geometry curriculum map 2014-2015

5/21/2018 Geometry Curriculum Map 2014-2015

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Unit 1: Introduction to Geometry

Approximate Time: 11 days Month(s): August-Early September

ApproxTime

Concepts/Skills CCSS Vocabulary Text Resources

1 Review the basicterms/phrases thatare integral parts ofa geometry course

G.CO.1 Undefined Terms: point, line, plane;

collinear points, coplanar points,

line, (line) segment, endpoint, ray,

initial point, terminal point, opposite

rays, intersect, angle

1.2, Movie: The Dot and the Line

1 New Vocabulary G.CO.1 Postulate (Axiom), Theorem,

Corollary, 7 Basic Postulates

1.3

1 Measuring

Segments & Angles

G.GPE.4, length, distance, distance between

a point and a line, measure of an

angle, types of angles, congruent

segments, congruent angles,

segment addition postulate, angle

addition postulate

1.3,

1.4,1.5

include coordinate geometry problems

1 Distance formula G.GPE.4 Distance formula 1.5 Khan Academy Practice (5 in a row)https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formula

1 Segment and AngleBisectors

G.GPE.4, bisect, midpoint, segment bisector,

Midpoint formula, angle bisector

1.3,1.4,1.5

include coordinate geometry problems

Khan Academy Practice (midpoint formula)https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formula

Khan Academy Practice (Algebra and midpoints)https://www.khanacademy.org/math/cc-eighth-grade-

math/cc-8th-geometry/line-segment-
http://www.youtube.com/watch?v=4ZEuXA8Wr2ghttp://www.youtube.com/watch?v=4ZEuXA8Wr2ghttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/midpoint_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/distance_formulahttp://www.youtube.com/watch?v=4ZEuXA8Wr2g


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algebra/e/midpoint_of_a_segment

1 Constructions G.CO.12 Copy a segment, add segment

lengths, copy an angle, add angle

measures, construct the midpoint,

bisect an angle

Construction how-tos: Good for absentees or review athome (Math open Ref)http://www.mathopenref.com/tocs/constructionstoc.html

1 Equations of Paralleland PerpendicularLines

G.CO.12,G.GPE.4,G.GPE.5

parallel lines, perpendicular lines, 3.6,3.7

Parallel Perpendicular Songhttp://www.youtube.com/watch?v=HNw7KM-BYKM

Khan Academy Practice (Equations of Parallel andPerpendicular Lines)https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationships

1 Introduction toGeogebra

through-out

Construct segments, angles,parallel lines, perpendicular lines,

measure angles, measure

segments, construct midpoint,

angle bisector

8 Instructional Time

+3 Leeway/Quizzes/Test

Possible Tasks:MAP: Parallel & Perpendicular LInes (does refer to

rectangles)http://map.mathshell.org/materials/lessons.php?taskid=226
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segmenthttp://www.mathopenref.com/tocs/constructionstoc.htmlhttp://www.mathopenref.com/tocs/constructionstoc.htmlhttp://www.youtube.com/watch?v=HNw7KM-BYKMhttp://www.youtube.com/watch?v=HNw7KM-BYKMhttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttp://map.mathshell.org/materials/lessons.php?taskid=226http://map.mathshell.org/materials/lessons.php?taskid=226http://map.mathshell.org/materials/lessons.php?taskid=226http://map.mathshell.org/materials/lessons.php?taskid=226http://map.mathshell.org/materials/lessons.php?taskid=226https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttps://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/more-analytic-geometry/e/line_relationshipshttp://www.youtube.com/watch?v=HNw7KM-BYKMhttp://www.mathopenref.com/tocs/constructionstoc.htmlhttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/line-segment-algebra/e/midpoint_of_a_segment


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Unit 2: Polygons

Approximate Time: 11 days Month(s): September

ApproxTime


1 Polygons Polygons (sides 3-12 named andsketched), vertices, sides,interior/exterior, convex/concave,equilateral/equiangular/regular,diagonals (maximum number ateach vertex, total number inpolygon), congruent polygons

6.1,11.1

1 Interior and ExteriorAngles of Polygons

Interior angle of a polygon, exteriorangle of a polygon, triangle sumtheorem, Polygon interior angle

sum, Exterior Angle Theorem

6.1,11.1

Extra credit opportunity? Octagon frisbee

1 Types of Triangles right triangle, acute triangle, obtuse

triangle, equilateral triangle,

isosceles triangle, scalene triangle

Khan Academy Practice (Recognizing Triangle Types)https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangles

Is this a rectangle?http://www.illustrativemathematics.org/illustrations/1302

Include coordinate geometry examples

1 PythagoreanTheorem & ItsConverses

G.CO.9,G.GPE.5,

Pythagorean Theorem,

Pythagorean triple, converse of the

Pythagorean theorems (9.5-9.7),

9.2,9.3,

Math Teacher Link (Good teacher resource. Check outthe Just Do It and Assignment links on each pagefor examples/problems for Pyth. Thm)http://mtl.math.uiuc.edu/node/29

I like the first two probs on this page (Pyth Thm)http://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmPyth Thm and its Converse activityhttp://campuses.fortbendisd.com/campuses/documents

/Teacher/2013%5Cteacher_20130124_1719.pdf
http://almostunschoolers.blogspot.com/2012/05/paper-frisbee-geometry.htmlhttp://almostunschoolers.blogspot.com/2012/05/paper-frisbee-geometry.htmlhttps://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangleshttps://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangleshttps://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangleshttp://www.illustrativemathematics.org/illustrations/1302http://www.illustrativemathematics.org/illustrations/1302http://www.illustrativemathematics.org/illustrations/1302http://mtl.math.uiuc.edu/node/29http://mtl.math.uiuc.edu/node/29http://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmhttp://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmhttp://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmhttp://campuses.fortbendisd.com/campuses/documents/Teacher/2013%5Cteacher_20130124_1719.pdfhttp://campuses.fortbendisd.com/campuses/documents/Teacher/2013%5Cteacher_20130124_1719.pdfhttp://campuses.fortbendisd.com/campuses/documents/Teacher/2013%5Cteacher_20130124_1719.pdfhttp://campuses.fortbendisd.com/campuses/documents/Teacher/2013%5Cteacher_20130124_1719.pdfhttp://campuses.fortbendisd.com/campuses/documents/Teacher/2013%5Cteacher_20130124_1719.pdfhttp://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmhttp://faculty.wiu.edu/JR-Olsen/wiu/ps/topics/pythag/prob1.htmhttp://mtl.math.uiuc.edu/node/29http://www.illustrativemathematics.org/illustrations/1302http://www.illustrativemathematics.org/illustrations/1302https://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangleshttps://www.khanacademy.org/math/geometry/congruent-triangles/isoscleles_equil/e/recognizing-triangleshttp://almostunschoolers.blogspot.com/2012/05/paper-frisbee-geometry.html


