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2015 – 2016

Honors GeometryThis course offers advanced concepts of plane (Euclidean) geometry through a series of conjectures and formal proofs. Prisms, Pyramids, cylinders, cones and spheres as well as an introduction to applied trigonometry are also included. Much emphasis is placed on the application of algebra skills. This course also covers basic probability concepts not addressed in Geometry.

Course Information:

Frequency & Duration: Daily for 42 minutesText: Pearson Geometry Common Core (2012)

Mathematics: Honors Geometry v. 2015 - 2016

Content: Tools of Geometry Duration: Aug./ Sept. (3 weeks)

Essential Question: What are the building blocks of Geometry?

Skill:

Understand basic terms and postulates of geometry. Find and compare lengths of segments and the measures of angles. Identify special angle pairs and use them to find angle measures. Use a straightedge and compass to make basic constructions. Use distance and midpoint formulas when given 2 points in the coordinate

plane. Find the perimeter, circumference, and/or area of basic shapes.

Assessment:

Use a compass and a straightedge to bisect angle ABC. Using a diagram of a plane, lines, and points, name 3 collinear points, 4

coplanar points, and the intersection of a line and a plane. Find the perimeter of triangle ABC with vertices A(-2,8), B(3,13), and

C(14,2). Find the area of a circle with diameter 9 cm. The intersection of two planes is a point? (True or false?) LJ and TJ are opposite rays. (True or false?)

Resources: Pearson Geometry Common Core: Chapter 1, pages 1-75

Standards:

CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.CC.2.3.8.A.2- Understand and apply congruence, similarity, and geometric transformations using various tools.CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.

Vocabulary:

Angle bisector- is a ray that divides an angle into two congruent angles; Congruent segments- segments that have the same length; Construction- is a geometric figure made with only a straightedge and compass; Linear pair- a pair of adjacent angles whose non-common sides are opposite rays; Perpendicular bisector- is a line, segment, or ray that is perpendicular to the segment at its midpoint; Postulate- is an accepted statement of fact; Supplementary angles- two angles whose sum is 180 degrees; Segment bisector- a line, segment, ray, or plane that intersects a segment at its midpoint; Vertical angles- two angles whose sides form two pairs of opposite rays

Comments:


Content: Reasoning and Proof Duration: September/ October (3 weeks)

Essential Question: How can you make a conjecture and prove that it is true?

Skill:

Use inductive reasoning to make conjectures. Recognize conditional statements. Write converses, inverses, and contrapositives of conditionals. Use deductive reasoning to reach a conclusion. Connect reasoning in Algebra and Geometry. Prove and apply theorems about angles.

Assessment:

Explain the difference between inductive and deductive reasoning. What is a counterexample? Find the next two terms of: -16, 8, -4, 2, … Identify the hypothesis and conclusion of: If x + 9 = 11, then x = 2. The measure of an angle is 52 more than the measure of its complement.

What is the measure of the angle?


Standards:CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.

Vocabulary:

Conditional- is an if-then statement; Conjecture- a conclusion reached by using inductive reasoning; Converse- a statement obtained by reversing the hypothesis and conclusion of a conditional; Co-Theorem- is a conjecture that can be proven; Deductive reasoning- a process of reasoning logically from given facts to a conclusion; Inductive reasoning- a type of reasoning that reaches conclusions based on a pattern of specific examples or past events

Comments:


Content: Parallel and Perpendicular Lines

Duration: October (3 weeks)

Essential Question: How do you prove that two lines are parallel, perpendicular, or neither?

Skill:

Identify relationships between figures in space. Identify angles formed by two lines and a transversal. Prove theorems about parallel lines. Use properties of parallel lines to find angle measures. Use parallel lines to prove a theorem about triangles. Find measures of angles of triangles. Construct parallel and perpendicular lines. Graph and write linear equations. Relate slope to parallel and perpendicular lines.

Assessment:

x and 20 are two angle measures of a triangle. What is the measure of the third angle?

