module 1 congruence, proof, and constructions … geometry fall...module 1 congruence, proof, and...

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MODULE 1 CONGRUENCE, PROOF, AND CONSTRUCTIONS

EUREKA MATH MODULE 1, TOPICS 1-30

(Approximately 20 Days ● 8/08/19 - 9/5/19)

Module 1 Overview

In previous grades, students were asked to draw triangles based on given measurements. They also have prior experience with rigid motions—translations, reflections, and rotations—and have strategically applied a rigid motion to informally show that two triangles are congruent. In this module, students establish triangle congruence criteria, based on analyses of rigid motions and formal constructions. They build upon this familiar foundation of triangle congruence to develop formal proof techniques. Students make conjectures and construct viable arguments to prove theorems— using a variety of formats—and solve problems about triangles, quadrilaterals, and other polygons. They construct figures by manipulating appropriate geometric tools (e.g., compass, ruler, protractor) and justify why their written instructions produce the desired figure. Specifically, students will

establish triangle congruence criteria, based on analyses of rigid motions and formal constructions make conjectures and construct viable arguments to prove theorems— using a variety of formats—and solve

problems about triangles, quadrilaterals, and other polygons. construct figures by manipulating appropriate geometric tools (e.g., compass, ruler, protractor) and justify why their

written instructions produce the desired figure students will prove congruence of triangles

Focus Standards

Addressed in Eureka Math Resource – Use of supplemental resources is not needed Partially Addressed in Eureka Math Resource – Use of supplemental resources may/may not be needed Not Adequately Addressed in Eureka Math Resource – Use of supplemental resources is necessary LOUISIANA CONNECTORS When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

https://www.louisianabelieves.com/docs/default-source/students-with-disabilities/k-12-louisiana-connectors-for-students-with-significant-disabilities.pdf?sfvrsn=6

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G-CO.A.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.

Remediation Standard(s): 4.MD.C.5, 4.G.A.1, and 4.G.A.2

6.NS.B.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).

G-CO.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.

Remediation Standard(s): 8.G.A.2, and 8.G.A.3

G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.


G-CO.A.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.


G-CO.B.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.

Remediation Standard(s): 8.G.A.2

G-CO.B.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.


G-CO.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.


G-CO.C.9 Prove theorems about lines and angles. 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

Remediation Standard(s): 4.MD.C.7, 7.G.B.5, and 8.G.A.5

G-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are

Remediation Standard(s):

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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

7.G.A.2, and 8.G.A.5

G-CO.C.11 Prove theorems about parallelograms. 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.

Remediation Standard(s): 5.G.B.3

G-CO.D.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

Remediation Standard(s): 4.MD.C.6, and 7.G.A.2

G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.


Focus Standards for Mathematical Practice

MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision.

Unit Terms & Tools Spanish cognates are included (if applicable) for Tier 3 and Tier 2 vocabulary terms. Spanish cognates will be shown as follows: Vocab Term/Spanish Cognate.

New Unit Terms (Tier 3 Vocabulary)

Isometry (Anisomery of the plane is a transformation of the plane that is distance-preserving.)

Familiar Terms (Tier 3 Vocabulary)

Congruence, Reflection, Rotation

transformation, translation

Cross-Curricular Terms (Tier 2 Vocabulary)

Suggested Tools Compass and straightedge Geometer’s Sketchpad or Geogebra Software Patty paper

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Sample Calendar

Coding: 1.1-A represents Eureka Math Module 1. Lesson 1 – Lesson 30 ● Addressed standard(s) listed below lesson Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.

