Download Scope Geometry Regular 2016-2017.xlsx

The School District of Palm Beach County
GEOMETRY REGULAR
Sections 1 & 2: Introduction to Geometry, Transformations, & Constructions
2016 - 2017
Topic & Suggested
Student Target
Core
Pacing
Math Nation
August 16 ‐ Mathematics Florida Standards
Students will …
1.1
August 30
• defining and representing points, lines, line segments, planes, rays, 1.2
and angles, as the building blocks of Geometry. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined 1.3
Basics of Geometry • defining and representing points, lines, line segments, planes, rays, notions of point, line, distance along a line, and distance around a circular arc.
1.4
and angles, as the building blocks of Geometry. 1.5
Midpoint and • midpoint and distance, and applications on a coordinate plane by 1.6
Distance in the either finding midpoint coordinates, endpoint coordinates or length of 1.7
Coordinate Plane segments.
1.8
• use the commutative and associative properties to identify Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as 2.1
Partitioning a Line equivalent expressions. Students will determine which properties functions that take points in the plane as inputs and give other points as outputs. Compare transformations that 2.2
Segment (distribute, associative, and commutative) have been used when preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
2.3
writing equivalent expressions.
2.4
Parallel and • finding the point on a directed line segment between two given 2.5
Perpendicular Lines points that partitions the segment in a given ratio.
2.6
• finding the point on a directed line segment between two given 2.7
Introduction to points that partitions the segment in a given ratio.
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel 2.8
Transformations • identifying parallel and perpendicular lines, and writing equations of lines, and line segments.
lines parallel or perpendicular to another line. Examining and • introducing rigid and non‐rigid transformations, translation, Using Translations reflection, rotation, and dilation.
• performing translations of points and line segments on a coordinate Examining and plane.
Using Dilations • performing dilations of points and line segments on a coordinate plane.
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, Examining and • performing dilations of points and line segments on a coordinate tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Using Rotations plane.
• performing rotation of points and line segments on a coordinate Examining and plane.
Using Reflections • performing reflection of points and line segments on a coordinate plane.
Basic Constructions • constructions of line segments.
Standards
MAFS.912.G‐CO.1.1
MAFS.912.G‐CO.1.2
MAFS.912.G‐CO.1.4
MAFS.912.G‐CO.1.5
MAFS.912.G‐CO.4.12
Calculator: Neutral MAFS.912.G‐GPE.2.5
Calculator: Neutral
MAFS.912.G‐GPE.2.6
MAFS.912.G‐GPE.2.7
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
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). Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
FSQ Sections 1 & 2
1 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 3: Angles
2016 - 2017
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
August 31 ‐ September 16
MAFS.912. G‐CO.1.1
MAFS.912. G‐CO.1.2
MAFS.912. G‐CO.1.4
Student Target
Core
Students will ...
Math Nation
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
• use the precise definitions of angles, circles, perpendicular lines, parallel lines, and line segments, basing the definitions on the Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined undefined notions of point, line, distance along a line, and distance notions of point, line, distance along a line, and distance around a circular arc.
Introduction to around a circular arc.
Angles
• represent transformations in the plane.
• describe transformations as functions that take points in the plane Angle Pairs
as inputs and give other points as outputs.
• compare transformations that preserve distance and angle to those Special Types of that do not.
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as Angle Pairs Formed • use definitions of rotations, reflections, and translations in terms of functions that take points in the plane as inputs and give other points as outputs. Compare transformations that by Transversals and angles, circles, perpendicular lines, parallel lines, and line segments.
preserve distance and angle to those that do not.
Non‐Parallel Lines • prove theorems about lines.
• prove theorems about angles.
Angle Pairs Formed • use theorems about lines to solve problems.
by Transversals and • use theorems about angles to solve problems.
Parallel Lines
• identify the result of a formal geometric construction.
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel • determine the steps of a formal geometric construction.
lines, and line segments.