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1 Types ofQuadrilaterals

parallelogram, rectangle, rhombus,

square, trapezoid, isosceles

trapezoid, trapezium, kite

Khan Academy (Quadrilateral Types)https://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_types


1 Review ofarea/perimeter ofparallelograms,rectangles, squares,trapezoids,triangles, circles

G.GPE.7 Area, Perimeter, Circumference, 1.7 Areas of squareshttp://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxDan Meyer 3 Act Obscure Geometryhttps://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0

A set of all points (Area of a Triangle)

http://www.illustrativemathematics.org/illustrations/1348Five Triangles #22 (Rect Perim), 72 (Para Area), 55(Rect Area), 23 (composite), 65, (trapezoid), Site hasLOTS of Triangle Area ProblemsMathaliciousViewmongus

2 ConstructingPolygons UsingGeogebra

G.CO.12G.CO.13

Construct: equilateral triangle,

isosceles triangle, right triangle,

parallelogram, rectangle, rhombus,

square, trapezoid, isosceles

trapezoid, kite, find area/perimeter


+3 Leeway/Quizzes/Tests

Possible Task/Project: Recreate an image usingconstruction tools. Have students write-up theirconstruction steps. Trade directions (but not images)and have partner recreate your image based on yourinstructions. Compare results.http://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Co

nstruction%20Project.pdf
https://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_typeshttps://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_typeshttps://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_typeshttp://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxhttp://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxhttp://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxhttps://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0http://www.illustrativemathematics.org/illustrations/1348http://www.illustrativemathematics.org/illustrations/1348http://www.illustrativemathematics.org/illustrations/1348http://www.mathalicious.com/lesson/viewmongus/http://www.mathalicious.com/lesson/viewmongus/http://www.mathalicious.com/lesson/viewmongus/http://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://doversherborn.comcastbiz.net/highschool/academics/math/baroody/GeometryHonors/Miscellaneous/Construction%20Project.pdfhttp://www.mathalicious.com/lesson/viewmongus/http://www.illustrativemathematics.org/illustrations/1348http://www.illustrativemathematics.org/illustrations/1348https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0https://docs.google.com/spreadsheet/ccc?key=0AjIqyKM9d7ZYdEhtR3BJMmdBWnM2YWxWYVM1UWowTEE#gid=0http://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxhttp://fawnnguyen.com/2012/03/25/investigating-area-with-paper-folding.aspxhttps://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_typeshttps://www.khanacademy.org/math/geometry/quadrilaterals-and-polygons/quadrilaterals/e/quadrilateral_types


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Finding the Quadrilateral with largest possible areagiven one side http://fawnnguyen.com/don-stewards-complete-quadrilateral/

Perplexing Parallelograms by NCTMhttp://illuminations.nctm.org/uploadedFiles/Content/Les

sons/Resources/9-12/Para-AS-PerPara.pdf
http://fawnnguyen.com/don-stewards-complete-quadrilateral/http://fawnnguyen.com/don-stewards-complete-quadrilateral/http://fawnnguyen.com/don-stewards-complete-quadrilateral/http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Para-AS-PerPara.pdfhttp://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Para-AS-PerPara.pdfhttp://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Para-AS-PerPara.pdfhttp://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Para-AS-PerPara.pdfhttp://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Para-AS-PerPara.pdfhttp://fawnnguyen.com/don-stewards-complete-quadrilateral/http://fawnnguyen.com/don-stewards-complete-quadrilateral/


6/25

Unit 3: Rigid Transformations

Approximate Time: 14 days Month(s): September/October

ApproxTime


1 Introduction toTransformationsUsing Geogebra

preimage, image, Reflect polygonover various lines, Translatepolygon using various vectors,Rotate polygons about varyingpoints, and Dilate polygons tovarious points Have studentscompare preimage and image.(Congruent vs Similar),

7.1 Challenge students to create a line that will reflect apreimage onto itself. What must be true of the polygonfor this to work? What do we call this line of reflection?(Line of symmetry)

Challenge students to find a point of rotation that willrotate a figure onto itself. Is this possible for allpolygons? If not, what must be true of the polygon for itto work? Describe where the point of rotation lies.(Intersection of the diagonals - Center of the polygon)

2 Reflection G.CO.2,G.CO.3,G.CO.4,G.CO.5,G.CO.6

isometry, rigid transformation,reflection, line symmetry, function,line of reflection, coordinatenotation,

7.2 isos & equil tri,http://illuminations.nctm.org/LessonDetail.aspx?ID=U139---http://www.illustrativemathematics.org/illustrations/983 ---http://www.illustrativemathematics.org/illustrations/982 ---http://www.illustrativemathematics.org/illustrations/984 MathaliciousFace-Off

2 Translation G.CO.2,G.CO.4,G.CO.5,G.CO.6

translate (aka glide or slide),vector, magnitude, direction,component form, sum of 2 vectors,theorem 7.5

