Grade Level: Honors GeometryChapter #1: The Tools of Geometry

Key Learning(s): Students will learn the basic geometry terms and there use for continuing geometry.

Unit Essential Question(s): Why is it important to learn the basic geometry terms and concepts before continuing the course?

Concept:Points, Lines & Planes

(1.1 – 1 day)

Concept:Segment Measure(1.2, 1.3 – 3 days)

Concept:Angle Measure(1.4 – 2 days)

Lesson EQ’s: What are the basic terms and their importance to Geometry?

Lesson EQ’s:How are the lengths of segments used in everyday life?

Lesson EQ’s:Why do we need to understand and use angles in Geometry?

Vocabulary:Point, line, plane, collinear, coplanar, space

Vocabulary:Line segment, segment addition postulate, between, congruent, precision, constructions, midpoint, segment bisector, distance

Vocabulary:Degree, vertex, ray, opposite ray, angles, sides, interior, exterior, acute angle, obtuse angle, right angle

Standards: Standards:M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane G.2.1.2.1 Calculate the distance and/or midpoint between two points on a number line or on a coordinate planeCC2.3HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.

Standards:M11.B.2.1.1 Measure and/or compare angles in degrees (up to 360) (protractor must be provided or drawn).

Concept:Angle Pairs(1.5 – 1 day)

Lesson EQ’s: How are the pairs of angles classified?Vocabulary:Vertical angles, linear angles, adjacent angles, complementary angles, supplementary anglesStandards:M11.B.2.1.1 Measure and/or compare angles in degrees (up to 360) (protractor

Honors Geometry Learning Map (updated 3/13)

Optional Instructional ToolsRuler, protractor, graph/number

line paper

must be provided or drawn).

Grade Level: Honors GeometryChapter #2: Reasoning and Proofs

Key Learning(s): inductive reasoning, paragraph proofs, two-column algebraic and geometric proofs

Unit Essential Question(s): What strategies can we use to base conclusions in geometry and how are they used?

Concept:Types of Reasoning

(2.1, 2.3 – 2 days)

Concept:Paragraph proofs

(supplemental 2.5 – 2 days)

Concept:Constructing Proofs

(2.6 – 2 days)

Lesson EQ’s: Why are conjectures and counterexamples essential to inductive reasoning?

Lesson EQ’s:How can we use paragraphs to explain problems?

Lesson EQ’s:How are postulates, axioms, and theorems used to show that a statement is valid?

Vocabulary:conjecture, counterexample, hypothesis, conclusion

Vocabulary:Paragraph proof, open ended, explain, support

Vocabulary:Postulate, axiom, theorem, proof, two-column proof, algebra proofs

Standards: Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Honors Geometry Learning Map (updated 3/13)

Concept:Proving Segment

Relationships (2.7- 1 days)

Concept:Proving Angle Relationships(2.8 - 1 days)

Lesson EQ’s:What is the proof of the segment addition postulate?

Lesson EQ’s:If two congruent angles form a linear pair, then what type of angles are they?

Vocabulary: Vocabulary:Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Concept:Logic

(2.2 – 1 day)

Concept:Deductive Reasoning

(2.4 – 1 day)Lesson EQ’s:How do you set up a truth table?

Lesson EQ’s:What is the difference between the Law of Detachment and the Law of Syllogism?

Vocabulary: disjunction, conjunction, truth table, compound statement, negation, truth value, statement

Vocabulary: Deductive Reasoning, Law of Detachment, Law of Syllogism

Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculate

Standards:G.1.3.2.1 Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction)CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.CC2.3.HS.A.8Apply geometric theorems to

Honors Geometry Learning Map (updated 3/13)

trigonometric ratios. verify properties of circles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Grade Level: Honors GeometryChapter #3: Perpendicular and Parallel Lines

Key Learning(s): Students will learn about perpendicular and parallel lines. They will be able to write the equation of a line given certain characteristics.

Unit Essential Question(s): How are points, lines, and planes related?

