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Mathematics Pacing GuideTime Frame: 6 Weeks – September/October High School GeometryUnit 1: Congruence
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
WHST 10.2d Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesExperiment with transformations in the planeG.CO.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.
What is congruence?
How do you use coordinates to prove simple geometric theorems algebraically?
BeforeDraw pictures based on a precise definition.
DuringAssess students by assigning three or four proofs involving lines and
adjacentalternate interior
angleangleareacirclecircular arccollinear
Geoboard – circular:http://nlvm.usu.edu/en/nav/topic_t_3.htmlwww.math-aids.com
Geogebrahttp://geogebra.com
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 1- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcesangles to be completed over a weekend.
Have students defend a proof before their classmates in groups/pairs.
AfterGive students four figures to construct using a compass and straightedge. Make certain that the figures those defined in standard.
Use distance formula and Pythagorean Theorem to prove a given triangle on a coordinate axis is a right triangle.
Use distance formula and given coordinates to find the perimeter of a given polynomial.Use similar triangles to determine length of a segment through the ratio of similarity.
complementary angles
concaveconcurrentcongruentconvexcoplanarcorollarycorresponding
angleendpointEuclidean hexagoninterior anglelineline segmentlinearn-gonparallel lineperimeterperpendicular
bisectorperpendicular
linepointpolygonpostulaterayrectanglesimilar figureskewsquarestraightsupplementary
angles
NCTM Illuminations http://illuminations.nctm.org
http://illuminations.nctm.org/LessonDetail.aspx?id=L661 http://illuminations.nctm.org/LessonDetail.aspx?id=L745
Texas Instrumentshttp://education.ti.com/calculators/downloads/US/Activities/Detail?id=3888
Betweenness http://education.ti.com/calculators/downloads/US/Activities/Detail?id=4032
Investigating the Slopes of Parallel and Perpendicular Lineshttp://education.ti.com/calculators/downloads/US/Activities/Detail?id=6880
Points on the Perpendicular Bisector of a Segmenthttp://education.ti.com/calculators/downloads/US/Activities/Detail?id=6860
Shortest Distance Between Points and Lineshttp://education.ti.com/calculators/downloads/US/Activities/Detail?
G.CO.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.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.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.
Understand congruence in terms of rigid motionsG.CO.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.- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 2- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcestheoremtransversaltrianglevertexvertical angle
id=4036
Geogebra Exploring Linear Functions: http://www.geogebratube.org/material/show/id/2020
Geogebra for Constructions: http://www.geogebratube.org/material/show/id/13478
Applying Angle Theorems: http://map.mathshell.org/materials/lessons.php?taskid=214&subpage=concept
This site has additional resources for teachers and students:http://apps.svsu.edu/mathsci-center/uploads/math/HighSchool.html
Prove geometric theoremsG.CO.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.
Make geometric constructionsG.CO.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.
G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
Use coordinates to prove simple geometric theorems algebraicallyG.GPE.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 - Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 3- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcesdisprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 4- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 3 Weeks – October High School GeometryUnit 2: Congruence (continued)
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.
WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically.
WHST 10.7 Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 5- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resources
Prove geometric theoremsG.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 degrees; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
How do you prove geometric theorems?
BeforeDraw examples of interior angles of a triangle, base angels of isosceles triangles, and the segment joining midpoints of two sides.
DuringWrite a proof demonstrating that the base angles of an isosceles triangle are congruent.
Write a proof demonstrating that the diagonals of a rhombus are perpendicular.
AfterGive a cumulative assessment test that asks students to prove theorems about parallelograms.
acutealtitudediagonalequilateralexterior angleshypotenuseinterior anglesisosceleslegmedianmidpointmid-segmentobtuseoppositeparallelogramrhombusrightscalenetriangles
Right Triangle Solver:http://nlvm.usu.edu/en/nav/topic_t_3.html
Also use Resources from Unit 1
G.CO.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.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 6- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 3 Weeks – November High School GeometryUnit 3: Expressing Geometric Properties with Equations
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesTranslate between the geometric description and the equation for a conic section
How do you use coordinates to prove geometric theorems
BeforeUse slope to prove that two lines are parallel/
plane Geoboard x,y coordinate:http://nlvm.usu.edu/en/nav/topic_t_3.html
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 7- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary ResourcesG.GPE.2 Derive the equation of a parabola give focus and directrix.
