atlas - geometry (plc) - flemington-raritan regional … · web viewfind and use the areas of...

FRSD Geometry Curriculum Grade 8Collins, Dana; Hering, Carly; McAnlis, Melissa

Unit Essential Questions

Enduring Understandings

Knowledge/Skills

Assessments Learning Experiences Resources Differen

tiation

Building Blocks of Geometry

(Week 1, 2 Weeks)

How can you use dynamic geometry software to visualize geometric concepts?

How can you measure and construct a line segment?

How can you find the midpoint, length of a line segment, perimeter and area in a coordinate plane?

How can you measure and classify an angle?

How can you describe angle pair relationships and use these descriptions to

The undefined concepts of point, line, and plane are the basis of geometry.

Geometric concepts can be better explained and understood by using constructions.

Students will be able to:

Understand the undefined concepts of point, line, and plane.

Apply the undefined concepts of point, line, and plane to define and use collinear points, coplanar points, line segment, ray, opposite rays, intersections of lines, planes, and

Learning Activities

Basic Geometry Language Video https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-basic-geometry OR

http://tube.geogebra.org/student/m98533 (Links Attached)

Angle Bisector and Perpendicular Bisector of a Line Segment GeoGebra Exploration Perpendicular bisector and Angle Bisector.pdf

Modern Art Project with Geometer's Sketchpad (adapt from Introduction Activity pg. 8 - 10 Introduction to GeoGebra.pdf)

https://www.khanacademy.org/math/geometry/intro_euclid/v/language-and-notation-of-basic-geometry

http://tube.geogebra.org/student/m98533Perpendicular bisector and Angle Bisector.pdfIntroduction to GeoGebra.pdf

http://www.mathwarehouse.com/algebra/distance_formula/interactive-distance-formula.php

https://www.khanacademy.org/math/basic-geo/basic-geo-pythagorean-topic/basic-geo-pythagorean-theorem/v/soccer-thiago

Exploring Geometry with GeoGebra

Big Ideas Textbook

Chromebooks

Unit Review and Answers (*attached) Ch1 Test Review.docx Ch1 Test Review Answers.docx

Quiz Review Answers (*attached) Quiz Review sheet Answers.pdf

Solving Equations in One Variable Video Review (*link attached) https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/complicated_equations/v/multi-step-equations

Teacher created materials

Ch1 Test Review.docxCh1 Test Review

https://frsdk12.rubiconatlas.org/Atlas/View/File?AttachmentID=353&










http://tube.geogebra.org/student/m98533




http://tube.geogebra.org/student/m98533









Knowledge/Skills


tiation

find angle measures? segments.

Use the Ruler Postulate to understand measurement and length

.

Understand and use the Segment Addition Postulate to determine lengths of segments.

Copy segments and compare segments for congruence.

Students

Answers.docxQuiz Review sheet

Answers.pdf

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/complicated_equations/v/multi-step-equations











Knowledge/Skills


tiation

will be able to compare, contrast, and classify polygons.

Define an angle and identify its parts.

Compare, contrast, ad classify angles obtuse, acute, right, straight, and reflex)*

Define and identify congruent angles and angle bisectors.

Define and identify complementary and



Knowledge/Skills


tiation

supplementary angles.

Define and identify a linear pair and vertical angles.

Use dynamic geometry software to visualize and represent geometric concepts.

Reasoning and Proofs

(Week 3, 4 Weeks)

When is a conditional statement true or false?

How can you use reasoning to solve problems?

In a diagram, what can be assumed and what needs to

Proofs of theorems are a form of deductive reasoning.

Reasoning skills allow one to successfully prove ideas and


Write conditional and biconditional statements.


Big Ideas Textbook

Chromebooks




Knowledge/Skills


tiation

be labeled? How can

algebraic properties help you solve an equation?

How can you prove a mathematical statement?

solve problems. Use and

understand definitions as biconditionals.

Compare and contrast inductive and deductive reasoning.

Identify postulates using diagrams.

Sketch and interpret diagrams of points, lines, planes

Apply Algebraic Properties and the Distributive Property to justify



Knowledge/Skills


tiation

steps in solving equations and involving segment lengths and angle measures.

Develop and write two-column proofs on segment and angle relationships.


Parallel and Perpendic

● What does it mean when two lines are

● Certain relationships exist between

Students will be

https://www.khanacademy.org/math/geometry/parallel-and-perpendicular-lines/triang_prop_tut/v/proof-corresponding-angle-equivalence-implies-parallel-lines








Knowledge/Skills


tiation

ular Lines

(Week 7, 3 Weeks)

parallel, intersecting, coincident or skew?