Concept: Parallel lines,

transversals, and angles(3.1, 3.2, 3.5 – 4 days)

Concept:Lines in the coordinate

plane(3.3, 3.4 – 3 days)

Concept:Perpendicular lines and

distance(3.6 – 2 days)

Lesson EQ’s: What relationships are created with lines and planes?

Lesson EQ’s:How do slope and linear equations relate to parallel and perpendicular lines?

Lesson EQ’s: Why are perpendicular lines important to distance in geometry?

Vocabulary:Parallel lines and planes, perpendicular lines, skew lines, transversal, consecutive, alternate, corresponding, interior/exterior

Vocabulary:Slope, rate of change, slope-intercept form, point-slope form

Vocabulary:Equidistant

Standards:M11.B.2.1.1 Measure and/or compare angles in degrees (up to 360) (protractor must be provided or drawn).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 anglesG.2.2.1.1 Use properties of angles formed by intersecting lines to find the measures of missing anglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.

Standards:M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)M11.D.3.2.1 Apply the formula for the slope of a line to solve problems (formula given on reference sheet)M11.D.3.2.2 Given the graph of the line, 2 points on the line, or the slope and a point on a line, write or identify the linear equation in point-slope, standard and/or slope-intercept formM11.D.3.2.3 Compute the slope and/or y-intercept represented by a linear equation or graphG 2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations)CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.

Standards:M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)G 2.1.2.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations)CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.G.2.1.4.1 Solve or graph systems of equations or systems of inequalities within a problem situation using coordinate geometry.CC2.2.HS.D.9 Use reasoning to solve equations and justify the solution method.CC2.2.HS.D.10 Represent, solve and interpret equations/inequalitiesand systems of equations/inequalities algebraically and graphically.

Honors Geometry Learning Map (updated 3/13)

Grade Level: Honors GeometryChapter #4: Congruent Triangles

Key Learning(s): We will discuss how triangles sides and angles can relate to geometry.

Unit Essential Question(s): How are the sides and angles of triangles used in geometry?Concept:Classifying triangles and

angle measures of triangles

(4.1, 4.2 – 2 days)

Concept:Triangle Congruence

(4.3, 4.4, 4.5, HL – 4 days)**two column proofs

Concept:Isosceles Triangle

Theorem(4.6 – 2 days) **two

column proofsLesson EQ’s: How can we use sides and angles of triangles to classify them?

Lesson EQ’s:How can we use the triangle theorems to prove triangles are congruent?

Lesson EQ’s:What properties of isosceles triangles help us to find unknown measurements?

Vocabulary: acute, obtuse, right, equilangular, scalene, isosceles, equilateral

Vocabulary: Congruent triangles, included angle, included side

Vocabulary:Vertex angle, base angle

Standards: M11.C.1.2.3 Identify and/or use properties of isosceles and equilateral trianglesG1.2.1.3 Identify and/or use properties of isosceles and equilateral trianglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Standards: M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solidsG1.2.1.3 Identify and/or use properties of isosceles and equilateral trianglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Standards: M11.C.1.2.3 Identify and/or use properties of isosceles and equilateral trianglesG.1.2.1.1 Identify and/or use properties of trianglesG1.2.1.3 Identify and/or use properties of isosceles and equilateral trianglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Honors Geometry Learning Map (updated 3/13)

Grade Level: Honors GeometryChapter #5: Relationships in Triangles

Key Learning(s): We will discuss how triangles sides and angles can relate to geometry.

Unit Essential Question(s): How are the sides and angles of triangles used in geometry?

Concept:Bisectors, medians and altitudes (5.1 – 1 days)

Concept:Triangle Inequalities

(5.2,5.4 – 2 days)

Concept:Indirect Proofs(5.3 – 2 days)

Lesson EQ’s: How do we use medians, altitudes and bisectors in triangles?

Lesson EQ’s:How can inequalities be used in triangles?

Lesson EQ’s:How does indirect reasoning work?

