Download CC tentative lesson plans for 2016

**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week ½: (August 3-5) Basic Skills Review
The students will:
8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x3 = p,
where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small
perfect cubes. Know that √2 is irrational.
8.EE.7 Solve linear equations in one variable.
a. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions.
Show which of these possibilities is the case by successively transforming the given equation into simpler forms,
until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).
8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function
is the set of ordered pairs consisting of an input and the corresponding output.
8.G.1 Verify experimentally the properties of rotations, reflections, and translations:
8.G.3 Describe the effects of dilations, translations, rotations, and reflections on two-dimensional figures using
coordinates.
8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and
mathematical problems in two and three dimensions.
8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.
Unit Zero
Algebraic Review
• Graphing on the Coordinate Plane*
• Solving Algebraic Equations*
• Linear Functions*
• Radicals*
• Basic Geometric Figures*
Objectives
The students will be able to…
• plot and identify points in the coordinate plane.
• solve various algebraic equations in one variable.
• graph linear functions.
• use various forms of linear equations.
• perform operations on radicals.
• demonstrate a basic understanding of geometric
figures.
Teacher Resources
• Mathematics Pre-test
Essential Question
How are the concepts of algebra related to the study
of geometry?
Media Resources
Kuta Software Pre-Algebra Worksheet/Test
Generator
Kuta Software Algebra 1 Worksheet/Test Generator
Kuta Software Geometry Worksheet/Test Generator
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 1: (August 8-12) TOOLS OF GEOMETRY
The students will:
G-CO.A.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.
G-CO.D.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.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle.
G-CO.C.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.
Module One
Geometric Constructions
8/5/16: Construct an Equilateral Triangle
8/8/16: Copy and Bisect an Angle, Construct a Perpendicular Bisector
8/9/16: Points of Concurrencies, Solve for Unknown Angles—Angles and Lines at a Point
8/10/16: Solve for Unknown Angles—Transversals, Solve for Unknown Angles—Angles in a
Triangle
8/11/16: Unknown Angle Proofs—Writing Proofs, Unknown Angle Proofs—Proofs with
Constructions
8/12/16: Unknown Angle Proofs—Proofs of Known Facts, Transformations—The Next Level
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 2: (August 15-19)
The students will:
G-CO.A.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.A.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the
rotations and reflections that carry it onto itself.
G-CO.A.4 Develop definitions of rotations, reflections, and translations in terms of angles,
circles, perpendicular lines, parallel lines, and line segments.
G-CO.A.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.
G-CO.B.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.
G-CO.B.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.D.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.
Unit Two
8/15/16: Rotations, Reflections
8/16/16: Rotations, Reflections, and Symmetry, Translations
8/17/16: Characterize Points on a Perpendicular Bisector, Looking More Carefully at Parallel
Lines
8/18/16: Construct and Apply a Sequence of Rigid Motions, Applications of Congruence in
Terms of Rigid Motions
8/19/16: Correspondence and Transformations
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 3: (August 22-26)
The students will:
G-CO.B.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.B.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS)
follow from the definition of congruence in terms of rigid motions.
Module One
8/22/16: Mid-Module Review
8/23/16: Mid-Module Assessment
8/24/16: Congruence Criteria for Triangles—SAS,
Base Angles of Isosceles Triangles
8/25/16: Congruence Criteria for Triangles—ASA and SSS, Congruence Criteria for
Triangles—AAS and HL
8/26/16: Triangle Congruency Proofs
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 4: (August 31-Sept 4)
The students will:
G-CO.C.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.
G-CO.C.10 Prove theorems about triangles. Theorems include: measures of interior angles of
a triangle sum to 180°; 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.
G-CO.C.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.
G-CO.D.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a
circle. 2
Unit Three
8/29/16: Properties of Parallelograms
8/30/16: Special Lines in Triangles
8/31/16: Construct a Square and a Nine-Point Circle, Construct a Nine-Point Circle
9/1/16: Review/Remediation
9/2/16: Review/Remediation
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 5: (September 5-9) LABOR DAY HOLIDAY (9/5)
The students will:
G-SRT.A.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.B.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-MG.A.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)
9/5/16: LABOR DAY
9/6/16: Module 1 Review
9/7/16: Module 1 Test
9/8/16:
Scale Drawings; Making Scale Drawings Using the Ratio Method
Making Scale Drawings Using the Parallel Method; Comparing the Ratio Method with
the Parallel Method
9/9/16:
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 6 (September 12-16)
The students will:
G-SRT.A.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.B.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.A.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.
9/12/16: Scale Factors; Dilations as Transformations of the Plane;
9/13/16: How Do Dilations Map Segments?; How Do Dilations Map Lines, Rays, and
Circles?;
9/14/16: How Do Dilations Map Angles?; Dividing the King’s Foot into 12 Equal Pieces
9/15/16: Dilations from Different Centers; What Are Similarity Transformations, and Why
Do We Need Them?
9/16/16: Properties of Similarity Transformations; Similarity
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 7: (September 19-23)
The students will:
G-SRT.A.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.A.3 Use the properties of similarity transformations to establish the AA criterion for
two triangles to be similar.
G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and prove
relationships in geometric figures.
G-MG.A.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).
9/19/16: The Angle-Angle (AA) Criterion for Two Triangles to Be Similar; Between-Figure
and Within-Figure Ratios
9/20/16: The Side-Angle-Side (SAS) and Side-Side-Side (SSS) Criteria for Two Triangles to
Be Similar; Similarity and the Angle Bisector Theorem
9/21/16: Families of Parallel Lines and the Circumference of the Earth; How Far Away Is the
Moon?