● When two parallel lines are cut by a transversal, which of the resulting pairs of angles are congruent? Supplementary?

● For which of the theorems involving parallel lines and transversals is the converse true?

● What conjectures can you make about perpendicular lines?

● How can you write an equation of a line that is parallel or perpendicular to

lines and angles.

● Logical arguments can be made based on known information or deduced information

able to:

Identify lines and planes, parallel and perpendicular lines and pairs of angles formed by transversals.

Use properties to prove theorems about parallel and perpendicular lines and apply these properties to real-life problems.

Construct parallel and perpendicu

http://www.pleasanton.k12.ca.us/avhsweb/kiyoi/Sketchpad/Constructing_Parallel_Lines_Guide.pdf

https://www.khanacademy.org/math/geometry/geometric-constructions/geo-bisectors/v/constructing-a-perpendicular-line-using-a-compass-and-straightedge

http://tube.geogebra.org/student/mETI8RCVi?mobile=true

Big Ideas Textbook

Chromebooks















Knowledge/Skills


tiation

a given line passing through a given point?

lar lines.

Use slope to partition directed line segments and to find the distance from a point to a line.

Write equations of parallel and perpendicular lines.


Transform How can you ● Rigid Students Geogebra Exploring Exploring Geometry with





Knowledge/Skills


tiation

ations

(Week 10, 3 Weeks)

translate, reflect, and rotate a figure in a coordinate plane?

What conjectures can you make about a figure reflected in two lines?

What does it mean to dilate a figure?

When a figure is translated, reflected, rotated or dilated in a plane, is the image always congruent and/or similar to the original figure?

motions are connected to congruence.

● Dilations are connected to similarity.

● There are certain relationships that exist between figures before and after transformations

are applied.

will be able to:

Perform translations, reflections, rotations, dilations, and compositions of transformations.

Solve real-life problems involving transformations.

Identify lines of symmetry and rotational symmetry.

Describe and perform congruence transformat

TransformationsGEOGEBRA .docxGeogebra Transformations.ggbinvestigate rotation.doc

GeoGebra

Big Ideas Textbook

Chromebooks









Knowledge/Skills


tiation

ions and similarity transformations.


Congruent Triangles

(Week 13, 5 Weeks)

● How are the angle measures of a triangle related?

● Given two congruent triangles, how can you use rigid motions to map one triangle to the other triangle?

● What can you conclude about two triangles

● Congruence and rigid transformations are related.

● Triangles can be prove congruent in several ways with certain given information.

● There is a relationship between the sides and

Students will be able to

Identify and use corresponding parts of triangles prove or show that triangles are congruent.

Use theorems

http://illuminations.nctm.org/activity.aspx?id=3504explore triangle congruenceHandsON.docExploring Congruent TrianglesHANDSON.docxhttp://tube.geogebra.org/student/mc9xn98go?

mobile=true


Big Ideas Textbook

Chromebooks


http://tube.geogebra.org/student/mc9xn98go?mobile=true




http://illuminations.nctm.org/activity.aspx?id=3504

http://illuminations.nctm.org/activity.aspx?id=3504






Knowledge/Skills


tiation

when you know that two pairs of corresponding sides and the corresponding included angles are congruent?

● What conjectures can you make about the side lengths and angle measures of an isosceles triangle?

● What can you conclude about two triangles when you know that the corresponding sides are

congruent?

● What information is sufficient to determine whether two triangles are congruent?

angles of triangles.

● Properties of congruent triangles can be used to solve real-life problems.

about the angles of a triangle

Use SAS, SSS, HL, ASA and AAS to prove two triangles congruent

Construct an equilateral triangle and explore its properties.

Write coordinate proofs.




Knowledge/Skills


tiation

● How can you use congruent triangles to make an indirect measurement?

Relationships Within Triangles

(Week 18, 4 Weeks)

What conjectures can you make about a point on the perpendicular bisector of a segment and

on the bisector of an angle?

What conjectures can you make about the perpendicular bisectors and the angle bisectors of a

triangle?

What conjectures can you make about the medians

● Sides and angles of a triangle are related to each other.

● Indirect proof is an alternate way of explaining or reasoning.


Understand and use angle bisectors and perpendicular bisectors to find measures.

Find and use the circumcenter, incenter, centroid and orthocenter of a triangle.

http://tube.geogebra.org/student/mVhBlIUTF?mobile=true

http://tube.geogebra.org/student/mGWqCQCEN?mobile=true

http://tube.geogebra.org/student/mJ7BkiwqL?mobile=true


Big Ideas Textbook

Chromebooks










Knowledge/Skills


tiation

and altitudes of a triangle?