Vocabulary:Perpendicular bisectorMedian, altitude

Vocabulary:Triangle Inequality Theorem

Vocabulary:Proof by contradiction, indirect reasoning, indirect proof

Standards: M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem)G.1.2.1.1 Identify and/or use properties of trianglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Standards: M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem)G.1.2.1.1 Identify and/or use properties of trianglesCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Honors Geometry Learning Map (updated 3/13)

Grade Level: Honors GeometryChapter #6 and Lesson 1-6: Polygons

Key Learning(s): polygons, parallelograms, rectangle, rhombus, square, trapezoid

Unit Essential Question(s): How can we apply the properties of polygons to determine certain figures?Concept:

Basics of Polygons(1.6, 6.1 – 1 days)

Concept: Basic Parallelograms

(6.2, 6.3 – 3 days)

Concept:Rectangles(6.4 – 1 day)

Lesson EQ’s: How dose the name of a polygon relate to finding their angle measures?

Lesson EQ’s:How can the properties of sides and angles of polygons be used to ensure a quadrilateral is a parallelogram?

Lesson EQ’s:How do the properties of special parallelograms differ?

Vocabulary:Polygon, diagonal, concave, convex, n-gon, regular polygon, interior angle sum, exterior angle sum

Vocabulary:parallelogram

Vocabulary:Rectangle, rhombus, square

Standards:M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and G.1.2.1.4 Identify and/or use properties of regular polygonsCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Standards:M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and G.1.2.1.2 Identify and/or use properties of quadrilateralsCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Standards:M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and G.1.2.1.2 Identify and/or use properties of quadrilateralsCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Honors Geometry Learning Map (updated 3/13)

Concept: Rhombi, Squares, Kites

(6.5 and Kites ext– 2 days)

Concept: Trapezoids

(6.6 – 2 days)Lesson EQ’s: How can we identify a shape on the coordinate plane using the slope and distance formula?

Lesson EQ’s:How can we use the properties of trapezoids to find missing values?

Vocabulary:none

Vocabulary:Trapezoid, Isosceles trapezoid, median

Standards:M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and M11.C.3.1.1 Calculate the distance and/or midpoint between 2 points on a number line or on a coordinate plane (formula provided on the reference sheet).M11.C.3.1.2 Relate slope to perpendicularity and/or parallelism (limit to linear algebraic expressions; slope formula provided on the reference sheet)G.1.2.1.2 Identify and/or use properties of quadrilateralsG 2.1.2.3: Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a 2-dimensional shapeCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.

Standards:M11.C.1.2.2 Identify and/or use properties of quadrilaterals (e.g.,parallel sides, diagonals, bisectors, congruent sides/angles and G.1.2.1.2 Identify and/or use properties of quadrilateralsG 2.1.2.3: Use slope, distance, and/or midpoint between two points on a coordinate plane to establish properties of a 2-dimensional shapeCC2.3.HS.A.3 Verify and apply geometric theorems as they relate togeometric figures.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.CC2.3.HS.A.11 Apply coordinate geometry to prove simple geometric theorems algebraically.

**High School Midterms after this unit**

Grade Level: Honors GeometryChapter #7: Proportions and Similarity

Key Learning(s): Ratios, similar figures, proportions

Honors Geometry Learning Map (updated 3/13)

Unit Essential Question(s): How can ratios and proportions be used to find similarity in figures?

Concept:Proportions

(7.1 – 1 days)* word problems

Concept:Similar Figures

(7.2,7.3 – 3 days)

Concept:Proportional Parts(7.4, 7.5 – 3 days)

Lesson EQ’s: How can we use proportions to determine missing information?

Lesson EQ’s:How do we use proportions to determine missing sides or lengths of figures?

Lesson EQ’s:How can we use proportional relationships of similar figures in order to find other measurements?

Vocabulary:Proportion, ratio, cross product

Vocabulary:Similar polygons, scale factor

Vocabulary:midsegment

Standards:M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settingsG.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solidsG.1.3.1.2 Identify and/or use proportional relationships in similar figuresCC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.