7.4 http://illuminations.nctm.org/LessonDetail.aspx?ID=L474

2 Rotation G.CO.2,G.CO.3,G.CO.4,G.CO.5,G.CO.6

rotation, rotational symmetry,order of rotation, theorem 7.3

7.3 http://illuminations.nctm.org/LessonDetail.aspx?ID=U138

2 Dilation G.CO.2, scale factor, dilate, similar 8.6 Recreate an image (by hand) using a given scale factor
http://illuminations.nctm.org/LessonDetail.aspx?ID=U139http://illuminations.nctm.org/LessonDetail.aspx?ID=U139http://illuminations.nctm.org/LessonDetail.aspx?ID=U139http://www.illustrativemathematics.org/illustrations/983http://www.illustrativemathematics.org/illustrations/983http://www.illustrativemathematics.org/illustrations/982http://www.illustrativemathematics.org/illustrations/982http://www.illustrativemathematics.org/illustrations/984http://www.illustrativemathematics.org/illustrations/984http://www.mathalicious.com/lesson/face-off/http://www.mathalicious.com/lesson/face-off/http://www.mathalicious.com/lesson/face-off/http://illuminations.nctm.org/LessonDetail.aspx?ID=L474http://illuminations.nctm.org/LessonDetail.aspx?ID=L474http://illuminations.nctm.org/LessonDetail.aspx?ID=L474http://illuminations.nctm.org/LessonDetail.aspx?ID=U138http://illuminations.nctm.org/LessonDetail.aspx?ID=U138http://illuminations.nctm.org/LessonDetail.aspx?ID=U138http://illuminations.nctm.org/LessonDetail.aspx?ID=U138http://illuminations.nctm.org/LessonDetail.aspx?ID=U138http://illuminations.nctm.org/LessonDetail.aspx?ID=L474http://illuminations.nctm.org/LessonDetail.aspx?ID=L474http://www.mathalicious.com/lesson/face-off/http://www.illustrativemathematics.org/illustrations/984http://www.illustrativemathematics.org/illustrations/982http://www.illustrativemathematics.org/illustrations/983http://illuminations.nctm.org/LessonDetail.aspx?ID=U139http://illuminations.nctm.org/LessonDetail.aspx?ID=U139


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G.SRT.1,G.SRT.2

polygons, reduction, enlargment

2 Compositions ofTransformations

G.CO.2,G.CO.5,G.CO.6

composition, glide reflection,double reflection across parallel orintersecting lines, theorem 7.6

7.5 http://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspx


+3 Leeway/Quizzes/Test

Representing and Combining Transformations Taskhttp://map.mathshell.org/materials/lessons.php?taskid=490

Transforming 2D figureshttp://map.mathshell.org/materials/download.php?fileid=1538
http://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://map.mathshell.org/materials/lessons.php?taskid=490http://map.mathshell.org/materials/lessons.php?taskid=490http://map.mathshell.org/materials/lessons.php?taskid=490http://map.mathshell.org/materials/download.php?fileid=1538http://map.mathshell.org/materials/download.php?fileid=1538http://map.mathshell.org/materials/download.php?fileid=1538http://map.mathshell.org/materials/download.php?fileid=1538http://map.mathshell.org/materials/download.php?fileid=1538http://map.mathshell.org/materials/lessons.php?taskid=490http://map.mathshell.org/materials/lessons.php?taskid=490http://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspxhttp://180days2012-13.fawnnguyen.com/2013/05/13/day-152---geometric-transformations.aspx


8/25

Unit 4: Angles & Lines

Approximate Time: 9 days Month(s): October

ApproxTime


2 Angle Pairs G.CO.9 complementary/supplementaryangles, complement, supplement,adjacent angles, vertical angles,linear pair, vertical anglestheorem, linear pair postulate,theorems 3.1, 3.2, 3.3

1.6 Khan Academy (Equations with Vertical Angles)https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2

1 Transversals ofLines

transversal, corresponding angles,consecutive interior angles,alternate interior angles, alternateexterior angles

2 Transversals ofParallel Lines

G.CO.9 Corresponding angles postulate,consecutive interior anglestheorem, alternate interior anglestheorem, alternate exterior anglestheorem, perpendicular transversaltheorem

Geogebra Investigation Angle Pairs and Transversals(Made by me)

Parking Lot Mathematics

Khan Academy (Equations with Congruent Angles)https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2

2 Proving Lines areParallel

G.CO.9 Corresponding angles converse,consecutive interior anglesconverse, alternate interior anglesconverse, alternate exterior anglesconverse, if two lines are parallelto the same line..., if two lines areperpendicular to the same line...

Jen Silvermath Variation tothis


2 Quiz/Test Check summer school stuff (Placing restaurant, post
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttps://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttp://www.indiana.edu/~iucme/perspectives/44rigsby.pdfhttp://www.indiana.edu/~iucme/perspectives/44rigsby.pdfhttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2http://www.jensilvermath.com/2013/07/17/a-new-way-to-build-a-geometric-system/http://www.jensilvermath.com/2013/07/17/a-new-way-to-build-a-geometric-system/http://www.jensilvermath.com/2013/07/17/a-new-way-to-build-a-geometric-system/http://www.jensilvermath.com/2013/07/17/a-new-way-to-build-a-geometric-system/https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/parallel_lines_2http://www.indiana.edu/~iucme/perspectives/44rigsby.pdfhttps://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttps://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-geometry/cc-8th-angles-between-lines/e/vertical_angles_2


9/25

office, etc)


10/25

Unit 5: Triangle Congruence

Approximate Time: 11 Month(s): October/November

ApproximateTime

ncepts/Skills CCSS Vocabulary Text Resources

1 Triangles & theirangles

G.CO.10 triangle sum theorem, exteriorangle theorem, corollary to thetriangle sum theorem,

Five Triangles has LOTS of Triangle Sum ProblemsRevisit theGeogebra Investigation#2,4.Paper Folding Triangle Activity

1 Inequalities inTriangles

Unnamed theorems (the smallestside is opp. the smallest angle &vice versa) exterior angleinequality, triangle inequality,hinge theorem and its converse

NCTM Triangle Inequalities Investigationhttp://illuminations.nctm.org/Lesson.aspx?id=2339

Khan Academy Triangle Inequality Practicehttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequa

lity_theorem

1 Congruence andTriangles

G.CO.6,G.CO.7

congruent polygons, third anglestheorem

Are the triangles congruent?http://www.illustrativemathematics.org/illustrations/33

2 Proving trianglesare congruent

G.CO.8,G.CO.10,G.GPE.4

SAS, SSS, ASA, AAS, HL Khan Academy Congruent Triangles 1https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1

Khan Academy Congruent Triangles 2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2