Write the definition and draw a diagram of each: skew lines, parallel lines, and perpendicular lines.

Write an equation of a line that passes through (1, 5) and (3, -13). If the slope of a line is m = 1.5, then the slope of another line that is

perpendicular would be? Draw a diagram of two parallel lines cut by a transversal and then identify a

pair of: alternate interior angles, alternate exterior angles, corresponding angles, and same-side interior angles.


Standards: CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.

Vocabulary:

Parallel lines- lines that lie in the same plane and never intersect; Skew lines- lines that do not lie in the same plane; Transversal- a line that intersects two or more lines at distinct points.

Comments:


Content: Congruent Triangles Duration: November (3 weeks)

Essential Question: How do you prove that two triangles are congruent?

Skill:

Recognize congruent figures and their corresponding parts. Use SSS, SAS, ASA, AAS, or HL to prove that triangles are congruent. Use CPCTC to prove that corresponding parts of congruent triangles are

congruent. Use and apply properties of isosceles and equilateral triangles. Identify congruent overlapping triangles.

Assessment:

What are the 5 tests that we have learned in order to prove that triangles are congruent?

Triangle CEO is congruent to triangle HDF. Name all of the pairs of corresponding congruent parts.

In triangle HFD, what angle is included between DH and DF? When do you use CPCTC?


Standards:

CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.

G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.G.1.2.1.1-Identify and/or use properties of triangles.G.1.2.1.3-Identify and/or use properties of isosceles and equilateral triangles.G.1.3.1-Use properties of congruence, correspondence, and similarity in problem-solving settings involving two- and three-dimensional figures.G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.

Vocabulary:

Base angles of an Isosceles triangle- the angles opposite the legs of an isosceles triangle; Congruent polygons- polygons that have the same size and the same shape; Corollary- a theorem that can be proved easily using another theorem; Hypotenuse- in a right triangle, the side that is opposite the right angle; Vertex angle of an Isosceles triangle- the angle that is opposite the base of an isosceles triangle

Comments:


Content: Relationships Within Triangles

Duration: December (3 weeks)

Essential Question:

How do you solve problems that involve measurements of triangles and how do you use coordinate geometry to find relationships within triangles?

Skill:

Use properties of mid-segments to solve problems. Use properties of perpendicular bisectors and angle bisectors. Identify properties of perpendicular bisectors and angle bisectors. Identify properties of medians and altitudes of a triangle. Use indirect reasoning to write proofs. Use inequalities involving angles and sides of triangles. Apply inequalities in two triangles.

Assessment:

Find the coordinates of the circumcenter of triangle ABC given A(3, -1), B(-2, -1), and C(3, -8).

Find the coordinates of the orthocenter of triangle DEF given D(-1, -1), E(-1, -5), and F(-4, -1).

If AB = 9, BC = 4.5, and AC = 12, list the angles of triangle ABC from smallest to largest.

Describe a centroid of a triangle.


Standards:

CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically

G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.G.1.2.1.1-Identify and/or use properties of triangles.G.1.2.1.3-Identify and/or use properties of isosceles and equilateral triangles.CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.G.1.3.2.1-Write, analyze, complete, or identify formal proofs.G.2.1.2-Solve problems using analytical geometry.G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a two-dimensional shape.G.2.2.1-Use and/or compare measurements of angles.G.2.2.1.2-Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles.


Vocabulary:

Altitude of a triangle- is the perpendicular segment from a vertex to the line containing the side opposite that vertex; Centroid of a triangle- is the point of concurrency of the medians of the triangle; Circumcenter of a triangle- is the point of concurrency of the perpendicular bisectors of the sides of the triangle; Concurrent lines- three or more lines that meet in one point; Distance from a point to a line- the length of the perpendicular segment from the point to the line

Comments:


Content: Polygons and Quadrilaterals Duration: January (3 weeks)

Essential Question:

How can you classify quadrilaterals and how do you find the sum of the measures of polygon angles?