Use coordinates to prove simple geometric theorems algebraically.G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
algebraically? perpendicular.
DuringUse slope to prove that the diagonals of a rhombus are perpendicular.
AfterDisprove that a figure defined by four given points in the coordinate plane is a rectangle.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 8- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 4 Weeks – November/December High School GeometryUnit 4: Circles
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 9- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary ResourcesUnderstand and apply theorems about circlesG.C.1 Prove that all circles are similar.
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
G.C.4 (+) Understand and apply theorems about circles. Construct a tangent line from a point outside a given circle to the circle.
Find arc lengths and areas of sectors of circlesG.C.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.
How do you apply theorems to circles?
Before Use a compass and straightedge to draw chords, inscribed angles, and radii and describe their relationships.
DuringGive students a construction problem using a compass and straightedge to show that all circles are similar.
Use a compass and straightedge to construct inscribed, circumscribed figures and tangent lines in and around circles.
AfterAsk students to demonstrate the relationship between degree and radian measure.
arccentercentral anglechordcirclecircumferencecircumscribedconcentricdiameterinscribemajorminorradian measureradiusright anglesecantsectortangent line
Virtual Manipulatives:http://nlvm.usu.edu/en/nav/topic_t_3.html
Radian Measure:http://www.projectmaths.ie/documents/radian_activity_1.pdf
Chords, Radii, Tangents, Secants, and Arcs: http://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/CMA_LP_S03_BC_L10_I10_01.pdf
Circle Conjectures: http://www.math.uakron.edu/amc/Geometry/HSGeometry Lessons/5.1CircleConjectures.pdf
Texas Instrumentshttp://education.ti.com/calculators/downloads/US/Activities/Detail?id=3888
Exploring the Equation of a Circle (TI-Nspire): http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5024&t=5047&id=13173
Secants, Tangents, and Arcs (TI-Nspire): http://education.ti.com/calculators/timathnspired/US/Activities/Detail?
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 10- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcessa=5024&t=5047&id=13176 Tangents to a Circle (TI-Nspire): http://education.ti.com/calculators/timathnspired/US/Activities/Detail?sa=5024&t=5047&id=13174 Constructing Circles (Ti-84+): .http://education.ti.com/calculators/downloads/US/Activities/Detail?id=4063 Angles Formed by Intersecting Chords, Secants, and Tangents (TI-84+): http://education.ti.com/calculators/downloads/US/Activities/Detail?id=4065
NUMB3RS - Season 1 - "Pilot" - The Center of it All (TI-84+): http://education.ti.com/calculators/downloads/US/Activities/Detail?id=7719 NUMB3RS - Season 2 - "Harvest" - Meltdown (TI-84+): http://education.ti.com/calculators/downloads/US/Activities/Detail?id=6521
NCTM Illuminations http://illuminations.nctm.org
Power of Points: - Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 11- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resources
http://illuminations.nctm.org/LessonDetail.aspx?id=L700
Circle Packing: http://illuminations.nctm.org/LessonDetail.aspx?ID=U175
Equations of Circles 1: http://map.mathshell.org/materials/lessons.php?taskid=406&subpage=concept Equations of Circles 2: http://map.mathshell.org/materials/lessons.php?taskid=425&subpage=concept
Modeling: Rolling Cups: http://map.mathshell.org/materials/download.php?fileid=1254
Articles from National Council of Teachers of Mathematics (www.nctm.org) http://www.nctm.org/publications/article.aspx?id=26421
http://www.nctm.org/publications/article.aspx?id=18091
Temple Geometry: http://map.mathshell.org/materials/tasks.php?