Week Beginning: Monday Tuesday Wednesday Thursday Friday

August 5th No school for students

No school for students

No school for students

FLEX (First day of school for students) Module 1, Lesson 1-2 GM: G-CO.A.1*, GM: G-CO.D.12, GM: G-CO.D.1

LEAP 360 Diagnostic (Window provided for administration)

August 12th Module 1, Lesson 3-4 GM: G-CO.A.1*, GM: G-CO.D.12

Module 1, Lesson 7 7.G.B.5, 8.G.A.5

Module 1, Lesson 6/8 7.G.B.5, 8.G.A.5

Module 1, Lesson 9/11 GM: G-CO.C.9, GM: G-CO.D.12

FLEX

August 19th Module 1, Lesson 12(Discussion ONLY) Lesson 16 (additional support)

Module 1, Lesson 14 (Lesson 15) GM: G-CO.A.2, GM: G-CO.A.3, GM: G-CO.D.12

Module 1, Lesson 13 (Lesson 15) GM: G-CO.A.2, GM: G-CO.A.4, GM: G-CO.A.5, GM: G-CO.D.12

FLEX Module 1, Lesson 19-21 (additional support) GM: G-CO.A.2, GM: G-CO.A.5, GM: G-CO.B.6, GM: G-CO.B.7

August 26th Module 1, Lesson 22-23 GM: G-CO.C.10, GM: G-SRT.B.5*

Module 1, Lesson 24 GM: G-CO.B.7, GM: G-CO.B.8, GM: G-SRT.B.5*

Module 1, Lesson 25 GM: G-CO.B.7, GM: G-CO.B.8, GM: G-SRT.B.5*

FLEX Module 1, Lesson 26-27 GM: G-SRT.B.5

September 2nd Labor Day (Holiday)

FLEX Module 1, Lesson 28 GM: G-CO.C.11

Module 1, Lesson 29-30 GM: G-CO.C.9, GM: G-CO.C.10

LEAP 360 Interim 1

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Additional Information

Remediation Support (LDOE Remediation Guide)

Teachers may choose appropriate questions, activities, and or lessons from the table below to support students who have prior unfinished learning. Teachers should be strategic when choosing problems from suggested lessons in order to differentiate instruction to have the most impact on student achievement. For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Geometry Remediation Guide

Remedial Skills Support in Eureka Use to help students struggling with mastery of Lesson 6 7.G.B.5

While this Lesson does not present new content, it does provide more formal definitions of previously defined terms, and students may benefit from the review of Grade 7 content. Additionally, there exists problems within the Lesson that require algebraic skills beyond that of Grade 7 standards. The decision to use this Lesson should be made at the teacher level. Grade 7 Module 6 Lesson 1-4

Use to help students struggling with mastery of Lesson 7 7.G.B.5, 8.G.A.5

While this Lesson does not present new content, it does provide more formal definitions of previously defined terms, and students may benefit from the review of Grade 8 content. Additionally, the Lesson requires students to combine their algebraic skills with their understanding of Grade 8 concepts to solve missing angle problems. The decision to use this Lesson should be made at the teacher level. Grade 8 Module 2 Lesson 11-14

Use to help students struggling with mastery of Lesson 11-16 Transformations/ /Rigid Motions G-CO.A.4

Use these prior grade lesson, to help with remediation skills dealing with transformation Grade 8 Module 2 Lessons: 1-10

Additional Lessons (Optional for remediation and enrichment)

Lesson 12: *Discussion only *Rule chart should be distributed Lesson 13: Additional support Rotation on graphs not around the center & rotation symmetric, multi-select. --- Use EAGLE. Lesson 14: Reflection, Additional support on graph and line symmetry. --- Use EAGLE. Lesson 16: Additional support translations--- Use EAGLE.

https://achievethecore.org/coherence-map/HS/A

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/new-standards---geometry-remediation-guide.pdf?sfvrsn=46838a1f_8

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Lesson 19-21: Additional support comp of transformations/ Flower Pot--- Use EAGLE.

Assessment Information (Mid-Module and End-of-Module)

The mid-module assessment is designed to be given after completing Topic B. The end-of-module assessment is designed to be given after completing Topic D.