2 Using congruenttriangles

G.CO.10,G.GPE.4

CPCTC

1 Right, isosceles,and equilateraltriangles

G.CO.10,G.GPE.4

Base angles theorem and itsconverse, corollary to the baseangles theorem,

8 Instructional
https://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttps://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttps://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edithttps://docs.google.com/document/d/1djSnDy1R2xR2J9YVwoQAssjBGfKl4nKv4R3F3m8H6zk/edithttps://docs.google.com/document/d/1djSnDy1R2xR2J9YVwoQAssjBGfKl4nKv4R3F3m8H6zk/edithttp://illuminations.nctm.org/Lesson.aspx?id=2339http://illuminations.nctm.org/Lesson.aspx?id=2339https://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttp://www.illustrativemathematics.org/illustrations/33http://www.illustrativemathematics.org/illustrations/33https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_2https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1https://www.khanacademy.org/math/geometry/congruent-triangles/cong_triangle/e/congruent_triangles_1http://www.illustrativemathematics.org/illustrations/33https://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttps://www.khanacademy.org/math/geometry/basic-geometry/triangle_inequality_theorem/e/triangle_inequality_theoremhttp://illuminations.nctm.org/Lesson.aspx?id=2339https://docs.google.com/document/d/1djSnDy1R2xR2J9YVwoQAssjBGfKl4nKv4R3F3m8H6zk/edithttps://docs.google.com/document/d/1DYQemfwlEHIsP9tSH3-RLd3UZ_kwHjfLYHZCJfYxQb0/edit


11/25

Time


Congruent Triangles Task MAPhttp://map.mathshell.org/materials/download.php?fileid=1302
http://map.mathshell.org/materials/download.php?fileid=1302http://map.mathshell.org/materials/download.php?fileid=1302http://map.mathshell.org/materials/download.php?fileid=1302http://map.mathshell.org/materials/download.php?fileid=1302http://map.mathshell.org/materials/download.php?fileid=1302


12/25

Unit 6: Triangle Centers

Approximate Time: 9 Month(s): November/December

ApproximateTime

Concepts/Skills CCSS Vocabulary Text-book

Resources

1 Perpendicular &angle bisectors

G.CO.10 equidistant, perpendicular bisectortheorem, angle bisector theorem

http://www.illustrativemathematics.org/illustrations/508 ---http://www.illustrativemathematics.org/illustrations/967 Five Triangles #41

1 InvestigatingPoints ofConcurrency usingGeogebra

through-out

2 Bisectors of aTriangle

G.CO.10,G.CO.12,G.CO.13,G.C.3,G.GPE.4

concurrent lines, point ofconcurrency, perpendicularbisectors of a triangle, anglebisectors of a triangle,circumcenter, circumscribed circle,incenter, inscribed circle,concurrency of perpendicularbisectors of a triangle theorem,concurrency of angle bisectors ofa triangle theorem

Construct these by hand, as well as with patty paper.

2 Medians andAltitudes of aTriangle


median of a triangle, centroid,concurrency of the medians of atriangle, altitude of a triangle,orthocenter, concurrency of thealtitudes of a triangle

Construct these by hand, as well as with patty paper.

6 InstructionalTime


Possible Tasks:Circumcenter Task

http://www.utdanacenter.org/k12mathbenchmarks/tasks
http://www.illustrativemathematics.org/illustrations/508http://www.illustrativemathematics.org/illustrations/508http://www.illustrativemathematics.org/illustrations/967http://www.illustrativemathematics.org/illustrations/967http://www.utdanacenter.org/k12mathbenchmarks/tasks/4_chineserestaurant.phphttp://www.utdanacenter.org/k12mathbenchmarks/tasks/4_chineserestaurant.phphttp://www.illustrativemathematics.org/illustrations/967http://www.illustrativemathematics.org/illustrations/508


13/25

/4_chineserestaurant.php

Could this be modified?http://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdf

THIS SHOULD BE THE END OF FIRST SEMESTER. (I think.)
http://www.utdanacenter.org/k12mathbenchmarks/tasks/4_chineserestaurant.phphttp://www.utdanacenter.org/k12mathbenchmarks/tasks/4_chineserestaurant.phphttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdfhttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdfhttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdfhttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdfhttp://www.nsa.gov/academia/_files/collected_learning/high_school/algebra/geometer_jones.pdfhttp://www.utdanacenter.org/k12mathbenchmarks/tasks/4_chineserestaurant.php


14/25

Unit 7: Quadrilaterals

Approximate Time: 13 Month(s): January

ApproxTime


1 Review of

polygons

Interior angles sum, exterior

angles sum, definitions ofquadrilaterals

Five Triangles #11 (Students may need to use patty

paper to make a physical model.)

2 Properties ofParallelograms

G.CO.11,G.GPE.4

If a quadrilateral is aparallelogram, then: both pairs ofopposite sides are congruent, bothpairs of opposite angles arecongruent, an interior angle issupplementary to both of itsconsecutive interior angles, thediagonals bisect each other

Five Triangles #43http://fivetriangles.blogspot.com/2013/01/43-parallelograms.html

FIve Triangles #121http://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.html

2 Proving aquadrilateral is aparallelogram

G.CO.11,G.GPE.4

A quadrilateral is a parallelogramif: (converse of the 4 theoremslisted in cell above), one pair ofopposite sides are congruent andparallel, both pairs of oppositesides are parallel

2 Rhombuses,Rectangles andSquares


A parallelogram is a rhombus ifand only if its diags are perp, apara is a rhom iff each diag bisects

a pair of opp angles, a para is arect iff its diags are congruent

Five Triangles #55http://fivetriangles.blogspot.com/2013/04/55-squares.html

Five Triangles #92 September Squareshttp://fivetriangles.blogspot.com/2013/09/92-september-squares.html

Five Triangles #22 Perimeter and Areahttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.html

2 Trapezoids andKites

G.CO.11,G.CO.12.

If a trap is isosceles, then eachpair of base angles are congruent.