Perpendicular Transversals
Angle‐Preserving Transformations
MAFS.912.G‐CO.1.5
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
MAFS.912. G‐CO.3.9
Prove theorems about lines and angles; use theorems about lines and angles to solve problems. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.
MAFS.912. G‐CO.4.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. Construction of Angles, Perpendicular and Parallel Lines
FSQ Section 3
2 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 4 & 5: Introduction to Polygons
2016 - 2017
Topic & Suggested
Pacing
Standards
MAFS.912. G‐CO.1.3
MAFS.912. G‐CO.1.4
MAFS.912. G‐CO.1.5
MAFS.912.G‐CO.2.6
MAFS.912.G‐CO.2.7
MAFS.912. G‐CO.3.10
MAFS.912.G‐MG.1.1
MAFS.912. G‐SRT.1.1
MAFS.912.G‐SRT.1.2
Core
Math Nation
4.1
Represent transformations in the plane using, e.g., transparencies and geometry software; describe
4.2
transformations as functions that take points in the plane as inputs and give other points as outputs.
4.3
Introduction to Compare transformations that preserve distance and angle to those that do not 4.4
Polygons
4.5
• distinguish between a rectangle, parallelogram, trapezoid, or regular Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto 4.6
Angles of Polygons polygon.
itself.
4.7
• describe the rotations and reflections a rectangle, parallelogram, Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel 4.8
Translation of trapezoid, or regular polygon carries onto itself.
lines, and line segments.
5.1
Polygons
• apply two or more transformations to a given figure to draw a 5.2
transformed figure.
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, 5.3
Reflection of • specify a sequence of transformations that will carry a figure onto tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
5.4
Polygons
another.
5.5
• provide descriptions of rigid motions and explain how each Rotation of preserves distance and angle.
Polygons
• be able to predict the effect of a given rigid motion on a given Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a figure.
given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are Dilation of • prove theorems about triangles using deductive reasoning (such as congruent.
Polygons
the law of syllogism).
• prove a theorem about triangles such as measures of interior angles Compositions of of a triangle sum to 180°.
Transformations of • use geometric shapes to describe objects.
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if Polygons
• use the measures of geometric shapes to describe objects.
corresponding pairs of sides and corresponding pairs of angles are congruent.
• use the properties of geometric shapes to describe objects.
Symmetries of • explain the properties of dilations given by a center and a scale Regular Polygons factor.
• perform dilations given by a center and a scale factor on figures in a Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of Congruence and plane.
interior angles of a triangle sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; Similarity of • verify that a dilation takes a line not passing through the center of the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of Polygons
the dilation to a parallel line, and leaves a line passing through the a triangle meet at a point.
center unchanged.
• verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
• explain similarity in terms of similarity transformations where angle Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human measure is preserved and side length changes proportionally.
torso as a cylinder).
• determine if two figures are similar, including triangles.
September 19 ‐ October 17
Mathematics Florida Standards
MAFS.912. G‐CO.1.2
Student Target
Students will …
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.
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.
USA Sections 1 ‐ 5
3 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 6 & 7: Triangles
2016 - 2017
Topic & Suggested
Student Target
Core
Pacing
Students will…
October 24 ‐ Math Nation
Mathematics Florida Standards
November 10
6.1
• distinguish between inscribed and circumscribed circles of a triangle.
6.2
• prove properties of angles for a quadrilateral inscribed in a circle, Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition of 6.3
Introduction to such as opposite angles in an inscribed quadrilateral are congruence in terms of rigid motions.
6.4
Triangles
supplementary.
6.5
• recognize triangle congruence (ASA, SAS, SSS) in terms of rigid 6.6
Area and Perimeter motions that preserve distance (S) and angle (A).
6.7
on the Coordinate • show how preserving correlating distances (S) and angles (A) Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior
6.8
Plane
between two triangles results in congruence.
angles of a triangle sum to 180°; triangle inequaliy theorem; base angles of isosceles triangles are congruent; the 6.9
• prove theorems about triangles using deductive reasoning segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a 7.1
Triangle • prove a theorem about triangles such as measures of interior angles triangle meet at a point.