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MODULE 2 – SIMILARITY, PROOF, AND TRIGONOMETRY

Eureka Math Module 2, Topics 1-34

(Approximately 18 Days ● 09/09/19-10/03/19)

Module 2 Overview

During this unit students apply their earlier experience with dilations and proportional reasoning to build a formal understanding of similarity. They identify criteria for similarity of triangles, make sense of and persevere in solving similarity problems, and apply similarity to right triangles to prove the Pythagorean theorem. Students attend to precision in showing that trigonometric ratios are well defined and apply trigonometric ratios to find missing measures of general (not necessarily right) triangles. Students model and make sense out of indirect measurement problems and geometry problems that involve ratios/rates. Specifically, students will

identify criteria for similarity of triangles attend to precision in showing that trigonometric ratios apply trigonometric ratios to find missing measures of general (not necessarily right) triangles. model and make sense out of indirect measurement problems and geometry problems that involve ratios/rates.

Focus Standards


G-SRT.A.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.



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G-SRT.A.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.


G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.


G-SRT.B.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.


G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G-SRT.C.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.

G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.


G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★

Remediation Standard(s): 8.G.B.7 HSN-RN.B.3

G-MG.A.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).★

G-MG.A.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).★


MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure

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Cosine Dilation (Sides of a Right Triangle Similar (Two figures in a plane are similar)

Similarity Transformation ( Sine Tangent


Composition Dilation Pythagorean theorem Rigid motions

Scale drawing Scale factor Slope


Suggested Tools Compass and straightedge

Sample Calendar



September 9th Module 2, Lesson 1 & 5 GM: G-CO.D.12, GM: G-SRT.A.1, GM: G-MG.A.3

Module 2, Lesson 2 GM: G-CO.D.12, GM: G-SRT.A.1, GM: G-MG.A.3

FLEX Module 2, Lesson 7-9 GM: G-SRT.A.1

FLEX

September 16th District PD Module 2, Lesson 14 & 16 GM: G-SRT.A.2, GM: G-C.A.1

Module 2, Lesson 12 & 15 GM: G-SRT.A.3, GM: G-SRT.B.5*

Module 2, Lesson 17 & 18 GM: G-SRT.B.4, GM: G-SRT.B.5

FLEX (Quiz/assessment)

September 23rd FLEX Module 2, Lesson 21

Module 2, Lesson 24

Module 2, Lesson 25-26 GM: G-SRT.C.6*

Module 2, Lesson 28-29

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(Lesson 22-23) for additional radical support) GM: G-SRT.B.4, GM: G-SRT.B.5

GM: G-SRT.B.4, GM: G-SRT.B.5*, GM: G-SRT.C. 6

GM: G-SRT.C.7, GM: G-SRT.C.8

September 30th FLEX Module 2, Lesson 27 & 34

Module 2, Lesson 30

FLEX Begin Module 3




Remedial Skills Support in Eureka Use to help students struggling with mastery of Lesson 7-9 G-SRT.A.1

Use these prior grade lesson, to help with remediation skills dealing with transformation Grade 8 Module 3 Lessons: 1-4 (8.G.A.3)


Lesson 2: Additional support on dilating on a graph on & off the origin. --- Use EAGLE. Lesson 7-9: Make sure teachers know when dilating the slope stays the same. Lesson 17 & 18: Lesson 18 should be touched on during constructions. Lesson 21: If students need additional help with radicals see Lesson 22 & 23 Lesson 24: Additional support Pythagorean theorem with real world scenarios. Lesson 30: additional support type III Leap Questions --- EAGLE.





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MODULE 3 – EXTENDING TO THREE DIMENSIONS



Module 3 Overview

Students’ experience with two-dimensional and three-dimensional objects is extended to include informal explanations of circumference, area, and volume formulas. Additionally, students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line. They reason abstractly and quantitatively to model problems using volume formulas. Specifically, students will

students apply their knowledge of two-dimensional shapes to consider the shapes of cross-sections and the result of rotating a two-dimensional object about a line

students find the volume of three dimensional figures.

Focus Standards


G-GMD.A.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.


G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.


G-GMD.B.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.


G-MG.A.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).

Remediation Standard(s):


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6.G.A.4, and 7.G.B.6 G-MG.A.2 Apply concepts of density based on area and volume in modeling

situations (e.g., persons per square mile, BTUs per cubic foot). Remediation Standard(s): 7.G.B.6, and 8.G.C.9

G-MG.A.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).