Five Triangles #86 (Hint: unfold the paper)http://fivetriangles.blogspot.com/2013/07/86-
http://fivetriangles.blogspot.com/2013/01/43-parallelograms.htmlhttp://fivetriangles.blogspot.com/2013/01/43-parallelograms.htmlhttp://fivetriangles.blogspot.com/2013/01/43-parallelograms.htmlhttp://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.htmlhttp://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.htmlhttp://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.htmlhttp://fivetriangles.blogspot.com/2013/04/55-squares.htmlhttp://fivetriangles.blogspot.com/2013/04/55-squares.htmlhttp://fivetriangles.blogspot.com/2013/04/55-squares.htmlhttp://fivetriangles.blogspot.com/2013/09/92-september-squares.htmlhttp://fivetriangles.blogspot.com/2013/09/92-september-squares.htmlhttp://fivetriangles.blogspot.com/2013/09/92-september-squares.htmlhttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.htmlhttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.htmlhttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.htmlhttp://fivetriangles.blogspot.com/2013/07/86-boomerang.htmlhttp://fivetriangles.blogspot.com/2013/07/86-boomerang.htmlhttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.htmlhttp://fivetriangles.blogspot.com/2012/04/21-perimeter-and-area.htmlhttp://fivetriangles.blogspot.com/2013/09/92-september-squares.htmlhttp://fivetriangles.blogspot.com/2013/09/92-september-squares.htmlhttp://fivetriangles.blogspot.com/2013/04/55-squares.htmlhttp://fivetriangles.blogspot.com/2013/04/55-squares.htmlhttp://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.htmlhttp://fivetriangles.blogspot.com/2013/12/121-parallelogram-exercise.htmlhttp://fivetriangles.blogspot.com/2013/01/43-parallelograms.htmlhttp://fivetriangles.blogspot.com/2013/01/43-parallelograms.html


15/25

G.GPE.4 If a trap has a pair of congruentbase angles, then it is isosceles.

A trapezoid is isos iff its diags arecongruent. midsegment of atrapezoid, The midsegment of atrapezoid is parallel to both basesand its length is the average of the

lengths of the two bases. If aquad is a kite, then its diags areperp. If a quad is a kite, thenexactly one pair of opp angles arecongruent.

boomerang.html

Five Triangles #144 (Modify to accommodate for thelack of knowledge about points of tangency and radii.)http://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.html

1 Quadrilaterals andCoordinateGeometry

G.GPE.4 6.6

10 InstructionalTime

+ 3 Leeway/Quizzes/Tests

Some of the days allotted abovecould be used with Geogebra.

Possible Tasks:

Dividing a Parallelogram into 2 congruent partshttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.php

Five Triangles #72: Areas in Parallelogramshttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.html(See Fawns post regarding thisproblem and a solution/extension)

Five Triangles #23: Changing Areahttp://fivetriangles.blogspot.com/2012/04/23-changing-area.html
http://fivetriangles.blogspot.com/2013/07/86-boomerang.htmlhttp://fivetriangles.blogspot.com/2013/07/86-boomerang.htmlhttp://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.htmlhttp://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.htmlhttp://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.htmlhttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.phphttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.phphttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.phphttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.htmlhttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.htmlhttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.htmlhttp://fivetriangles.blogspot.com/2012/04/23-changing-area.htmlhttp://fivetriangles.blogspot.com/2012/04/23-changing-area.htmlhttp://fivetriangles.blogspot.com/2012/04/23-changing-area.htmlhttp://fivetriangles.blogspot.com/2012/04/23-changing-area.htmlhttp://fivetriangles.blogspot.com/2012/04/23-changing-area.htmlhttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.htmlhttp://fivetriangles.blogspot.com/2013/05/72-parallelogram.htmlhttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.phphttp://www.utdanacenter.org/k12mathbenchmarks/tasks/8_congruence.phphttp://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.htmlhttp://fivetriangles.blogspot.com/2014/02/144-semicircle-inscribed-in.htmlhttp://fivetriangles.blogspot.com/2013/07/86-boomerang.html


16/25

Unit 8: Similarity

Approximate Time: 11 Month(s): January/February

ApproxTime


1 Review ofDilations

G.SRT.1a,G.SRT.1b,G.CO.12

dilation, scale factor, reduction,enlargement, similar polygons

Illustrative Mathematics Similar Quadrilateralshttps://www.illustrativemathematics.org/illustrations/1858

Class Project Idea (Dont show them the finished image.Give each student one square to enlarge)http://www.pinterest.com/pin/273664114829950796/

2 Similar Triangles G.SRT.2,G.SRT.3,

G.SRT.4,G.SRT.5,G.GPE.4,G.GPE.6,G.CO.10,

similar triangles, AA~, SAS~,SSS~,

Five Triangles #83http://fivetriangles.blogspot.com/2013/07/83-

construction-of-equal-angles.html

Five Triangles #56http://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.html

Illustrative Mathematics Similar Triangles (omit part c)https://www.illustrativemathematics.org/illustrations/1901

1 Proportions &Similar Triangles

G.SRT.4,G.SRT.5,

Midsegment Theorem ofTriangles, Triangle ProportionalityTheorem, Converse of theTriangle Proportionality Theorem

1 Proportions &similar triangles

G.SRT.4,G.SRT.5,G.GPE.4,G.GPE.6,G.CO.10

thms 8.6 and 8.7 in the textbook, Five Triangles #16 (Shadows)http://fivetriangles.blogspot.com/2012/04/16-shadows.html
https://www.illustrativemathematics.org/illustrations/1858https://www.illustrativemathematics.org/illustrations/1858https://www.illustrativemathematics.org/illustrations/1858http://www.pinterest.com/pin/273664114829950796/http://www.pinterest.com/pin/273664114829950796/http://fivetriangles.blogspot.com/2013/07/83-construction-of-equal-angles.htmlhttp://fivetriangles.blogspot.com/2013/07/83-construction-of-equal-angles.htmlhttp://fivetriangles.blogspot.com/2013/07/83-construction-of-equal-angles.htmlhttp://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.htmlhttp://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.htmlhttp://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.htmlhttps://www.illustrativemathematics.org/illustrations/1901https://www.illustrativemathematics.org/illustrations/1901https://www.illustrativemathematics.org/illustrations/1901http://fivetriangles.blogspot.com/2012/04/16-shadows.htmlhttp://fivetriangles.blogspot.com/2012/04/16-shadows.htmlhttp://fivetriangles.blogspot.com/2012/04/16-shadows.htmlhttp://fivetriangles.blogspot.com/2012/04/16-shadows.htmlhttp://fivetriangles.blogspot.com/2012/04/16-shadows.htmlhttps://www.illustrativemathematics.org/illustrations/1901https://www.illustrativemathematics.org/illustrations/1901http://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.htmlhttp://fivetriangles.blogspot.com/2013/04/56-obtuse-triangle-area.htmlhttp://fivetriangles.blogspot.com/2013/07/83-construction-of-equal-angles.htmlhttp://fivetriangles.blogspot.com/2013/07/83-construction-of-equal-angles.htmlhttp://www.pinterest.com/pin/273664114829950796/https://www.illustrativemathematics.org/illustrations/1858https://www.illustrativemathematics.org/illustrations/1858


