedures

Mathematical Practices

MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.2.1 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

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Mathematical Practices

MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.4.1 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.5.1 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Context Complexity: Level 2: Basic Application of Skills & Concepts

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Mathematical Practices

MAFS.K12.MP.6.1 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.7.1 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Context Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

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Literacy Standards

LAFS.910.SL.1.1 Initiate and participate effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grades 9–10 topics, texts, and issues, building on others’ ideas and expressing their own clearly and persuasively. a. Come to discussions prepared having read and researched material under study; explicitly draw on that preparation by referring to evidence from

texts and other research on the topic or issue to stimulate a thoughtful, well-reasoned exchange of ideas. b. Work with peers to set rules for collegial discussions and decision-making (e.g., informal consensus, taking votes on key issues, presentation of

alternate views), clear goals and deadlines, and individual roles as needed. c. Propel conversations by posing and responding to questions that relate the current discussion to broader themes or larger ideas; actively incorporate

others into the discussion; and clarify, verify, or challenge ideas and conclusions. d. Respond thoughtfully to diverse perspectives, summarize points of agreement and disagreement, and, when warranted, qualify or justify their own

views and understanding and make new connections in light of the evidence and reasoning presented. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

LAFS.910.SL.1.2 Integrate multiple sources of information presented in diverse media or formats (e.g., visually, quantitatively, orally) evaluating the credibility and accuracy of each source. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

LAFS.910.SL.1.3 Evaluate a speaker’s point of view, reasoning, and use of evidence and rhetoric, identifying any fallacious reasoning or exaggerated or distorted evidence. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

LAFS.910.SL.2.4 Present information, findings, and supporting evidence clearly, concisely, and logically such that listeners can follow the line of reasoning and the organization, development, substance, and style are appropriate to purpose, audience, and task. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

LAFS.910.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. Context Complexity: Level 2: Basic Application of Skills & Concepts

LAFS.910.RST.2.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. Context Complexity: Level 2: Basic Application of Skills & Concepts

LAFS.910.RST.3.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. Context Complexity: Level 2: Basic Application of Skills & Concepts

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Literacy Standards

LAFS.1112.WHST.1.1 Write arguments focused on discipline-specific content. a. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and

create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths

and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.

c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented.

Context Complexity: Level 4: Extended Thinking &Complex Reasoning

LAFS.1112.WHST.2.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

LAFS.1112.WHST.3.9 Draw evidence from informational texts to support analysis, reflection, and research. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

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