Download The School District of Palm Beach County GEOMETRY REGULAR

The School District of Palm Beach County
GEOMETRY REGULAR
Sections 1 & 2: Introduction to Geometry, Transformations, & Constructions
2016 - 2017
Standards
Mathematics Florida Standards
MAFS.912.G-CO.1.1
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MAFS.912.G-CO.1.2
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MAFS.912.G-CO.1.4
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MAFS.912.G-CO.1.5
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MAFS.912.G-CO.4.12
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MAFS.912.G-GPE.2.5
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MAFS.912.G-GPE.2.6
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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.
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).
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel
lines, and line segments.
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.
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).
Topic & Suggested
Student Target
Core
Pacing
August 16 Math Nation
Students will …
August 30
1.1
• defining and representing points, lines, line segments, planes, rays,
1.2
and angles, as the building blocks of Geometry.
Basics of
1.3
• defining and representing points, lines, line segments, planes, rays,
Geometry
1.4
and angles, as the building blocks of Geometry.
1.5
• midpoint and distance, and applications on a coordinate plane by
Midpoint and either finding midpoint coordinates, endpoint coordinates or length
1.6
Distance in the of segments.
1.7
Coordinate Plane • use the commutative and associative properties to identify
1.8
2.1
equivalent expressions. Students will determine which properties
Partitioning a Line (distribute, associative, and commutative) have been used when
2.2
Segment
2.3
writing equivalent expressions.
2.4
• finding the point on a directed line segment between two given
Parallel and
2.5
points that partitions the segment in a given ratio.
Perpendicular • finding the point on a directed line segment between two given
2.6
Lines
2.7
points that partitions the segment in a given ratio.
2.8
• identifying parallel and perpendicular lines, and writing equations
Introduction to of lines parallel or perpendicular to another line.
Transformations • introducing rigid and non-rigid transformations, translation,
reflection, rotation, and dilation.
Examining and • performing translations of points and line segments on a
Using Translations coordinate plane.
• performing dilations of points and line segments on a coordinate
Examining and plane.
Using Dilations • performing dilations of points and line segments on a coordinate
plane.
Examining and • performing rotation of points and line segments on a coordinate
Using Rotations plane.
• performing reflection of points and line segments on a coordinate
Examining and plane.
Using Reflections • constructions of line segments.
Basic
Constructions
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Geo_S1-2_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 3: Angles
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.
August 31 September 16
Introduction to
Angles
Angle Pairs
MAFS.912. G-CO.1.2
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.
MAFS.912. G-CO.1.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel
lines, and line segments.
Special Types of
Angle Pairs
Formed by
Transversals and
Non-Parallel Lines
Angle Pairs
Formed by
Transversals and
Parallel Lines
Student Target
Core
Students will ...
Math Nation
3.1
• use the precise definitions of angles, circles, perpendicular lines,
3.2
parallel lines, and line segments, basing the definitions on the
3.3
undefined notions of point, line, distance along a line, and distance
3.4
around a circular arc.
3.5
• represent transformations in the plane.
3.6
• describe transformations as functions that take points in the plane
3.7
as inputs and give other points as outputs.
3.8
• compare transformations that preserve distance and angle to
3.9
those that do not.
3.10
• use definitions of rotations, reflections, and translations in terms
of angles, circles, perpendicular lines, parallel lines, and line
segments.
• prove theorems about lines.
• prove theorems about angles.
• use theorems about lines to solve problems.
• use theorems about angles to solve problems.
• identify the result of a formal geometric construction.
• determine the steps of a formal geometric construction.
Perpendicular
Transversals
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.
Angle-Preserving
Transformations
Parallel Lines and
Transversals
Constructions
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.
Geo_S3_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 4 & 5: Introduction to Polygons
2016 - 2017
Topic & Suggested
Pacing
Standards
Student Target
Core
September 19 Students will …
Math Nation
October 17
4.1
• distinguish between a rectangle, parallelogram, trapezoid, or
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
4.2
regular polygon.