Skill:

Find the sum of the measures of the interior angles of a polygon. Find the sum of the measures of the exterior angles of a polygon. Use relationships among sides and angles of parallelograms. Use relationships among diagonals of parallelograms. Determine whether a quadrilateral is a parallelogram. Define and classify special types of parallelograms. Use properties of diagonals of rhombuses and rectangles. Determine whether a parallelogram is a rhombus or rectangle. Verify and use properties of trapezoids and kites. Classify polygons in the coordinate plane. Name coordinates of special figures by using their properties. Prove theorems using figures in the coordinate plane.

Assessment:

What is the sum of the interior angle measures of a polygon with 17 sides? What is the measure of an exterior angle of a 23-gon? Determine the most precise name of quadrilateral ABCD when given: A(3, -

2), B(5, 4), C(3, 6), and D(1,4) Prove that the diagonals of a square are congruent.


Standards:

CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.

G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.G.1.2.1.2-Identify and/or use properties of quadrilaterals.G.1.2.1.4-Identify and/or use properties of regular polygons.CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.G.1.3.2.1-Write, analyze, complete, or identify formal proofs.G.2.1.2-Solve problems using analytical geometry.G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a two-dimensional shape.


Vocabulary:

Equiangular polygon- polygon with all of its angles congruent; Equilateral polygon- polygon with all of its sides congruent; Isosceles trapezoid- trapezoid with its legs congruent; Kite- quadrilateral with two pairs of consecutive sides congruent; Parallelogram- quadrilateral with opposite sides parallel; Rectangle- parallelogram with four right angles; Regular polygon- polygon that is both equilateral and equiangular; Rhombus- parallelogram with four congruent sides; Square- parallelogram with four right angles and four congruent sides; Trapezoid- quadrilateral with exactly one pair of parallel sides

Comments:


Content: Similarity Duration: February (3 weeks)

Essential Question:

How do you use proportions to find side lengths in similar polygons and how do you show two triangles are similar?

Skill:

Write ratios and solve proportions. Identify and apply similar polygons. Use AA, SAS, and SSS to prove that triangles are similar. Use similarity to find indirect measurements. Find and use relationships in similar right triangles. Use the Side-Splitter Theorem and the Triangle-Angle-Bisector Theorem.

Assessment:

What are similar figures? Find the geometric mean between 5 and 12.

Solve: 4x+2

=169

What three tests prove that triangles are similar?


Standards:

CC.2.3.HS.A.6-Verify and apply theorems involving similarity as they relate to plane figures.CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.CC.2.3.HS.A.14-Apply geometric concepts to model and solve real-world problems.G.1.3.1-Use properties of congruence, correspondence, and similarity in problem-solving settings involving two- and three-dimensional figures.

G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.G.1.3.1.2-Identify and/or use proportional relationships in similar figures.G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.G.1.2.1.1-Identify and/or use properties of triangles.G.1.2.1.2-Identify and/or use properties of quadrilaterals.G.1.2.1.3- Identify and/or use properties of isosceles and equilateral triangles.

Vocabulary:

Extended proportion- when three or more ratios are equal; Extended ratio- compares three or more numbers; Extremes- the first and last numbers in a proportion; Means- the middle numbers in a proportion; Proportion- two ratios that equal each other; Ratio- a comparison of two quantities by division; Scale factor- the ratio of corresponding linear measurements of two similar figures; Similar polygons- polygons with corresponding angles congruent and corresponding sides in proportion

Comments:


Content: Right Triangles and Trigonometry

Duration: March (3 weeks)

Essential Question: How do you find a side length or angle measure in a right triangle?

Skill:

Use the Pythagorean Theorem and its converse. Use properties of special right triangles. Use sine, cosine, and tangent ratios. Use angles of elevation and depression to solve problems. Apply the Law of Sines. Apply the Law of Cosines.

Assessment:

Find the hypotenuse of a right triangle with side lengths 7 and 11. Given triangle side lengths of 5 in., 6 in., and 10 in., identify the triangle as

acute, right, or obtuse. Sin A = ___ What is the mnemonic device that helps us remember the trigonometric

ratios? In triangle KLP, k = 13 mi, l = 10 mi, and p = 8 mi. Find the measure of

angle K to the nearest tenth.