How are the midsegments of a triangle related to the sides of a triangle?

How are the sides of a triangle related to the angles of the triangle?

How are any two sides of a triangle related to the third side?

Understand, use and apply the Triangle Midsegment Theorem and the Triangle Inequality Theorem.

Write indirect proofs.


Quadrilaterals and Other Polygons

(Week 22, 3 Weeks)

● What is the sum of the measures of the interior angles of a polygon?

● What are the

● Knowledge of parallelograms can be extended to learn properties of


Find and use the interior and

Learning Activity

Is this a Rectangle? Activity https://www.illustrativemathematics.org/content-standards/tasks/1302

Pooltastic Task and Student Sheet Pooltastic Task.doc &


Big Ideas Textbook

Chromebooks



Knowledge/Skills


tiation

properties of parallelograms?

● How can you prove that a quadrilateral is a parallelogram?

● What are the properties of the diagonals of rectangles, rhombuses and squares?

● What are the properties of trapezoids and kites?

special parallelograms.

● Information about polygons enables one to solve real-world problems.

exterior angle measures of polygons

Use properties of parallelograms and special parallelograms

Prove that a quadrilateral is a parallelogram

Identify and use properties of trapezoids and kites

Use dynamic geometry software to visualize and

Pooltastic Backyard Blueprint.docx

Pooltastic Backyard Blueprint.docxPooltastic Task.dochttps://www.illustrativemathematics.org/content-

standards/tasks/1302Kite Template.docxParallelograms Exploration.docxRectangles Exploration.docxTrapezoid Exploration.docxIsoscelesTrapezoid.ggbKite.ggbParallelogram.ggbproperty chart- blankGEOGEBRA.docRectangle.ggbRhombus.ggbSquare.ggb













https://www.illustrativemathematics.org/content-standards/tasks/1302




















Knowledge/Skills


tiation

represent geometric concepts.

Similarity

(Week 25, 3 Weeks)

How are similar polygons related?

What can you conclude about two triangles when you know that two pairs of corresponding

angles are congruent?

What are two ways to use corresponding sides of two triangles to determine that the triangles

are similar?

What proportionality relationships exist in a

● Similar figures and triangles can be explored through dilations.

● Proportions are used to solve many real-life problems, including triangle problems.

● There exist relationships between various segments in triangles.


Use the AA, SSS and SAS Similarity Theorems to prove triangles are similar.

Determine whether triangles are similar.

Use similarity criteria to solve problems about lengths, perimeters and areas.

http://tube.geogebra.org/student/mLd9sFYbd?mobile=true

http://tube.geogebra.org/student/mkVXuNspo?mobile=true

http://tube.geogebra.org/student/myZKotF6i?mobile=true


Big Ideas Textbook

Chromebooks













Knowledge/Skills


tiation

triangle intersected by an angle bisector or by a

line parallel to one of the sides?

Prove the slope criteria using similar triangles.

Use the Triangle Proportionality Theorem and other proportionality theorems.


Right Triangles and Trigonom

● How can you prove the Pythagorean Theorem?

● Relationships exist between side lengths and angles of


Use the

Hands on activity- Trig River : https://www.teachengineering.org/view_activity.php?url=collection/cub_/activities/cub_navigation/cub_navigation_lesson03_activity2.xml


Big Ideas Textbook



Knowledge/Skills


tiation

etry

(Week 28, 5 Weeks)

● What is the relationship among the side lengths of 45-45-90 and 30-60-90 triangles?

● How are altitudes and geometric means of right triangles related?

● How is a right triangle used to find the tangent, sine and cosine of a right triangle?

● What are the Law of Sines and the Law of Cosines?

right triangles.

● Trigonometry can help one to find unknown information about triangles.

● The Law of Sines and the Law of Cosines enable one to find unknown information about

triangles.

Pythagorean Theorem and its converse to solve problems

Understand and use geometric means

Find side lengths and tangent, sine and cosine ratios to solve real-life problems involving right triangles

Derive the formula A=½ absin(c) for the area of a triangle by drawing an auxiliary

http://education.ti.com/en/timathnspired/us/detail?id=C3E70398468F4DD390DA749899086DA1&t=9D03A938D0834CEB912366FC09ED1DBE

https://www.teachengineering.org/view_activity.php?url=collection/cub_/activities/cub_navigation/cub_navigation_lesson03_activity2.xml


Daves_NTTI_lesson_plan_1302179828.docxExplore Sin,Cos,Tan.docxSpecial Right Triangles Explore.pdfhttp://tube.geogebra.org/student/ml25E2eBn?

mobile=truehttp://tube.geogebra.org/student/mLxpvJn5x?