7.2
Congruence – SSS of a triangle sum to 180°.
7.3
and SAS
• use coordinates to compute perimeters of polygons and areas of 7.4
triangles and rectangles.
7.5
Triangle Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; • explain similarity in terms of similarity transformations where angle 7.6
explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs Congruence – ASA measure is preserved and side length changes proportionally.
7.7
and AAS
of angles and the proportionality of all corresponding pairs of sides.
• determine if two figures are similar, including triangles.
7.8
• explain why, if two angle measures are known, the third angle is also Using Triangle known using the properties of similarity transformations.
Congruency to Find • prove theorems about triangles.
Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
Missing Variables • apply the concepts of congruence and similarity criteria to solve problems involving triangles.
Triangle Similarity • apply the concepts of congruence and similarity criteria to prove relationships in geometric figures.
Prove theorems about triangles.
Triangle Mid‐
Segment Theorem
Standards
MAFS.912.G‐CO.2.8
MAFS.912.G‐CO.3.10
MAFS.912.G‐SRT.1.2
MAFS.912.G‐SRT.1.3
MAFS.912.G‐SRT.2.4
MAFS.912.G‐SRT.2.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Triangle Inequalities
Triangle Proofs
MAFS.912.G‐GPE.2.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Inscribed and Circumscribed Circles of Triangle
Medians in Triangles
MAFS.912. G‐C.1.3
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
FSQ Sections 6 & 7
4 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 8: Right Triangles
2016 - 2017
Topic & Suggested
Pacing
Standards
Student Target
Core
Math Nation
Students will... 8.1
November 14 – • recognize triangle congruence (ASA, SAS, SSS) in terms of rigid 8.2
November 22
motions that preserve distance (S) and angle (A).
8.3
• show how preserving correlating distances (S) and angles (A) Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse‐Leg) follow from the definition of 8.4
The Pythagorean between two triangles results in congruence.
congruence in terms of rigid motions.
8.5
Theorem
• use the Pythagorean Theorem to determine if the point (a, b) lies on 8.6
a circle centered at the origin and containing the point (x, y).
8.7
The Converse of • use coordinates to compute perimeters of polygons and areas of 8.8
the Pythagorean triangles and rectangles.
8.9
Theorem
• prove theorems about triangles, such as a line parallel to one side of a triangle divides the other two proportionally, and conversely.
Use coordinates to prove simple geometric theorems algebraically.
Right Triangle • prove theorems about triangles, such as using triangle similarity to Congruency
prove the Pythagorean Theorem.
• apply the concepts of congruence and similarity criteria to solve Special Right problems involving triangles.
Triangles 45‐45‐90 • apply the concepts of congruence and similarity criteria to prove Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance relationships in geometric figures.
Special Right formula.
• explain by angle‐angle similarity of two right triangles that side Triangles 30‐60‐90 ratios are properties of the angles in the triangle.
• use similarity to define trigonometric ratios (tangent, sine, and Right Triangle cosine) for acute angles in right triangles.
Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two
Similarity
• determine cosine and sine rations for acute angles in right triangles proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
given the lengths of two sides.
Introduction to • explain the relationship between sine and cosine of complementary Trigonometry angles and construct a diagram to illustrate the relationship.
• express the Pythagorean Theorem as a2 + b2 + c2 and use it to find the unknown length of a right triangle side.
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
• use trigonometric ratios and the Pythagorean Theorem to solve real‐
world application problems.
Mathematics Florida Standards
MAFS.912. G‐CO.2.8
MAFS.912. G‐GPE.2.4
MAFS.912.G‐GPE.2.7
MAFS.912.G.SRT.2.4
MAFS.912.G‐SRT.2.5
MAFS.912.G‐SRT.3.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
MAFS.912.G‐SRT.3.7
Explain and use the relationship between the sine and cosine of complementary angles
MAFS.912.G‐SRT.3.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
USA Sections 6 ‐ 8
5 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 9 & 10: Quadrilaterals
2016 - 2017
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
MAFS.912.G‐CO.1.1
Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
MAFS.912. G‐CO.3.11
Prove theorems about parallelograms; use theorems about parallelograms to solve problems.