Standards:M11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solidsG.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solidsG.1.3.1.2 Identify and/or use proportional relationships in similar figuresCC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.

Standards:M11.A.2.1.3 Identify and/or use proportional relationships in problem solving settingsM11.C.1.3.1 Identify and/or use properties of congruent and similar polygons or solidsG.1.3.1.1 Identify and/or use properties of congruent and similar polygons or solidsG.1.3.1.2 Identify and/or use proportional relationships in similar figuresCC2.3.HS.A.2 Apply rigid transformations to determine and explain congruence.CC2.3.HS.A.5 Create justifications based on transformations to establish similarity of plane figures.CC2.3.HS.A.6 Verify and apply theorems involving similarity as they relate to plane figures.

Grade Level: Honors GeometryChapter #8: Right Triangles and Trigonometry

Key Learning(s): radicals, geometric mean, right triangles, trigonometry

Unit Essential Question(s): What relationships exist with sides and angles of

Honors Geometry Learning Map (updated 3/13)

right triangles?

Concept: Radicals

(supplemental – 1 days)

Concept: Geometric Mean

(8.1 – 2 days)

Concept: Right Triangles

(8.2, 8.3 – 2 days)Lesson EQ’s: How can we use square roots in geometry?

Lesson EQ’s:How do you use the geometric mean to find unknown sides in right triangles?

Lesson EQ’s:How can we apply the Pythagorean Theorem to solve real world problems?

Vocabulary: radical, rationalized denominator

Vocabulary: geometric mean Vocabulary: Pythagorean theorem, special right triangles

Standards:M11.A.1.1.3 Simplify square roots.A1.1.1.1.2 Simplify square roots CC(ALg1)2.1.8.E.1 Distinguish between rational and irrational numbers using their properties.CC(Alg1)2.1.8.E.4 Estimate irrational numbers by comparing them to rational numbers.CC(Alg1)2.1.HS.F.1 Apply and extend the properties of exponents to solveproblems with rational exponents.CC(Alg1)2.1.HS.F.2 Apply properties of rational and irrational numbers to solve real world or mathematical problems.

Standards:M11.C.1.2.1 Identify and/or use properties of triangles (e.g., medians, altitudes, angle bisectors, side/angle relationships, Triangle Inequality Theorem)

Standards:M11.C.1.4.1 Find the measure of a side of a right triangle using the Pythagorean Theorem (Pythagorean Theorem included on the reference sheet)G.2.1.1.1 Use the Pythagorean theorem to write and/or solve problems involving right trianglesCC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Concept: Trigonometry

(8.4, 8.5 – 3 days)

Concept: Law of Sines and Cosines

(8.6, 8.7 – 3 Days)Lesson EQ’s: How do fractions contribute to solving problems in right triangles?

Lesson EQ’s: How can we use the laws to solve for missing measures in non right triangles?

Vocabulary: trigonometry, trig ratio, sine, cosine, tangent, angle of elevation, angle of depression

Vocabulary: Law of Sines, Law of Cosines, Solving a Triangle

Standards:G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right trianglesCC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Standards:G.2.1.1.2 Use trigonometric ratios to write and/or solve problems involving right trianglesCC2.3.HS.A.7 Apply trigonometric ratios to solve problems involving right triangles.CC2.2.HS.C.9 Prove the Pythagorean identity and use it to calculatetrigonometric ratios.

Grade Level: Honors GeometryChapter #10: Circles

Key Learning(s): parts of circles, relationships with arcs, chords and diameters, inscribed angles and tangents of circles

Unit Essential Question(s): How do you apply the relationships among circles, lines, segments, and the angles they form? How does change in the linear

Honors Geometry Learning Map (updated 3/13)

dimension of a figure affect its perimeter, circumference and area?

Concept:Basics of Circles

(10.1,10.2 – 2 days)

Concept:Arcs and Chords

(10.3 – 2 days)

Concept:Inscribed Angles

(10.4 – 1 days)Lesson EQ’s: How can we use the parts of circles to solve problems about their dimension, length and measurement?