Introduction to • describe the rotations and reflections a rectangle, parallelogram,
4.3
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or
Polygons
4.4
trapezoid, or regular polygon carries onto itself.
geometry software. Specify a sequence of transformations that will carry a given figure onto another.
4.5
• apply two or more transformations to a given figure to draw a
Angles of Polygons transformed figure.
4.6
4.7
• specify a sequence of transformations that will carry a figure onto
Translation of another.
4.8
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
Polygons
5.1
figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
• provide descriptions of rigid motions and explain how each
5.2
preserves distance and angle.
Reflection of
5.3
• be able to predict the effect of a given rigid motion on a given
Polygons
5.4
figure.
5.5
• prove theorems about triangles using deductive reasoning (such as
Rotation of
Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of interior angles of a triangle
the law of syllogism).
sum to 180°; triangle inequality theorem; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a
Polygons
• prove a theorem about triangles such as measures of interior
triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
angles of a triangle sum to 180°.
Dilation of
• use geometric shapes to describe objects.
Polygons
• use the measures of geometric shapes to describe objects.
• use the properties of geometric shapes to describe objects.
Compositions of • explain the properties of dilations given by a center and a scale
Transformations factor.
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
of Polygons
• perform dilations given by a center and a scale factor on figures in
a plane.
Symmetries of • verify that a dilation takes a line not passing through the center of
Regular Polygons the dilation to a parallel line, and leaves a line passing through the
center unchanged.
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. Congruence and • verify that the dilation of a line segment is longer or shorter in the
Similarity of
b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
ratio given by the scale factor.
Polygons
• explain similarity in terms of similarity transformations where
angle measure is preserved and side length changes proportionally.
• determine if two figures are similar, including triangles.
Mathematics Florida Standards
MAFS.912. G-CO.1.3
MAFS.912. G-CO.1.5
MAFS.912.G-CO.2.6
MAFS.912. G-CO.3.10
MAFS.912.G-MG.1.1
MAFS.912. G-SRT.1.1
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.
Geo_S1-5_USA
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 6 & 7: Triangles
2016 - 2017
Topic & Suggested
Pacing
Standards
MAFS.912.G-CO.1.2
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MAFS.912.G-CO.1.5
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MAFS.912.G-CO.2.6
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Student Target
Core
Students will…
Mathematics Florida Standards
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).
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.
October 24 November 10
Introduction to
Triangles
Area and
Perimeter on the
Coordinate Plane
Triangle
Congruence – SSS
and SAS
Triangle
Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a Congruence – ASA
given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are
and AAS
congruent.
Using Triangle
Congruency to
Find Missing
Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if
Variables
corresponding pairs of sides and corresponding pairs of angles are congruent.
MAFS.912.G-CO.2.7
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Triangle Similarity
Math Nation
6.1
• distinguish between inscribed and circumscribed circles of a
6.2
triangle.
6.3
• prove properties of angles for a quadrilateral inscribed in a circle,
6.4
such as opposite angles in an inscribed quadrilateral are
6.5
supplementary.
6.6
• recognize triangle congruence (ASA, SAS, SSS) in terms of rigid
6.7
motions that preserve distance (S) and angle (A).
6.8
• show how preserving correlating distances (S) and angles (A)
6.9
between two triangles results in congruence.
7.1
• prove theorems about triangles using deductive reasoning (such as
7.2
the law of syllogism).
7.3
• prove a theorem about triangles such as measures of interior
7.4
angles of a triangle sum to 180°.
7.5
• use coordinates to compute perimeters of polygons and areas of
7.6
triangles and rectangles.
7.7
• explain similarity in terms of similarity transformations where
angle measure is preserved and side length changes proportionally.
• determine if two figures are similar, including triangles.
• Students can explain why, if two angle measures are known, the
third angle is also known using the properties of similarity
transformations.
• apply the concepts of congruence and similarity criteria to solve
problems involving triangles.
• apply the concepts of congruence and similarity criteria to prove
relationships in geometric figures.