MAFS.912. G‐CO.4.12
Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
MAFS.912.G‐GPE.2.4
Use coordinates to prove simple geometric theorems algebraically.
MAFS.912.G.GPE.2.5
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
January 9 – January 27
Student Target
Core
Students will ... Math Nation
9.1
9.2
9.3
9.4
9.5
9.6
9.7
10.1
10.2
10.3
10.4
10.5
10.6
10.7
• prove theorems about parallelograms using deductive reasoning
• prove theorems about parallelograms, such as the diagonals of a Introduction to parallelogram bisect each other
Quadrilaterals • create geometric constructions such as copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing Parallelograms perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a Rectangles and point not on the line.
Squares
• identify the appropriate algebraic method to prove or disprove simple geometric theorems given a set of coordinates.
Rhombi
• use slope to determine if lines in a polygon are parallel.
• determine if two lines are parallel by examining their slopes.
Kites
• determine if two lines are perpendicular by examining their slopes.
• use coordinates to compute perimeters of polygons and areas of Trapezoids
triangles and rectangles.
• use the properties of geometric shapes to describe objects.
Mid‐segment of Trapezoids
Quadrilaterals in the Coordinate Plane Parts 1 & 2
Constructions of Quadrilaterals
MAFS.912.G‐GPE.2.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula.
MAFS.912.G‐MG.1.1
Use geometric shapes, their measures, and their properties to describe objects.
FSQ Sections 9 & 10
6 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 11: Properties of N-Gons
2016 - 2017
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
MAFS.912. G‐SRT.2.5
Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
MAFS.912. G‐GPE.2.7
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
MAFS.912.G‐MG.1.1
Use geometric shapes, their measures, and their properties to describe objects.
MAFS.912.G‐MG.1.3
Apply geometric methods to solve design problems.
January 30 – February 10
Student Target
Core
Students will ... Math Nation
11.1
11.2
11.3
11.4
11.5
11.6
11.7
11.8
11.9
• apply the concepts of congruence and similarity criteria to solve problems involving triangles.
• apply the concepts of congruence and similarity criteria to prove Inroduction to N‐
relationships in geometric figures.
gons
• use coordinates to compute perimeters of polygons and areas of triangles and rectangles.
Angles of N‐gons
• use geometric shapes to describe objects Students will explain the relationship between the circumference and area of a circle.
Segments in • use the measures of geometric shapes to describe objects.
Regular N‐gons
• use the properties of geometric shapes to describe objects.
• apply geometric methods to solve design problems.
Area of N‐gons
Coordinate Geometry
FSQ Section 11
7 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 12 & 13: Circles
2016 - 2017
Topic & Suggested
Pacing
Standards
MAFS.912. G‐C.1.2
MAFS.912.G‐C.1.3
MAFS.912.G‐C.2.5
MAFS.912.G‐GPE.1.1
Core
February 13 – February 28
Math Nation
Students will … 12.1
• prove similarity among all circles by demonstrating that the pre 12.2
image of a dilation central to the circle is equal to the image in terms Circumference of a 12.3
of the measure of the central angles.
Identify and describe relationships among inscribed angles, radii, and chords
Circle
12.4
• define central angle, inscribed angle, circumscribed angle, diameter, 12.5
Area of a Circle radius, and chord.
12.6
• explain the relationship between central, inscribed, and 12.7
Sectors of a Circle circumscribed angles
12.8
• explain that inscribed angles on a diameter are right angles
Identify and describe relationships among inscribed angles, radii, and chords
13.1
• explain that the radius of a circle is perpendicular to the tangent Circles in the 13.2
Coordinate Plane where the radius intersects the circle.
13.3
• distinguish between inscribed and circumscribed circles of a triangle.
Circle 13.4
• prove properties of angles for a quadrilateral inscribed in a circle, Transformations such as opposite angles in an inscribed quadrilateral are 13.5
Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral 13.6
supplementary.