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 12- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcestaskid=261&subpage=apprentice
Circles in Triangles: http://map.mathshell.org/materials/tasks.php?taskid=256&subpage=apprentice
Sectors of Circles: http://map.mathshell.org/materials/lessons.php?taskid=441&subpage=concept
Equations of Circles 1: http://map.mathshell.org/materials/lessons.php?taskid=406&subpage=concept
Equations of Circles 2: http://map.mathshell.org/materials/lessons.php?taskid=425&subpage=concept
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 13- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 5 Weeks – January/February High School GeometryUnit 5: Geometric Measurement and Dimension
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 14- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary ResourcesExplain volume formulas and use them to solve problemsG.GMD.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.
How do you solve problems using volume formulas?
BeforeGive students a bell ringer that assesses their comprehension of volume formulas.
DuringHave a class discussion on the formulas for circles.
Have a class discussion on the formulas for spheres.
AfterGive students a comprehensive test on volumes of prisms, cylinders, pyramids, cones, and spheres. Stress use of Pythagorean Theorem, Special Triangles and Pythagorean Triples to find lengths of the parts of the figures. Use coordinate axis to help students create three dimensional figures through rotation.
apothemareaconecross sectioncylinderlateral areapolyhedronprismpyramid rotationspheresurface areathree-dimensionaltwo-dimensionalvolume
ACT Prep Materials:www.princetonreview.com
NCTM Illuminations http://illuminations.nctm.org/
Using Cubes and Isometric Drawings: http://illuminations.nctm.org/LessonDetail.aspx?ID=U166
Popcorn, Anyone?: http://illuminations.nctm.org/LessonDetail.aspx?id=L797
Texas Instrumentshttp://education.ti.com/calculators/timath/
Exploring Cavalieri's Principle(TI-84+): http://education.ti.com/calculators/downloads/US/Activities/Detail?ID=12581
NUMB3RS - Season 2 - "Rampage" - Tesseract (TI-84+): http://education.ti.com/calculators/downloads/US/Activities/Detail?ID=6899
Making Hay While the Sun
G.GMD.2 Give an informal argument using Cavalieri’s principle for the formulas for the volume of a sphere and other solid figures.
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.*
Visualize relationships between two-dimensional and three-dimensional objectsG.GMD.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.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 15- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary ResourcesShines & Not Losing It in the Rain(The Geometry of the Big Round Bale) (TI-Nspire): http://education.ti.com/calculators/downloads/US/Activities/Detail?ID=10559
Paint Can Dimensions (TI-Nspire): http://education.ti.com/calculators/downloads/US/Activities/Detail?ID=10586
Volume (TI-Nspire): http://education.ti.com/calculators/downloads/US/Activities/Detail?ID=9689
CPMP-Tools http://www.wmich.edu/cpmp/CPMP-Tools/
Shodor Interactivate http://www.shodor.org/interactivate/
Surface Area of a Rectangular Prism: http://www.shodor.org/interactivate/lessons/SurfaceAreaRectangular/
Surface Area of Prisms: http://www.shodor.org/
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 16- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcesinteractivate/lessons/SurfaceAreaPrisms/
Volume of Rectangular Prisms: http://www.shodor.org/interactivate/lessons/VolumeRectangular/
Volume of Prisms: http://www.shodor.org/interactivate/lessons/VolumePrisms/
Surface Area and Volume: http://www.shodor.org/interactivate/lessons/SurfaceAreaAndVolume/
Interactives, Geometry 3D Shapes: http://www.learner.org/interactives/geometry/index.html
GeoGebra http://www.geogebra.org/cms/
Unwrapping a Prism: http://www.slu.edu/classes/maymk/GeoGebra/prism.html
Rotating Pyramid: http://www.slu.edu/classes/maymk/GeoGebra/pyramid.html
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 17- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resources
GEOGEBRA 3D: http://dmentrard.free.fr/GEOGEBRA/Maths/Espace/Espace.htm
MARS Dead or Alive: http://www.pbs.org/wgbh/nova/teachers/activities/3101_mars.html#standards
Using Spheres to Examine Changes in Volume and Surface Area: http://mathbits.com/MathBits/TeacherResources/Algebra1/Algebra1.htm
Dan Meyer Blog Archive: Popcorn Picker: http://blog.mrmeyer.com/?p=14118#comment-451223
Evaluating Statements About Enlargements (2D and 3D): http://map.mathshell.org/materials/lessons.php?taskid=213 Calculating Volumes of Compound Objects: http://map.mathshell.org/materials/lessons.php?taskid=216
Focus in High School
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 18- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resources
Mathematics: Reasoning and Sense Making: http://www.nctm.org/catalog/product.aspx?ID=13494
Focus in High School Mathematics: Reasoning and Sense Making In Geometry: http://www.nctm.org/catalog/product.aspx?ID=13525
MAP Assessment TasksFunsize Cans: http://map.mathshell.org/materials/tasks.php?taskid=252