9/22/16: Review
9/23/16: Mid-Module Assessment
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 8: (September 26-30)
The students will:
G-SRT.B.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.C.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.C.7 Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
9/26/16: Special Relationships Within Right Triangles—Dividing into Two Similar SubTriangles; Multiplying and Dividing Expressions with Radicals
9/27/16: Adding and Subtracting Expressions with Radicals; Proving the Pythagorean
Theorem Using Similarity
9/28/16: Incredibly Useful Ratios; The Definition of Sine, Cosine, and Tangent
9/29/16: Sine and Cosine of Complementary Angles and Special Angles; Solving Problems
Using Sine and Cosine
9/30/16: Applying Tangents; Trigonometry and the Pythagorean Theorem
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 9: (October 3-7)
The students will:
G-SRT.C.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.C.7 Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
10/3/16: Teacher Workday
10/4/16: 9 weeks Test Review
10/5/16: Exam
10/6/16: Exam
10/7/16: Review
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 10: (October 12-16) POLYGONS & QUADRILATERALS
The students will:
G-SRT.C.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.C.7 Explain and use the relationship between the sine and cosine of complementary
angles.
G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in
applied problems.
10/10/16: FALL HOLIDAY
10/11/16: Using Trigonometry to Determine Area; Using Trigonometry to Find Side Lengths
of an Acute Triangle
10/12/16: Applying the Laws of Sines and Cosines; Unknown Angles
10/13/16: End of Module Review
10/14/16: End of Module Test
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 11: (October 17-21)
The students will:
G-GMD.A.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.
G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G-GMD.B.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
G-MG.A.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).
G-MG.A.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.A.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).
10/17/16: What is Area?; Properties of Area
10/18/16: The Scaling Principle for Area; Proving the Area of a Disk
10/19/16: Three-Dimensional Space; General Prisms and Cylinders and Their Cross-Sections
10/20/16: General Pyramids and Cones and Their Cross-Sections; Definition and Properties of Volume
10/21/16: Scaling Principle for Volumes; The Volume of Prisms and Cylinders and Cavalieri’s Principle
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 12: (October 24-28)
The students will:
G-GMD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula.
10/24/16: The Volume Formula of a Pyramid and Cone; The Volume Formula of a Sphere
10/25/16: How Do 3D Printers Work?
10/26/16: End of Module Review:
10/27/16: End of Module Assessment
10/28/16: Searching a Region in the Plane; Finding Systems of Inequalities That Describe Triangular and Rectangular Regions
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 13: (October 31 to November 4)
The students will:
G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula
G-GPE.B.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.B.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).
G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula.
10/31/16: Lines That Pass Through Regions; Designing a Search Robot to Find a Beacon
11/1/16: Criterion for Perpendicularity; Segments That Meet at Right Angles
11/2/16: Equations for Lines Using Normal Segments; Parallel and Perpendicular Lines
11/3/16: Perimeter and Area of Triangles in the Cartesian Plane
11/4/16: Mid-Module Assessment
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 14 (November 7-11)
The students will:
G-GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance
formula.
G-GPE.B.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.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
11/7/16: Perimeter and Area of Polygonal Regions in the Cartesian Plane; Perimeters and Areas of Polygonal Regions
Defined by Systems of Inequalities
11/8/16: Dividing Segments Proportionately; Analytic Proofs of Theorems Previously Proved by Synthetic Means
11/9/16: Motion Along a Line—Search Robots Again; The Distance from a Point to a Line
11/10/16: End of Module Review
11/11/16: End of Module Assessment
.
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 15 (November 14- 18)
The students will:
G-C.A.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.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
G-C.A.1 Prove that all circles are similar.
G-C.B.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.
11/14/16: Thales’ Theorem; Circles, Chords, Diameters, and Their Relationships
11/15/16: Rectangles Inscribed in Circles; Experiments with Inscribed Angles
11/16/16: Inscribed Angle Theorem and Its Applications; Unknown Angle Problems with Inscribed Angles in Circles
11/17/16: The Angle Measure of an Arc; Arcs and Chords
11/18/16: Arc Length and Areas of Sectors; Unknown Length and Area Problems
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 16: (November 28 – December 2)
The students will:
G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords.
G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
11/28/16- Mid-Module Review
11/29/16- Mid-Module Assessment
11/30/16 Properties of Tangents; Tangent Segments
12/1/16- The Inscribed Angle Alternate—A Tangent Angle; Secant Lines; Secant Lines That Meet
Inside a Circle
12/2/16- Secant Angle Theorem, Exterior Case; Similar Triangles in Circle-Secant (or Circle-SecantTangent) Diagrams
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 17: (December 5-9)
The students will:
G-GPE.A.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.A.4 Use coordinates to prove simple geometric theorems algebraically.
G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral
inscribed in a circle.
12/5/16: Writing the Equation for a Circle, Recognizing Equations of Circles
12/6/16: Equations for Tangent Lines for Circles, Cyclic Quadrilaterals
12/7/16: Ptolemny’s Theorem
12/8/16: End of Module Review
12/9/16: End of Module Assessment
**DATES AND OBJECTIVES SUBJECT TO CHANGE BASED ON STUDENT NEED**
Week 18: (December 12-16)
12/12/16: Review
12/13/16: Review
12/14/16: Review
12/15/16: Exams
12/16/16: Exams