Standards: CC.2.2.HS.C.9-Prove the Pythagorean identity and use it to calculate trigonometric ratios.CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.CC.2.3.8.A.3-Understand and apply the Pythagorean theorem to solve problems.CC.2.3.HS.A.11- Apply coordinate geometry to prove simple geometric theorems algebraically.CC.2.3.HS.A.14- Apply geometric concepts to model and solve real-world problems.

G.1.3.2.1-Write, analyze, complete, or identify formal proofs.G.1.3.2-Write formal proofs and/or use logic statements to construct or validate arguments.G.1.2.1.1-Identify and/or use properties of triangles.G.1.2.1.3- Identify and/or use properties of isosceles and equilateral triangles.G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.CC.2.3.HS.A.7-Apply trigonometric ratios to solve problems involving right triangles.G.2.1.1.1-Use the Pythagorean theorem to write and/or solve problems involving right triangles.


G.2.1.1.2-Use trigonometric ratios to write and/or solve problems involving right triangles.G.2.1.1-Solve problems involving right triangles.G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.G.2.1.2.2-Relate slope to perpendicularity and/or parallelism.G.2.1.2.3-Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a two-dimensional shape.G.2.1.2-Solve problems using analytical geometry.

Vocabulary:

Pythagorean triple- a set of three nonzero whole numbers that satisfy the Pythagorean theorem

Comments:


Content: Transformations Duration: April (3 weeks)

Essential Question:

What are the different types of transformations and how do they change a figures size and/or position?

Skill:

Identify isometries. Find translation images of figures. Find reflection images of figures. Draw and identify rotation images of figures. Find compositions of isometries. Classify isometries. Identify congruence transformations. Understand dilation images of figures. Identify similarity transformations.

Assessment:

Write the translation rule that maps P(-4, 2) to P’(-1, -1). What transformations represent a rigid motion. Is a dilation an isometry? Find the image of A(2,3), B(-4,9), and C(-2,-4) after each transformation:

R x=4 (ABC ) , T←6,8>¿ ( ABC ) ,r ( 90° ,O ) (ABC ), D 3(ABC)¿


Standards: CC.2.3.HS.A.1- Use geometric figures and their properties to represent transformations in the plane.CC.2.3.HS.A.2-Apply rigid transformations to determine and explain congruence.CC.2.3.HS.A.5-Create justifications based on transformations to establish similarity of plane figures.CC.2.3.HS.A.6--Verify and apply theorems involving similarity as they relate to plane figures.CC.2.3.HS.A.3-Verify and apply geometric theorems as they relate to geometric figures.CC.2.3.8.A.2- Understand and apply congruence, similarity, and geometric transformations using various tools.CC.2.3.8.A.2-Understand and apply congruence, similarity, and geometric transformations using various tools.CC.2.2.HS.C.1-Use the concept and notation of functions to interpret and apply them in terms of their context.

G.1.3.1.1-Identify and/or use properties of congruent and similar polygons or solids.G.1.3.1.2-Identify and/or use proportional relationships in similar figures.G.1.3.1-Use properties of congruence, correspondence, and similarity in


problem-solving settings involving two- and three- dimensional figures.G.2.1.2.1-Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.G.2.1.2-Solve problems using analytical geometry.G.2.2.1-Use and/or compare measurements of angles.

Vocabulary:

Dilation- an enlargement or reduction in the size of a figure; Image- is the resulting figure after a transformation takes place; Isometry-a transformation in which an original figure and its image are congruent; Rigid motion- a transformation that preserves distance and angle measure; Transformation- any change made to a figures size, shape, and/or position; Translation- is a slide of a geometric figure

Comments:


Content: Area Duration: April (2 weeks)

Essential Question:

How do you find the area of a polygon or find the circumference and area of a circle?

Skill:

Find the area of parallelograms, triangles, trapezoids, rhombuses, kites, and regular polygons.