Glasses: http://map.mathshell.org/materials/tasks.php?taskid=259
Fruit Boxes: http://map.mathshell.org/materials/tasks.php?taskid=275
Fearless Frames: http://map.mathshell.org/materials/tasks.php?taskid=277
Bestsize Cans: http://map.mathshell.org/materials/tasks.php?taskid=284
Propane Tanks:
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 19- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourceshttp://map.mathshell.org/materials/tasks.php?taskid=288
Security Camera: http://map.mathshell.org/materials/tasks.php?taskid=273&subpage=expert
Mathematics Pacing GuideTime Frame: 5 Weeks – February/March High School GeometryUnit 6: Similarity, Right Triangles, and Trigonometry
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.
RST 10.9 Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 20- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Standards for Mathematical Practice Literacy Standardscontradict previous explanations or accounts.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesUnderstand congruence in terms of rigid motionsG.CO.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.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
What is similarity in terms of similarity transformations?
BeforeDiscuss with students the meaning of dilation and have them represent their understanding.
DuringAsk the students to demonstrate the properties of dilations through constructions and the coordinate axis (or either).
arithmetic meandilationgeometric meanlocusscale factorsymmetrytransformation
ACT Prep Materials:www.princetonreview.com
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 21- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary ResourcesHave students participate in a class discussion to demonstrate the definition of similarity in the transformation of one triangle to a second.
AfterGive students a quiz on using AA to prove triangles similar.
Understand similarity in terms of similarity transformationsG.SRT.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.
G.SRT.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.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Prove theorems involving similarityG.SRT.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.5 Use congruence and similarity - Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 22- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcescriteria for triangles to solve problems and to prove relationships in geometric figures.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 23- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 4 Weeks – March/April High School GeometryUnit 7: Expressing Geometric Properties with Equations
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 24- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Standards for Mathematical Practice Literacy StandardsSL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesTranslate between the geometric description and the equation for a conic sectionG.GPE.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.
G.GPE.3 (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.
What is a conic section?
BeforeHave students to complete a bell ringer, where they have to derive at the equation of a line.
DuringUsing Pythagorean Theorem and completing the square have students derive the equations of a circle, parabola, ellipse and hyperbola.
Use slope to solve problems with different polynomials using parallel lines and perpendicular lines.
AfterUse coordinate geometry to prove the ratio of similarity of similar polygons.
conic sectionellipseshyperbolaparabola
Use coordinates to prove simple geometric theorems algebraicallyG.GPE.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).
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.*
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 25- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 3 Weeks – April/May High School GeometryUnit 8: Right Triangles
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and concepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
WHST 10.4 Produce clear and coherent writing in which the development, - Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 26- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Standards for Mathematical Practice Literacy Standardsorganization, and style are appropriate to task, purpose, and audience.
WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically.
WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
SL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesDefine trigonometric ratios and solve problems involving right trianglesG.SRT.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.7 Explain and use the relationship between the sine and cosine of complementary angles.*
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Apply trigonometry to general trianglesG.SRT.9 (+) Derive the formula A = (1/2) ab
How do you apply trigonometry to triangles?
BeforeHave students write discussing their understanding of what it means for triangles to be similar.
DuringHave students use the relationship of sine and cosine to determine the measure of complementary angles in a right triangle.