Remediation Standard(s): 7.G.A.1, 7.G.B.6, and •8.G.C.9


MP.6 Attend to precision MP.7 Look for and make sure of structure



Cavalieri’s Principle Cone General Cylinder Inscribed Rectangular Pyramid Right Rectangular Prism

Solid Sphere or Ball Sphere Tangent to a Circle Union


Disk Lateral Edge and Face of a Prism


Suggested Tools Three-dimensional models of rectangular prisms, right circular cylinders, right pyramids Deck of cards Stack of coins Images of sliced figures, such as a loaf of bread or a stack of deli cheese

Sample Calendar



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September 30th Finish Module 2

Module 3, Lesson 4 GM: G-GMD.A.1

October 7th Module 3, Lesson 6-7 GM: G-GMD.B.4

Module 3, Lesson 10 & 12 GM: G-GMD.A.1*, GM: G-GMD.A.3*

Module 3, Lesson 11 GM: G-GMD.A.1*, GM: G-GMD.A.3

Fall Break

October 14th FLEX FLEX LEAP 360 Interim 3 Begin Module 4




Remedial Skills Support in Eureka Use to help students struggling with mastery of Lessons 10-12 G-GMD.A.3

Use these prior grade lesson, to help with remediation skills dealing with transformation Grade 7 Module 6 Lessons: 25-27 (7.G.B.6)


Lesson 4: Additional support to touch on coordinate questions covered on Interim 3.and use --- Use EAGLE questions Lesson 6 & 7: If students are struggling with #D concept, see Lesson 3-5.





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MODULE 4 – CONNECTING ALGEBRA AND GEOMETRY THROUGH COORDINATES



Module 4 Overview

During this unit students are building on their work with the Pythagorean theorem in Grade 8 to find distances, students analyze geometric relationships in the context of a rectangular coordinate system, including area and perimeter of triangles, properties of quadrilaterals, and slopes of parallel and perpendicular lines, relating back to work done in the first module. They explore how to program a robot to move around a defined area in the coordinate plane, and in doing so, they leverage their knowledge from synthetic geometry by combining it with the solving power of algebra inherent in analytic geometry. Specifically, students will

Connect algebra and geometry through coordinates Use geometric shapes, their measures, and their properties to describe objects Prove the slope criteria for parallel and perpendicular lines and use them to solve

geometric problem Find the point on a directed line segment between two given points that partitions the

segment in a given ratio

Focus Standards


G-GPE.B.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).



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G-GPE.B.5 Prove3 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).

Remediation Standard(s): 8.EE.B.6, and 8.F.A.3

G-GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.

G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.★

8.G.B.8


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.



Normal Segment to a Line


Bisect Directed Line

Segment

Parallel Distance

Perpendicular Slope


Suggested Tools Graph Paper Graphing Calculator Wolfram Alpha Software Geometer’s Sketchpad Software

Sample Calendar



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October 14th

Finish Module 3

Module 4, Lesson 1 GM: G-MG.A.1★, GM: G-MG.A.3

Module 4, Lesson 5-6 GM: G-GPE.B.4, GM: G-GPE.B.5

October 21st Module 4, Lesson 7 GM: G-GPE.B.5*

Module 4, Lesson 8 GM: G-GPE.B.4, GM: G-GPE.B.5

FLEX Module 4, Lesson 9 GM: G-GPE.B.7

Module 4, Lesson 10 GM: G-GPE.B.7

October 28th FLEX Module 4, Lesson 12 GM: G-GPE.B.4, GM: G-GPE.B.6

Module 4, Lesson 13 GM: G-GPE.B.4, GM: G-GPE.B.6

Begin Module 5





Lessons 1-8: Flex for review of lessons before fall break.