Find the perimeters and areas of similar polygons. Find areas of regular polygons and triangles using trigonometry. Find the measures of central angles and arcs. Find the circumference and arc length. Find the areas of circles, sectors, and segments of circles. Use segment and area models to find the probabilities of events.

Assessment:

What is the area of a right triangle with side lengths of 5, 12, and 13? What is the area of a trapezoid with height 11 inches and bases 20 inches

and 14 inches? What is the area of a regular hexagon with a perimeter of 240cm? If the ratio of the areas of two similar hexagons is 8:25, what is the ratio of

their perimeters? A circle has a radius of 20 cm. What is the area of the smaller segment of

the circle formed by a 60 degree arc?


Standards: CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.CC.2.3.HS.A.9-Extend the concept of similarity to determine arc lengths and areas of sectors of circles.CC.2.3.HS.A.13-Analyze relationships between two-dimensional and three-dimensional objects.CC.2.3.HS.A.3--Verify and apply geometric theorems as they relate to geometric figures.

G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.G.1.2.1-Recognize and/or apply properties of angles, polygons, and polyhedra.G.2.2.2.1-Estimate area, perimeter, or circumference of an irregular figure.G.2.2.2.2-Find the measurement of a missing length, given the perimeter, circumference, or area.G.2.2.2.5-Find the area of a sector of a circle.G.2.2.2-Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area.G.2.2.3.1-Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area.G.2.2.3-Describe how a change in one dimension of a two-dimension figure


affects other measurements of that figure.G.2.2.4.1-Use area models to find probabilities.G.2.2.4-Apply probability to practical situations.G.1.1.1.3G.1.1.1

Vocabulary:

Adjacent arcs- are arcs of the same circle that have one point in common; Apothem-is the perpendicular distance from the center to a side of a regular polygon; Arc length-is a fraction of the circumference; Central angle-an angle whose vertex is at the center of a circle; Circumference-the distance around a circle; Concentric circles-coplanar circles that have the same center; Diameter-a segment that contains the center of a circle and has its endpoints on the circle; Major arc-an arc that measures greater than 180 degrees but less than 360 degrees; Minor arc-an arc that measures greater than zero degrees but less than 180 degrees; Radius-a segment from the center of a circle to a point on the circle; Sector of a circle-a region bounded by an arc of the circle and the two radii to the arc’s endpoints; Segment of a circle-a part of a circle bounded by an arc and the segment joining its endpoints.

Comments:


Content: Surface Area and Volume Duration: May (2 weeks)

Essential Question:

How do you find the surface area and volume of a solid and how do the surface areas and volumes of similar solids compare?

Skill:

Recognize polyhedral and their parts. Visualize cross sections of space figures. Find the surface area of a prism, a cylinder, a pyramid, and a cone. Find the volume of a prism, a cylinder, a cone, and a pyramid. Find the surface area and volume of a sphere. Compare and find the areas and volumes of similar solids.

Assessment:

What is the number of edges in a pyramid with seven faces? Describe the cross section formed in each diagram. Find the surface area and volume of each:

Sphere with radius 4 feet, square pyramid with slant height 9 in and base 8 in, cylinder with radius 3 cm and height 8 cm


Standards: CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.CC.2.3.HS.A.13-Analyze relationships between two-dimensional and three-dimensional objects.CC.2.3.HS.A.9-Extend the concept of similarity to determine arc lengths and areas of sectors of circles.CC.2.3.8.A.1-Apply the concepts of volume of cylinders, cones, and spheres to solve real-world and mathematical problems.CC.2.3.HS.A.12-Explain volume formulas and use them to solve problems.

G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.G.1.1.1.4-Identify and/or use the properties of a sphere or cylinder.G.1.1.1-Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.G.1.2.1.5-Identify and/or use properties of pyramids and prisms.G.2.2.2-Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area.G.2.3.1.1-Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres.G.2.3.1.2-Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres.