AfterHave students create
cosineratiosinetangenttrigonometry
ACT Prep Materials:www.princetonreview.com
Law of Cosines Tutorial:http://www.themathpage.com/aTrig/law-of-cosines.htm
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 27- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Common Core Essential Questions Assessment Vocabulary Resourcessin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
G.SRT.10 (+) Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11 (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).
their own word problem involving angle of elevation or depression to determine the measure of an angle or length of a side in a right triangle (solve using trig ratios).
Give students a series of non-right triangles and have them find the missing measurements and lengths using the laws of sine and cosine.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 28- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Mathematics Pacing GuideTime Frame: 4 Weeks – May/June High School GeometryUnit 9: Modeling with Geometry
Standards for Mathematical Practice Literacy Standards1. Make sense of problems and persevere in solving them
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
6. Attend to precision
7. Look for and make use of structure
8. Look for and express regularity in repeated reasoning
RST 10.1 Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or descriptions.
RST 10.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text.
RST 10.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics.
RST 10.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words.
RST 10.8 Assess the extent to which the reasoning and evidence in a text support the author’s claim or a recommendation for solving a scientific or technical problem.
RST 10.9 Compare and contrast findings presented in a text to those from other sources (including their own experiments), noting when the findings support or contradict previous explanations or accounts.
WHST 10.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes.a. Introduce a topic and organize ideas, concepts, and information to make
important connections and distinctions; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension.
c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among ideas and
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 29- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Standards for Mathematical Practice Literacy Standardsconcepts.
d. Use precise language and domain-specific vocabulary to manage the complexity of the topic and convey a style appropriate to the discipline and context as well as to the expertise of likely readers.
WHST 10.4 Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.
WHST 10.5 Develop and strengthen writing as needed by planning, revising, editing, rewriting, or trying a new approach, focusing on addressing what is most significant for a specific purpose and audience.
WHST 10.6 Use technology, including the Internet, to produce, publish, and update individual or shared writing products, taking advantage of technology’s capacity to link to other information and to display information flexibly and dynamically.
WHST 10.7 Conduct short as well as more sustained research projects to answer a question (including a self-generated question) or solve a problem; narrow or broaden the inquiry when appropriate; synthesize multiple sources on the subject, demonstrating understanding of the subject under investigation.
WHST 10.8 Gather relevant information from multiple authoritative print and digital sources, using advanced searches effectively; assess the usefulness of each source in answering the research question; integrate information into the text selectively to maintain the flow of ideas, avoiding plagiarism and following a standard format for citation.
WHST 10.9 Draw evidence from informational texts to support analysis, reflection, and research.
WHST 10.10 Write routinely over extended time frames (time for reflection and revision) and shorter time frames (a single sitting or a day or two) for a range of discipline-specific tasks, purposes, and audiences.
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 30- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
Standards for Mathematical Practice Literacy StandardsSL 10.5 Make strategic use of digital media (e.g., textual, graphical, audio, visual, and interactive elements) in presentations to enhance understanding of findings, reasoning, and evidence and to add interest.
Common Core Essential Questions Assessment Vocabulary ResourcesApply geometric concepts in modeling situationsG.MG.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).*
How do you apply geometric concepts to models?
BeforeStudents will compare objects’ shapes.
DuringStudents will estimate the number of marbles in a box using the volume of the sphere and the prism.
AfterStudents will find the volume of ice cream in different cones based on changes in the height and radius of the cone. They will also find the surface area of each cone to determine how much batter is needed to make the cone. (This involves a composite figure involving a hemisphere and a cone.)
Project-based problem to use surface area and volume to design a dog house for their dog. Also have students price out the materials for the project.
density How to Build A Dog House:http://hubpages.com/hub/How-to-Build-a-Dog-House
G.MG.2 Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).*
G.MG.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).*
- Additional mathematics that students should learn in order to take advanced courses such as calculus, advanced statistics, or discrete mathematics is indicated by (+) 31- Making mathematical models is a Standard for Mathematical Practice, and specific modeling standards appear throughout the high school standards indicated by a star symbol (★). The star symbol sometimes appears on the heading for a group of standards; in that case, it should be understood to apply to all standards in that group.
Geometry Pacing Guide Aligned to Common Core Standards – Revised March 2013
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