17/25

2 Similarity in RightTriangles

theorems 9.1-9.3

1 Areas of SimilarPolygons

Bubble Wrap Area and Popping Rate problemhttp://www.pinterest.com/pin/273664114829905483/

8 InstructionalTime


Mathematics Assessment Project (relates toproportional thinking not triangles specifically)http://map.mathshell.org/materials/download.php?fileid=816

Pigs in a Blanket (Geoff Krall)http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/

Floodlights (MAP)http://map.mathshell.org/materials/download.php?fileid=1257

Im not sure how to incorporate this...Fawn Nyugens posthttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspx...Use this and have Ss find the

ratio of the radii of the three circles. Then have students construct using Geogebra - use similar, concentric circles, perpendicular lines and angle

bisectors to create points. Connect points to make graph...possibility
http://www.pinterest.com/pin/273664114829905483/http://www.pinterest.com/pin/273664114829905483/http://map.mathshell.org/materials/download.php?fileid=816http://map.mathshell.org/materials/download.php?fileid=816http://map.mathshell.org/materials/download.php?fileid=816http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://map.mathshell.org/materials/download.php?fileid=1257http://map.mathshell.org/materials/download.php?fileid=1257http://map.mathshell.org/materials/download.php?fileid=1257http://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://map.mathshell.org/materials/download.php?fileid=1257http://map.mathshell.org/materials/download.php?fileid=1257http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://emergentmath.com/2012/11/08/more-math-food-blogging-i-may-need-some-help-from-my-southern-friends/http://map.mathshell.org/materials/download.php?fileid=816http://map.mathshell.org/materials/download.php?fileid=816http://www.pinterest.com/pin/273664114829905483/


18/25

Unit 9: Right Triangles and Trigonometry

Approximate Time: 11 Month(s): February

ApproxTime


1 Similarity andTrigonometricRatios

G.SRT.6,G.SRT.7

trigonometry, sine, cosine,tangent, secant, cosecant,cotangent

2 Special righttriangles

45-45-90, 30-60-90 triangles, Illustrative Mathematics (Trig Ratios in Special RightTriangles)https://www.illustrativemathematics.org/illustrations/1902

1 Using trig ratios to

find missing sides(right triangles)

G.SRT.8 solve a triangle @stephreilly Hallway neon string triangles (Find locker

height. Favorited on twitter 8/4/14)

Mathalicious51-Foot Ladder

1 Using trig ratios tofind missingangles (Righttriangles)

G.SRT.8 inverse, inverse sine, inversecosine, inverse tangent

Five Triangles #155 Three missing angleshttp://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.html

1 Solve non-righttriangles (law of

sines)

G.SRT.10,G.SRT.11

law of sines DERIVE it!

1 Solve non-righttriangles (law ofcosines)

G.SRT.10,G.SRT.11

law of cosines DERIVE it!

1 Areas of non-righttriangles

G.SRT.9 auxiliary line, MAP Circles and Triangles (Ratios)http://map.mathshell.org/materials/download.php?fileid=696

8 Instructional

Time
https://www.illustrativemathematics.org/illustrations/1902https://www.illustrativemathematics.org/illustrations/1902https://www.illustrativemathematics.org/illustrations/1902http://www.mathalicious.com/lesson/51-foot-ladder/http://www.mathalicious.com/lesson/51-foot-ladder/http://www.mathalicious.com/lesson/51-foot-ladder/http://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.htmlhttp://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.htmlhttp://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.htmlhttp://map.mathshell.org/materials/download.php?fileid=696http://map.mathshell.org/materials/download.php?fileid=696http://map.mathshell.org/materials/download.php?fileid=696http://map.mathshell.org/materials/download.php?fileid=696http://map.mathshell.org/materials/download.php?fileid=696http://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.htmlhttp://fivetriangles.blogspot.com/2014/04/155-three-angle-sum.htmlhttp://www.mathalicious.com/lesson/51-foot-ladder/https://www.illustrativemathematics.org/illustrations/1902https://www.illustrativemathematics.org/illustrations/1902


19/25


Illustrative Mathematics (angles in triangles)https://www.illustrativemathematics.org/illustrations/1905

IMP(Sine and Cosine of Complementary Angles)https://www.illustrativemathematics.org/illustrations/1443

Incorporate authentic modeling problems throughout this unit.
https://www.illustrativemathematics.org/illustrations/1905https://www.illustrativemathematics.org/illustrations/1905https://www.illustrativemathematics.org/illustrations/1905https://www.illustrativemathematics.org/illustrations/1443https://www.illustrativemathematics.org/illustrations/1443https://www.illustrativemathematics.org/illustrations/1443https://www.illustrativemathematics.org/illustrations/1443https://www.illustrativemathematics.org/illustrations/1443https://www.illustrativemathematics.org/illustrations/1905https://www.illustrativemathematics.org/illustrations/1905


20/25

Unit 10: Circles

Approximate Time: 18 Month(s): February/March

ApproxTime


1 Circles G.C.1,G.GPE.1,G.GPE.4

circle, congruent circles, similarcircles, equation of a circlecentered at the origin, equation ofa circle not centered at the origin

10.6 Khan Academy Practice identifying center and radius ofa circle given factored form.https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_1

Khan Academy Graphing Circles with equations givenin factored formhttps://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circles

Be sure to explain how the equation of a circle relates to

the Pythagorean Theorem.