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MODULE 5 – CIRCLES WITH AND WITHOUT COORDINATES

EUREKA MATH MODULE 5, TOPICS 1-19


Module 5 Overview

In this module, students prove and apply basic theorems about circles, such as a tangent line is perpendicular to a radius theorem, the inscribed angle theorem, and theorems about chords, secants, and tangents dealing with segment lengths and angle measures. They study relationships among segments on chords, secants, and tangents as an application of similarity. In the Cartesian coordinate system, students explain the correspondence between the definition of a circle and the equation of a circle written in terms of the distance formula, its radius, and coordinates of its center. Given an equation of a circle, they draw the graph in the coordinate plane and apply techniques for solving quadratic equations. The year-long study of geometry culminates as students use concepts studied such as the Pythagorean theorem, similarity, trigonometry, arcs, angles, and cyclic quadrilaterals to prove Ptolemy’s theorem. Specifically, students will

prove and apply basic theorems about circles explain the correspondence between the definition of a circle and the equation of a circle written in terms of the

distance formula, its radius, and coordinates of its center use concepts studied such as the Pythagorean theorem, similarity, trigonometry, arcs, angles, and cyclic

quadrilaterals to prove Ptolemy’s theorem.

Focus Standards


G-C.A.1 Prove that all circles are similar. G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords.

Include3 the relationship between central, inscribed, and circumscribed


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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.

G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.

G-C.B.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.

G-GPE.A.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.

Remediation Standard(s): 8.G.B.8, and HS: A-REI.B.4

G-GPE.B.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).



MP.1 Make sense of problems and persevere in solving them. MP.3 Construct viable arguments and critique the reasoning of others. MP.7 Look for and make use of structure.

Unit Terms & Tools

Spanish cognates are included (if applicable) for Tier 3 and Tier 2 vocabulary terms. Spanish cognates will be shown as follows: Vocab Term/Spanish Cognate.


Arc Length Central Angle Chord Cyclic Quadrilateral Inscribed Angle

Inscribed Polygon Secant Line Sector Tangent Line


Circle Diameter

Radius


Suggested Tools Compass and straightedge Geometer’s Sketchpad or GeoGebra Software White and colored paper, markers

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Sample Calendar

Coding: 1.1-A represents Eureka Math Module 5 Lesson 1 – Lesson 19 ● Addressed standard(s) listed below lesson Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.


October 28th Finish Module 4

Module 5, Lesson 1 & 3

LEAP 360 Interim 2/FLEX

November 4th Module 5, Lesson 2 GM: G-C.A.2

Module 5, Lesson 5 & 6 GM: G-C.A.2, GM: G-C.A.3

Module 5, Lesson 7 GM: G-C.A.2, GM: G-C.A.3

Module 5, Lesson 8 GM: G-C.A.2

Module 5, Lesson 9 GM: G-C.B.5

November 11th Student Holiday/ Parent Teacher

Conference

FLEX FLEX Module 5, Lesson 11 & 12 GM: G-C.A.2, GM: G-C.A.3

Module 5, Lesson 13 GM: G-C.A.2, GM: G-C.A.3

November 18th Module 5, Lesson 14 GM: G-C.A.2,

Module 5, Lesson 15 & 16 GM: G-C.A.2 GM: G-SRT.B.5,

Module 5, Lesson 17 GM: G-GPE.A.1*, GM: G-GPE.B.4

Module 5, Lesson 18 GM: G-GPE.A.1*, GM: G-GPE.B.4

FLEX

November 25th Thanksgiving Holiday

December 2nd Module 5, Lesson 19 Begin Alg. II Probability & Statistics



Teachers may choose appropriate questions, activities, and or lessons from the table below to support students who have prior unfinished learning. Teachers should be strategic when choosing problems from suggested lessons in order to differentiate instruction to have the most impact on

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student achievement. For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Geometry Remediation Guide


Lesson 1: *Relevant vocabulary* and Exercise 1-2 Lesson Summary 20-30 min max. Lesson 5-6: If students struggling refer to Module 5 Lesson 4 for additional support.