mobile=true

Chromebooks


http://tube.geogebra.org/student/mLxpvJn5x?mobile=true


http://tube.geogebra.org/student/ml25E2eBn?mobile=true




















Knowledge/Skills


tiation

line from a vertex perpendicular to the opposite side *

Prove the Law of Sines and the Law of Cosines and use them to solve triangles and problems.*


Circles

(Week 33,

What are the definitions of the lines and

● Several relationships exist within

Students will be

http://tube.geogebra.org/student/mBh173QeH?mobile=true

http://tube.geogebra.org/student/mBoibgqcf?


http://tube.geogebra.org/student/mBoibgqcf?mobile=true







Knowledge/Skills


tiation

5 Weeks) segments that intersect a circle?

How are circular arcs measured?

What are two ways to determine when a chord is a diameter of a circle?

How are inscribed angles related to their arcs?

What relationships exist among the angles formed when chords and tangents intersect?

What relationships exist among the segments formed when chords, secants and tangents

circles.

● Segments, angles, and triangles can all be explored in relation to circles.

able to:

Define and identify chords, diameters, radii, secants and tangents of circles.

Find arc and angle measures.

Use inscribed angles and polygons and use circumscribed angles to solve problems.

Use and apply properties of chords, tangents and secants to solve

mobile=truehttp://tube.geogebra.org/student/mlb6iK8kV?

mobile=truehttp://tube.geogebra.org/student/me97RO7CE?

mobile=true

Big Ideas Textbook

Chromebooks


http://tube.geogebra.org/student/me97RO7CE?mobile=true


http://tube.geogebra.org/student/mlb6iK8kV?mobile=true







Knowledge/Skills


tiation

intersect?

What is the equation of a circle with center (h, k) and radius r in the coordinate plane?

problems.

Write and graph equations of circles.

Construct a tangent line from a point outside a given circle to the circle. *


Circumference, Area and Volume

(Week 38,

● How can you find the length of a circular arc?

● How can you

● Area and volume can be used in real-life situations.


Measure angles in

http://tube.geogebra.org/student/mgAftSMzd?mobile=true

http://tube.geogebra.org/student/mWk1fxp9z?mobile=true

http://tube.geogebra.org/student/mx4NVGB2q?mobile=true


Big Ideas Textbook












Knowledge/Skills


tiation

3 Weeks)find the area of a sector of a circle?

● How can you find the area of a regular polygon?

● What is the relationship between the numbers of vertices, edges and faces of a polyhedron?

● How can you find the volume of a prism or cylinder that is not a right prism/cylinder?

● How can you find the volume of a pyramid?

● How can you find the surface area and volume of a cone and a sphere?

radians *

Find arc lengths and areas of sectors.

Find and use the areas of rhombuses, kites and regular polygons.

Find and use volumes of prisms, cylinders, pyramids, cones and spheres.

Describe cross-section and solids of revolution.

Use dynamic geometry software to

http://tube.geogebra.org/student/mftRPdDWg?mobile=true Chromebooks


http://tube.geogebra.org/student/mftRPdDWg?mobile=true





Knowledge/Skills


tiation

visualize and represent geometric concepts.

Probability

(Week 38, 3 Weeks)

How can you list the possible outcomes in the sample space of an experiment?

How can you determine whether two evens are independent or dependent?

How can you construct and interpret a two-way table?

How can you find probabilities of disjoint and overlapping events?

How can a tree diagram help

Probability can be used to solve real world problems.

There is a difference between theoretical and experimental probability.


Find sample spaces.

Find theoretical probabilities.

Find experimental probabilities.

Determine whether events are independent events.

Find

http://tube.geogebra.org/student/mZd5fLRjA?mobile=true

http://tube.geogebra.org/student/mOmL9WRU2?mobile=true

http://tube.geogebra.org/student/mwmc9YZqU?mobile=true

http://tube.geogebra.org/student/mGXy6rGjJ?mobile=true


Big Ideas Textbook

Chromebooks
















Knowledge/Skills


tiation

you visualize the number of ways in which two or more events can occur?

How can you determine the frequency of each outcome of an event?

probabilities of independent and dependent events.

Find conditional probabilities.

Make two-way tables.

Find relative and conditional relative frequencies.

Use conditional relative frequencies to find conditional probabilities.

Find probabilitie



Knowledge/Skills


tiation

s of compound events.

Use more than one probability rule to solve real-life problems.

Use the formula for the number of permutations.

Use the formula for the number of combinations.

Use combinations and the Binomial Theorem to expand binomials.



Knowledge/Skills


tiation

Construct and interpret probability distributions.

Construct and interpret binomial distributions.

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