MAP Equations of Circles 1http://map.mathshell.org/materials/download.php?fileid=1202Equations of Circles 2http://map.mathshell.org/materials/download.php?fileid=1247

1 Completing the

Square

trinomial, perfect square trinomial This is just meant to be a day to practice completing the

square for trinomials.

Khan Academy Practice with completing the squarehttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressions

1 Using Completingthe Square withEquations of

Circles

G..1,G.GPE.1,G.GPE.4

Khan Academy Identifying center and radius forequations not given in factored form.https://www.khanacademy.org/math/algebra2/conics_pr

ecalc/circles-tutorial-precalc/e/equation_of_a_circle_2
https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circleshttps://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circleshttps://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circleshttp://map.mathshell.org/materials/download.php?fileid=1202http://map.mathshell.org/materials/download.php?fileid=1202http://map.mathshell.org/materials/download.php?fileid=1202http://map.mathshell.org/materials/download.php?fileid=1247http://map.mathshell.org/materials/download.php?fileid=1247http://map.mathshell.org/materials/download.php?fileid=1247https://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_2https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_2https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_2https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_2https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/equation_of_a_circle_2https://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttps://www.khanacademy.org/math/algebra/quadratics/completing_the_square/e/completing_the_square_in_quadratic_expressionshttp://map.mathshell.org/materials/download.php?fileid=1247http://map.mathshell.org/materials/download.php?fileid=1247http://map.mathshell.org/materials/download.php?fileid=1202http://map.mathshell.org/materials/download.php?fileid=1202https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circleshttps://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circles


21/25

Khan Academy Graphing circles whose equations arenot given in factoredform.https://www.khanacademy.org/math/algebra2/conics_precalc/circles-tutorial-precalc/e/graphing_circles_2

2 G.C.2 chord, secant, tangent, point oftangency, secant segment,tangent segment, tangent circles,concentric circles, commontangents (internal and external),tangent is perpendicular to aradius drawn to the point oftangency (thm), 2 tangents drawnfrom same exterior point to thesame circle are congruent (thm)

10.1 Geogebra could be used here to discover thesetheorems.

Check the Circles book in closet for vocab practice.

2 Chords and Arcs G.C.2,G.C.3,G.C.5,

arc, minor arc, major arc,semicircle, congruent arcs,measure of an arc, congruentarcs, theorems 10.4-10.7 in thetextbook

10.2 Dan Meyers 3 Act Lucky Cowhttp://threeacts.mrmeyer.com/luckycow/

Mr. Stadels Elmo in a Microwavehttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.html

IMP Mutually Tangent Circleshttps://www.illustrativemathematics.org/illustrations/1006

2 Angles and Arcs G.C.2, central angle, inscribed angle,intercepted arc, theorems 10.8and 10.9

10.3

2 Polygons inCircles

G.C.2,G.C.3,G.GPE.4

Theorems 10.10 and 10.11 in thebook,

10.3 DIscuss what it means for a quadrilateral to be cyclic.Use Geogebra for this?

2 Tangents, Secantsand Chords of

circles

G.C.2, theorems 10.12-10.17 in thetextbook

10.4,10.5
http://threeacts.mrmeyer.com/luckycow/http://threeacts.mrmeyer.com/luckycow/http://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttps://www.illustrativemathematics.org/illustrations/1006https://www.illustrativemathematics.org/illustrations/1006https://www.illustrativemathematics.org/illustrations/1006https://www.illustrativemathematics.org/illustrations/1006https://www.illustrativemathematics.org/illustrations/1006http://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://mr-stadel.blogspot.com/2012/07/elmos-microwave-travel.htmlhttp://threeacts.mrmeyer.com/luckycow/


22/25

2 Circumference andArea of Sectors

length of an arc, sector, area of asector, arc length corollary,

11.4 Areas of circleshttp://map.mathshell.org/materials/download.php?fileid=758

Area of Circle 3 Act Car Caravanhttp://threeacts.mrmeyer.com/carcaravan/ http://www.illustrativemathematics.org/illustrations/918

Five Triangles #40, 18, 12, 45 (Circle Areas) 59 & 48(Circumference)

15 InstructionalTime


Im not sure how to incorporate this...Fawn Nyugens posthttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspx...Use this and have Ss find the

ratio of the radii of the three circles. Then have students construct using Geogebra - use similar, concentric circles, perpendicular lines and angle

bisectors to create points. Connect points to make graph...possibility
http://map.mathshell.org/materials/download.php?fileid=758http://map.mathshell.org/materials/download.php?fileid=758http://map.mathshell.org/materials/download.php?fileid=758http://threeacts.mrmeyer.com/carcaravan/http://threeacts.mrmeyer.com/carcaravan/http://www.illustrativemathematics.org/illustrations/918http://www.illustrativemathematics.org/illustrations/918http://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://fawnnguyen.com/2012/05/25/roman-mosaic.aspxhttp://www.illustrativemathematics.org/illustrations/918http://threeacts.mrmeyer.com/carcaravan/http://map.mathshell.org/materials/download.php?fileid=758http://map.mathshell.org/materials/download.php?fileid=758


23/25

Unit 11: Extending to Three Dimensions

Approximate Time: Month(s): April

ApproxTime


1 Review ofPolygons

Polygon Interior Angles Theorem,Polygon Exterior Angles Theorem

11.1

2 Areas of RegularPolygons

apothem, center of a polygon,central angle of a polygon, radiusof a polygon, circumscribed circle(inscribed polygon),

11.2

2 Polyhedra names of polyhedron, edge, face,vertex, Eulers theorem, lateralfaces, base, height, slant height,

hemisphere, oblique prism, net,Platonic solids, rightcone/prism/cylinder,

12.1 Preview of volume - I am a donuthttp://fawnnguyen.com/2012/04/16/i-am-a-donut.aspxVolume of a box (PreCalc type problem) - cut squares

from corner of paper and fold to make a box w/ no lid---Five Triangles #8 (visualizing exercise), 37

1 Representing 3Dobjects in 2D

cylinder, sphere, cone, prism,pyramid, cross-section

MAP 2D Representations of 3D objectshttp://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concept

IMP Tennis Ballshttps://www.illustrativemathematics.org/illustrations/512

This would also be a good time to use the pictures ofstacked blocks from various views and kids recreatethem.