Triangle MidSegment Theorem
MAFS.912.G-CO.2.8
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Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse Leg) follow from the definition of
congruence in terms of rigid motions.
Triangle
Inequalities
Triangle Proofs
MAFS.912.G-CO.3.10
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Prove theorems about triangles; use theorems about triangles to solve problems. Theorems include: measures of
interior angles of a triangle sum to 180°; triangle inequaliy theorem; 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.
Triangle
Constructions
Geo_S6-7_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 8: Right Triangles
2016 - 2017
Topic & Suggested
Pacing
Standards
November 14 –
November 22
Explain how the criteria for triangle congruence (ASA, SAS, SSS, and Hypotenuse-Leg) follow from the definition of congruence in terms of rigid
motions.
The Pythagorean
Theorem
The Converse of
the Pythagorean
Theorem
MAFS.912. G-GPE.2.4
Use coordinates to prove simple geometric theorems algebraically.
Right Triangle
Congruency
MAFS.912.G-GPE.2.7
Core
Students will...
Mathematics Florida Standards
MAFS.912. G-CO.2.8
Student Target
Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
Special Right
Triangles 45-45-90
Special Right
Triangles 30-60-90
MAFS.912.G.SRT.2.4
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.
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-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.
Right Triangle
Similarity
Introduction to
Trigonometry
• recognize triangle congruence (ASA, SAS, SSS) in terms of rigid
motions that preserve distance (S) and angle (A).
• show how preserving correlating distances (S) and angles (A)
between two triangles results in congruence.
• 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).
• use coordinates to compute perimeters of polygons and areas of
triangles and rectangles.
• prove theorems about triangles, such as a line parallel to one side
of a triangle divides the other two proportionally, and conversely.
• prove theorems about triangles, such as using triangle similarity to
prove the Pythagorean Theorem.
• apply the concepts of congruence and similarity criteria to solve
problems involving triangles.
• apply the concepts of congruence and similarity criteria to prove
relationships in geometric figures.
• explain by angle-angle similarity of two right triangles that side
ratios are properties of the angles in the triangle.
• use similarity to define trigonometric ratios (tangent, sine, and
cosine) for acute angles in right triangles.
• determine cosine and sine rations for acute angles in right triangles
given the lengths of two sides.
• explain the relationship between sine and cosine of
complementary 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 trigonometric ratios and the Pythagorean Theorem to solve
real-world application problems.
Math Nation
8.1
8.2
8.3
8.4
8.5
8.6
8.7
8.8
8.9
Geo_S6-8_USA
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 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.3.11
January 9 –
January 27
Prove theorems about parallelograms; use theorems about parallelograms to solve problems.
Introduction to
Quadrilaterals
Parallelograms
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.).
Rectangles and
Squares
Rhombi
Kites
MAFS.912.G-GPE.2.4
Use coordinates to prove simple geometric theorems algebraically.
Trapezoids
MAFS.912.G.GPE.2.5
Student Target
Core
Students will ...
Math Nation
9.1
• prove theorems about parallelograms using deductive reasoning
9.2
• prove theorems about parallelograms, such as the diagonals of a
9.3
parallelogram bisect each other
9.4
• create geometric constructions such as copying a segment; copying
9.5
an angle; bisecting a segment; bisecting an angle; constructing
9.6
perpendicular lines, including the perpendicular bisector of a line
9.7
segment; and constructing a line parallel to a given line through a
10.1
point not on the line.
10.2
• identify the appropriate algebraic method to prove or disprove
10.3
simple geometric theorems given a set of coordinates.
10.4
• use slope to determine if lines in a polygon are parallel.
10.5
• determine if two lines are parallel by examining their slopes.
10.6
• determine if two lines are perpendicular by examining their slopes.
10.7
• use coordinates to compute perimeters of polygons and areas of
10.8
triangles and rectangles.
• use the properties of geometric shapes to describe objects.
Mid-segment of
Trapezoids
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
Quadrilaterals in
the Coordinate
Plane Parts 1 & 2
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.