Lesson EQ’s:What relationships of arcs, chords and diameters are used in circles?

Lesson EQ’s:How can we find the measures of inscribed angles and polygons?

Vocabulary:Circle, center, chord, radius, diameter, circumference, semicircle, central angles, minor arc, major arc

Vocabulary:Inscribed, circumscribed

Vocabulary:intercepted

Standards:M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.1.1.1.1 Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circleCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.G.2.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area (e.g.,How does changing the length of the radius of a circle affect the circumference of the circle?).CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.

Standards:M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.1.1.1.1 Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circleG.1.1.1.2 Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circleCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.G.2.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area (e.g.,How does changing the length of the radius of a circle affect the circumference of the circle?).CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.

Standards:M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.1.1.1.1 Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circleG.1.1.1.2 Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circleCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

Concept:Tangents

(10.5 – 1 days)

Concept:Secants, tangents, and

angle measures(10.6 – 2 days)

Concept:Special Segments in

Circles(10.7 – 2 days)

Lesson EQ’s: How can you use the properties of a tangent to a circle?

Lesson EQ’s:How do you find measures of angles formed by lines intersecting on, inside or outside a circle?

Lesson EQ’s:What is the relationship of segments that intersect inside or outside a circle?

Vocabulary:Tangent, point of tangency

Vocabulary:Secant

Vocabulary:

Standards: Standards: Standards:

Honors Geometry Learning Map (updated 3/13)

M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measuresCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.1.1.1.3 Use chords, tangents, and secants to find missing arc measures or missing segment measuresCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.

M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central anglesG.2.2.2.5 Find the area of a sector of a circle.CC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.2.HS.C.1 Use the concept and notation of functions to interpretand apply them in terms of their context.

Concept:Equations of Circles

(10.8 – 1 days)

Lesson EQ’s: How do write the equation of a circle given the center and radius?

Vocabulary:

Standards:M11.C.1.1.1 Identify and/or use the properties of a radius, diameter and/or tangent of a circle (given numbers should be whole)M11.C.1.1.2 Identify and/or use the properties of arcs, semicircles, inscribed angles and/or central angles

Grade Level: Honors GeometryChapter #11: Area and Perimeter

Key Learning(s): Area and perimeter of different shapes

Unit Essential Question(s): How are the dimensions of two-Honors Geometry Learning Map (updated 3/13)

dimensional figures used in the real world? How does change in the linear dimension of a figure affect its perimeter, circumference and area?

Concept: Parallelograms(11.1 – 1 day)

Concept: Triangles, Trapezoids and

Rhombi(11.2 – 2 days)

Concept: Area of Regular

Polygons and Circles(11.3 – 2 Days)

Lesson EQ’s: How do you find the area and perimeter of basic figures?

Lesson EQ’s:What is the formula for the area of a trapezoid?

Lesson EQ’s:What does an apothem have to do with the formula for area of a regular polygon?

Vocabulary:Height of a parallelogram

Vocabulary: Vocabulary:Apothem

Standards:M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area or volume.M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference, or areaG.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygonCC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.2.HS.C.1 Use the concept and notation of functions to interpretand apply them in terms of their context.

Standards:M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area or volume.M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference, or areaG.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygonCC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.2.HS.C.1 Use the concept and notation of functions to interpretand apply them in terms of their context.

Standards:M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area or volume.M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.G.2.2.4.1 Use area models to find propertiesCC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.

Concept: Irregular or Composite

Figures and Shaded Figures

(11.4 – 1 day)

Concept: Geometric Probability and

Area of Sectors(11.5 – 2 days)

Lesson EQ’s: How do you find the area of a composite figure?

Lesson EQ’s:When calculating Geometric Probability what two conditions do we assume?