1 Surface Area &Volume of Prismsand Cylinders

G.GMD.3 surface area, lateral area, volume 12.2,12.3

3 Act You Pour I Choosehttp://mrmeyer.com/threeacts/youpourichoose/ Worlds Largest Coffee Cuphttp://mrmeyer.com/threeacts/hotcoffee/ Stadels 3 Act File Cabinet Stickieshttp://vimeo.com/album/1921928Maximizing Volume (MARS)

http://map.mathshell.org/materials/download.php?fileid=
http://fawnnguyen.com/2012/04/16/i-am-a-donut.aspxhttp://fawnnguyen.com/2012/04/16/i-am-a-donut.aspxhttp://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concepthttp://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concepthttp://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concepthttps://www.illustrativemathematics.org/illustrations/512https://www.illustrativemathematics.org/illustrations/512http://mrmeyer.com/threeacts/youpourichoose/http://mrmeyer.com/threeacts/youpourichoose/http://mrmeyer.com/threeacts/hotcoffee/http://mrmeyer.com/threeacts/hotcoffee/http://vimeo.com/album/1921928http://vimeo.com/album/1921928http://map.mathshell.org/materials/download.php?fileid=806http://map.mathshell.org/materials/download.php?fileid=806http://vimeo.com/album/1921928http://mrmeyer.com/threeacts/hotcoffee/http://mrmeyer.com/threeacts/youpourichoose/https://www.illustrativemathematics.org/illustrations/512http://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concepthttp://map.mathshell.org/materials/lessons.php?taskid=439&subpage=concepthttp://fawnnguyen.com/2012/04/16/i-am-a-donut.aspx


24/25

806Five Triangles #63, 30, 51, 31, 14, 66MathaliciousCanalysis

1 Surface Area &volume ofPyramids andCones

G.GMD.3 12.2,12.3

1 Surface Area &Volume ofSpheres

G.GMD.3 Five Triangles #78MathaliciousThe Cheese that Goes Crunch

1 Solids of Rotation G.GMD.4 Five Triangles #68

1 Similar Solids Area, surface area and volume ofsimilar solids

3 Act Pencil Cuphttp://vimeo.com/album/2014533

11 Instructional

Time


MAP Volumes Lessonhttp://map.mathshell.org/materials/download.php?fileid=1280

Ice Cream Cone Task (Love this!)https://www.illustrativemathematics.org/illustrations/414

Indiana Jones and The Golden Statuehttps://www.illustrativemathematics.org/illustrations/143

9

Formulas will be provided as they appear on the PARCC High School Assessment Reference Sheet
http://map.mathshell.org/materials/download.php?fileid=806http://map.mathshell.org/materials/download.php?fileid=806http://www.mathalicious.com/lesson/canalysis/http://www.mathalicious.com/lesson/canalysis/http://www.mathalicious.com/lesson/canalysis/http://www.mathalicious.com/lesson/the-cheese-that-goes-crunch/http://www.mathalicious.com/lesson/the-cheese-that-goes-crunch/http://www.mathalicious.com/lesson/the-cheese-that-goes-crunch/http://vimeo.com/album/2014533http://vimeo.com/album/2014533http://vimeo.com/album/2014533http://map.mathshell.org/materials/download.php?fileid=1280http://map.mathshell.org/materials/download.php?fileid=1280http://map.mathshell.org/materials/download.php?fileid=1280https://www.illustrativemathematics.org/illustrations/414https://www.illustrativemathematics.org/illustrations/414https://www.illustrativemathematics.org/illustrations/1439https://www.illustrativemathematics.org/illustrations/1439https://www.illustrativemathematics.org/illustrations/1439https://www.illustrativemathematics.org/illustrations/1439https://www.illustrativemathematics.org/illustrations/1439https://www.illustrativemathematics.org/illustrations/414http://map.mathshell.org/materials/download.php?fileid=1280http://map.mathshell.org/materials/download.php?fileid=1280http://vimeo.com/album/2014533http://www.mathalicious.com/lesson/the-cheese-that-goes-crunch/http://www.mathalicious.com/lesson/canalysis/http://map.mathshell.org/materials/download.php?fileid=806


25/25

1 day Conditional &BiconditionalStatements

conditional statement, hypothesis,

conclusion, converse, biconditional

statement

2.1,2.2

Card sort - Put em in order - as an intro.HW: Conditional and Biconditional Statements WS

1 Inductive &DeductiveReasoning

Inductive reasoning, deductive

reasoning, conjecture,

counterexample

1.1,2.3

Sherlock introhttps://www.youtube.com/watch?v=im4TYITM0VE

http://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdf---http://www.pbs.org/wgbh/nova/education/activities/3011

_redbaron.html

1+ Angles and theirmeasures

G.CO.9,G.CO.12,

Right angle congruence theorem, 1.4,1.5

Midpts in a quadhttp://www.illustrativemathematics.org/illustrations/605

Five Triangles #80 (Angle Bisector of a Triangle - Extend AD and BC until they meet at F. Bisect angle F. Point of intersection of bisector and DCis P.)
https://www.youtube.com/watch?v=im4TYITM0VEhttps://www.youtube.com/watch?v=im4TYITM0VEhttp://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdfhttp://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdfhttp://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdfhttp://www.pbs.org/wgbh/nova/education/activities/3011_redbaron.htmlhttp://www.pbs.org/wgbh/nova/education/activities/3011_redbaron.htmlhttp://www.pbs.org/wgbh/nova/education/activities/3011_redbaron.htmlhttp://www.illustrativemathematics.org/illustrations/605http://www.illustrativemathematics.org/illustrations/605http://www.illustrativemathematics.org/illustrations/605http://www.illustrativemathematics.org/illustrations/605http://www.pbs.org/wgbh/nova/education/activities/3011_redbaron.htmlhttp://www.pbs.org/wgbh/nova/education/activities/3011_redbaron.htmlhttp://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdfhttp://www.doe.virginia.gov/testing/solsearch/sol/math/G/m_ess_g-1_2.pdfhttps://www.youtube.com/watch?v=im4TYITM0VE

geometry curriculum map 2014-2015

Documents

line segment

distance betweena point

initial point

terminal point

segment bisector

academy practice algebra

segment addition postulate

geometry curriculum