Constructions of
Quadrilaterals
MAFS.912.G-MG.1.1
Use geometric shapes, their measures, and their properties to describe objects.
Geo_S9-10_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 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.
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
Segments in
Regular N-gons
Area of N-gons
Coordinate
Geometry
Geo_S11_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Sections 12 & 13: Circles
2016 - 2017
Topic & Suggested
Pacing
Standards
Mathematics Florida Standards
February 13 –
February 28
MAFS.912. G-C.1.1
Identify and describe relationships among inscribed angles, radii, and chords
Circumference of a
Circle
Area of a Circle
MAFS.912. G-C.1.2
Identify and describe relationships among inscribed angles, radii, and chords
Circles in the
Coordinate Plane
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.
Circle
Transformations
Radians and
Degrees
Arcs and Inscribed
Angles
MAFS.912.G-C.2.5
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.
Inscribed Polygons
Tangent Lines,
Secants and
Chords
MAFS.912.G-GPE.1.1
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.
MAFS.912.G-GPE.2.4
Use coordinates to prove simple geometric theorems algebraically.
Circumscribed
Angles and
Beyond
Student Target
Core
Students will …
Math Nation
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
12.3
of the measure of the central angles.
12.4
• define central angle, inscribed angle, circumscribed angle,
12.5
diameter, radius, and chord.
12.6
• explain the relationship between central, inscribed, and
12.7
circumscribed angles
13.1
• explain that inscribed angles on a diameter are right angles
13.2
• explain that the radius of a circle is perpendicular to the tangent
13.3
where the radius intersects the circle.
13.4
• distinguish between inscribed and circumscribed circles of a
13.5
triangle.
13.6
• prove properties of angles for a quadrilateral inscribed in a circle,
13.7
such as opposite angles in an inscribed quadrilateral are
13.8
supplementary.
13.9
• explain similarity in terms of similarity transformations where angle
measure is preserved and side length changes proportionally.
• derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius.
• define the radian measure of the angle as the constant of
proportionality.
• derive the formula for the area of a sector.
• derive the equation of a circle of radius (0,0) by applying the
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 circle (x, y).
• 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 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).
Geo_S9-13_USA
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016
The School District of Palm Beach County
GEOMETRY REGULAR
Section 14: Three Dimensional Geometry
2016 - 2017
Standards
Topic & Suggested
Pacing
Mathematics Florida Standards
March 6 – March
31
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
MAFS.912.G-SRT.1.2
Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by
rotations of two-dimensional objects.
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.
Student Target
Core
Students will…
Math Nation
14.1
• define the formulas for the circumference of a circle, area of a
14.2
circle, volume of a cylinder, pyramid, and cone.
Geometry Nets
14.3
• explain the relationship between the circumference and area of a
and Three
14.4
circle.
Dimensional
14.5
• inscribe a polygon to determine its area.
Figures
14.6
• calculate the base area for a prism, cylinder, cone, and pyramid.
14.7
• determine the volume for a prism, cylinder, cone, and pyramid.
Cavalieri’s
14.8
• explain the conceptual relationships among the volume formulas of
Principle for Area
14.9
prisms, cylinders, cones, and pyramids.
Cavalieri’s
14.10
• use dissection arguments, Cavalieri’s principle, and informal limit
Principle for
arguments.
Volume
Volume of Prisms
and Cylinders
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
Geo_S14_FSQ1
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 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
Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
Density
Minimizing and
Maximizing
MAFS.912. G-MG.1.2
MAFS.912.G-MG.1.3
Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).
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)
Angles of
Elevation and
Depression
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.
• use the measures of geometric shapes to describe objects.
• use the properties of geometric shapes to describe objects.
• apply concepts of density based on area in modeling situations.
• apply concepts of density based on volume in modeling situations.
• apply geometric methods to solve design problems.
Topographic Grid
System Based on
Ratios
Areas in RealWorld Contexts
Volume in RealWorld Contexts
Geo_S14-15_USA
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Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education
July 7, 2016