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ALG. II MODULE 4 – PROBABILITY



Alg. II Unit 4 Overview

In this module, students see how the visual displays and summary statistics they learned in earlier grades relate to different types of data and to probability distributions. They identify different ways of collecting data, including sample surveys, experiments, and simulations, and the role that randomness and careful design play in the conclusions that can be drawn. Students create theoretical and experimental probability models following the modeling cycle (see page 72 of CCSS). They compute and interpret probabilities from those models for compound events, attending to mutually exclusive events, independent events, and conditional probability. Specifically, students will

calculating Probabilities of Events Using Two-Way Tables use the probability rules to solve problems Recognize and explain the concepts of conditional probability and independence in everyday language and everyday Solve problems using Venn Diagram and events. Apply the Addition Rule, P (A or B) = P (A) + P(B) – P (A and B) , and interpret the answer in terms of the model

Focus Standards


S-ID.A.4 Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

Remediation Standard(s): 6.SP.B.5, HSS-ID.A.1, and HSS-ID.A.2

S-IC.A.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

Remediation Standard(s): 7.SP.A.2


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S-IC.A.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?

Remediation Standard(s): 7.SP.C.7

S-IC.B.3 Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

S-IC.B.4 Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

S-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

S-IC.B.6 Evaluate reports based on data. S-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using

characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”).

S-CP.A.2 Understand that two events ܣ and ܤ are independent if the probability of ܣ and ܤ occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.A.3 Understand the conditional probability of ܣ given ܤ as ܲ(ܤ and ܣ) ܲ

and), ܤ)/ interpret independence of ܣ and ܤ as saying that the conditional probability of ܣ given ܤ is the same as the probability of ܣ ,and the conditional probability of ܤ given ܣ is the same as the probability of ܤ

S-CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results.

Remediation Standard(s): HSS-ID.B.5

S-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer.

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S-CP.B.6 Find the conditional probability of A given B as the fraction of B‘s outcomes that also belong to, and interpret the answer in terms of the model.

S-CP.B.7 Apply the Addition Rule, P (A or B) = P (A) + P(B) – P(A and B) , and interpret the answer in terms of the model.


MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically.



Complement of an event Conditional probability Experiment Hypothetical 1000 Table Independent Events Intersection of Two Events Lurking Variable Margin of Error

Normal Distribution Observational Study Random Assignment Random Selection Sample Survey Treatment Union of Two Events


Association Chance experiment Conditional relative frequency Distribution shape (skewed, symmetric) Event

Mean Sample space Sampling variability Standard deviation


Suggested Tools ƒ Graphing calculator or graphing software ƒ Random number tables ƒ Random number software ƒ Normal distribution ƒ Two-way frequency tables ƒ Spreadsheets

Sample Calendar Coding: 1.1-A represents Eureka Math Module 1. Lesson 1 – Topic A ● Addressed standard(s) listed below lesson

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Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.


December 2nd

Finish Module 5

Alg. II Module 4, Lesson 1 & 2 S-IC.A.2, S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7

Alg. II Module 4, Lesson 3, 4, & 5 S-IC.A.2, S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7

FLEX Alg. II Module 4, Lesson 6 & 7 S-IC.A.2, S-CP.A.1, S-CP.A.2, S-CP.A.3, S-CP.A.4, S-CP.A.5, S-CP.B.6, S-CP.B.7

December 9th LEAP 2025 REVIEW/FLEX

December 16th LEAP 2025 Testing FINAL EXAMS

December 23rd CHRISTMAS HOLIDAYS

December 30th



Teachers may choose appropriate questions, activities, and or lessons from the table below to support students who have prior unfinished learning. Teachers should be strategic when choosing problems from suggested lessons in order to differentiate instruction to have the most impact on student achievement. For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Algebra II Remediation Guide


http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/new-standards---algebra-ii-remediation-guide.pdf?sfvrsn=cf828a1f_6

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Remedial Skills Support in Eureka

Use to help students struggling with mastery of Lesson 1-7 S-CP.A.1 S-CP.A.2 S-CP.A.3 S-CP.A.4 S-CP.A.5

Use these prior grade lesson, to help with remediation skills dealing with transformation Grade 7 Module 5 Lesson 2-7



module 1 congruence, proof, and constructions … geometry fall...module 1 congruence, proof, and...

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