Radians and Degrees
inscribed in a circle.
13.7
• explain similarity in terms of similarity transformations where angle 13.8
measure is preserved and side length changes proportionally.
Arcs and Inscribed 13.9
• derive using similarity the fact that the length of the arc intercepted Angles
by an angle is proportional to the radius.
Inscribed Polygons • define the radian measure of the angle as the constant of proportionality. Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and
• derive the formula for the area of a sector.
Constructing define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.
Inscribed Polygons in • derive the equation of a circle of radius (0,0) by applying the a Circle
Pythagorean Theorem to the right angle triangle formed by extending the radius as the hypotenuse from the circle’s center to a point on the Tangent Lines, circle (x, y).
Secants and Chords
• determine the center of a circle given the equation of the circle.
• complete the square to find the center and radius of a circle given by Circumscribed Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find
an equation.
Angles and Beyond
the center and radius of a circle given by an equation.
• use the Pythagorean Theorem to determine if the point (a, b) lies on a circle centered at the origin and containing the point (x, y).
Constructing Mathematics Florida Standards
MAFS.912. G‐C.1.1
Student Target
Inscribed and Circumscribed Circles of Triangles
MAFS.912.G‐GPE.2.4
Use coordinates to prove simple geometric theorems algebraically.
MAFS.912.G‐CO.4.13
Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
USA Sections 9 ‐ 13
8 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 14: Three Dimensional Geometry
2016 - 2017
Topic & Suggested
Pacing
Standards
MAFS.912. G‐GMD.1.1
Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
MAFS.912. G‐GMD.1.3
Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
MAFS.912.G‐GMD.2.4
Identify the shapes of two‐dimensional cross‐sections of three‐dimensional objects, and identify three‐dimensional objects generated by rotations of two‐dimensional objects.
MAFS.912.G‐SRT.1.2
Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar;
explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs
of angles and the proportionality of all corresponding pairs of sides.
Core
Math Nation
14.1
• define the formulas for the circumference of a circle, area of a circle, 14.2
volume of a cylinder, pyramid, and cone.
14.3
Geometry Nets and • explain the relationship between the circumference and area of a 14.4
Three Dimensional circle.
14.5
Figures
• inscribe a polygon to determine its area.
14.6
• calculate the base area for a prism, cylinder, cone, and pyramid.
14.7
Cavalieri’s Principle • determine the volume for a prism, cylinder, cone, and pyramid.
14.8
for Area Cavalieri’s • explain the conceptual relationships among the volume formulas of 14.9
Principle for prisms, cylinders, cones, and pyramids.
14.10
Volume
• use dissection arguments, Cavalieri’s principle, and informal limit arguments.
Volume of Prisms and Cylinders
March 6 – March 31
Mathematics Florida Standards
Student Target
Students will…
Surface Area of Prisms and Cylinders
Volume of Pyramids and Cones
Surface Area of Pyramids and Cones
Spheres
Similar Shapes
Cross Sections and Plane Rotations
FSQ Section 14
9 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 15: Additional Modeling with Geometry
2016 - 2017
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
April 3 – April 10
MAFS.912. G‐MG.1.1
MAFS.912. G‐MG.1.2
MAFS.912.G‐MG.1.3
Student Target
Core
Students will... Math Nation
15.1
15.2
15.3
15.4
15.5
15.6
• use geometric shapes to describe objects Students will explain the relationship between the circumference and area of a circle.
Density
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human • use the measures of geometric shapes to describe objects.
torso as a cylinder).
• use the properties of geometric shapes to describe objects.
Minimizing and • apply concepts of density based on area in modeling situations.
Maximizing
• apply concepts of density based on volume in modeling situations.
• apply geometric methods to solve design problems.
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per Angles of Elevation cubic foot).
and Depression
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)
Topographic Grid System Based on Ratios
Areas in Real‐
World Contexts
Volume in Real‐
World Contexts
USA Sections 14 & 15
10 of 10
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 27, 2016