G.2.3.1.3-Find the measurement of a missing length given the surface area or volume.G.2.3.1-Use and/or develop procedures to determine or describe measures of surface area and/or volume.G.2.3.2.1-Describe how a change in the linear dimension of a figure affects its surface area or volume.G.2.3.2-Describe how a change in one dimension of a three-dimensional figure affects other measurements of that figure.

Vocabulary:

Cross section-is the intersection of a solid and a plane; Cylinder-a solid that has two congruent parallel bases that are circles; Edge-is a segment that is formed by the intersection of two faces; Polyhedron-is a space figure whose surfaces are polygons; Prism-a polyhedron with two congruent parallel faces, called bases; Pyramid-is a polyhedron in which one face (the base) can be any polygon and the other faces are triangles that meet at a common vertex; Surface area-the sum of the area of all the surfaces of a 3 dimensional figure; Volume-is the space that a figure occupies.

Comments:


Content: Circles Duration: May (2 weeks)

Essential Question:

How do you find the equation of a circle in the coordinate plane and how can you prove relationships between angles and arcs in a circle?

Skill:

Use properties of a tangent to a circle. Use congruent chords, arcs, and central angles. Use perpendicular bisectors to chords. Find the measure of an inscribed angle. Find the measure of an angle formed by a tangent and a chord. Find measures of angles formed by chords, secants, and tangents. Find the lengths of segments associated with circles. Write the equation of a circle. Find the center and radius of a circle. Draw and describe a locus.

Assessment:

Graph: ( x+3 )2+( y−2 )2=9 Write an equation of the circle with center (3, 0) that passes through point

(-2, -4). Write an equation for the locus of points in the coordinate plane that are 4

units from (-5, 2). What is the difference between a tangent and secant of a circle?


Standards:

CC.2.3.HS.A.8-Apply geometric theorems to verify properties of circles.

G.1.1.1.1-Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.G.1.1.1.2-Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.G.1.1.1.3-Use chords, tangents, and secants to find missing arc measures or missing segment measures.G.1.1.1--Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.

Vocabulary:

Chord-a segment with both of its endpoints on a circle; Inscribed angle-an angle whose vertex is on the circle and whose sides are chords of the circle ; Point of tangency-the point where a tangent and a circle intersect; Secant-is a line that intersects a circle at two points; Tangent to a circle-is a line in the plane of a circle that intersects the circle in exactly one point.

Comments:


Content: Probability Duration: May/June(2 weeks)

Essential Question:

What is the difference between experimental probability and theoretical probability and what is a frequency table?

Skill:

Calculate experimental and theoretical probability. Make and use frequency tables and probability distributions. Use permutations and combinations to solve problems. Identify independent and dependent events. Find compound probabilities. Construct and use probability models. Understand and calculate conditional probabilities. Understand random numbers. Use probabilities in decision-making.

Assessment:

P(odd number when you select a number from 1 to 10 at random) P(1 or 4 when you select a number from 1 to 10 at random) P(a number greater than 10 when you select a number from 1 to 10 at

random) Is playing a stringed instrument and playing a percussion instrument

independent or dependent events.


Standards:G.2.2.4-Apply probability to practical situations.G.2.2.4.1-Use area models to find probabilities.CC.2.3.HS.A.14-Apply geometric concepts to model and solve real-world problems.

Vocabulary:

Combination- is a selection of items in which order is not important.; Complement of an event-consists of all of the possible outcomes in the sample space that are not part of the event.; Conditional probability-the probability that an event will occur, given that another event has already occurred; Dependent events-when the occurrence of an event does affect how another event occurs; Event-may be a single outcome or a group of outcomes; Experimental probability-measures the likelihood that the event occurs based on the actual results of an experiment; Outcome-is the possible result of a situation or experiment; Probability-is a numerical value from 0 to 1 that measures the likelihood of an event when the outcomes in a sample space are equally likely to occur; Theoretical probability-describes the likelihood of an event based on mathematical reasoning.


Comments:

consensus map grade level - · web viewhow do you prove that two lines are parallel,...

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