Vocabulary: Vocabulary:Honors Geometry Learning Map (updated 3/13)

Composite figure Geometric probability, sector, segment

Standards:M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area or volume.M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.G.2.2.2.2 Find the measurement of a missing length, given the perimeter, circumference, or areaG.2.2.2.3 Find the side lengths of a polygon with a given perimeter to maximize the area of the polygonCC2.3.HS.A.3 Verify and apply geometric theorems as they relate to geometric figures.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.2.HS.C.1 Use the concept and notation of functions to interpretand apply them in terms of their context.

Standards:M11.B.2.2.4 Find the measurement of a missing length given the perimeter, circumference, area or volume.M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.G.2.2.4.1 Use area models to find propertiesCC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.

Grade Level: Honors GeometryChapters #12 & 13 and Lesson 1-7: Surface Area and Volume

Key Learning(s): Surface area and volume of different shapesUnit Essential Question(s): How are the dimensions of three-dimensional figures used in the real world?How does change in the linear dimension of a figure affect its surface area and volume? How do you find

Honors Geometry Learning Map (updated 3/13)

the measurement of the missing length given the surface area or volume?

Concept: Three dimensional figures

(1.7, 12.1 – 2 days)

Concept: Prisms

(12.2, 13.1 – 2 days)

Concept: Pyramids

(12.4, 13.2 – 2 days)Lesson EQ’s: How does the two-dimensional make up of three-dimensional figures relate to their formulas?

Lesson EQ’s:Why are there several ways to solve for the dimensions of prisms?

Lesson EQ’s:How do you find the volume and surface area of a pyramid?

Vocabulary:Face, edges, prism, regular prism, pyramid, platonic solids, cylinder, cone, sphere

Vocabulary:Surface area, volume, Dimension change

Vocabulary:

Standards: Standards:M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.M11.B.2.2.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetM11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetG.1.1.1.4: Identify and/or use the properties of pyramids and prismsG.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetG.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects CC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.CC2.3.HS.A.12 Explain volume formulas and use them to solve problems..

Standards:M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.M11.B.2.2.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetM11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetG.1.1.1.4: Identify and/or use the properties of pyramids and prismsG.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetG.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects.CC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.CC2.3.HS.A.12 Explain volume formulas and use them to solve problems..

Concept:Cylinders & Cones

(12.3, 13.1, 12.5, 13.2 –3 days)

Concept:Sphere

(12.6, 13.3 – 2 days)

Concept:Congruent and Similar

Solids(13.4 – 1 days)

Lesson EQ’s: How do you find the surface area and volume of a cylinder?What are the parts of the cone

Lesson EQ’s:What uses do volume and surface area have for a sphere?

Lesson EQ’s:How do you determine if two solids are congruent or similar?

Honors Geometry Learning Map (updated 3/13)

necessary to find surface area nd volume?Vocabulary:Axis, right cylinder Circular cone, right cone, oblique cone

Vocabulary: Vocabulary:Similar Solids, Congruent Solids

Standards:M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.M11.B.2.2.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetM11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetG.1.1.1.4 Identify and/or use the properties of a cylinder or sphereG.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetG.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects CC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.CC2.3.HS.A.12 Explain volume formulas and use them to solve problems.G.2.3.2.1 Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?).CC2.3.HS.A.13 Analyze relationships between two-dimensional and three-dimensional objects.

Standards:M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.M11.B.2.2.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetM11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetG.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetG.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects CC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.CC2.3.HS.A.12 Explain volume formulas and use them to solve problems..G.2.3.2.1 Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?).CC2.3.HS.A.13 Analyze relationships between two-dimensional and three-dimensional objects.

Standards:M11.B.2.3.1 Describe how a change in the linear dimension of a figure affects its perimeter, circumference, area or volume.M11.B.2.2.1 Calculate the surface area of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetM11.B.2.2.2 Calculate the volume of prisms, cylinders, cones, pyramids and/or spheres. Formulas are provided on the reference sheetG.1.1.1.4 Identify and/or use the properties of a cylinder or sphereG.2.3.1.1 Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetG.2.3.1.2 Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheetCC2.3.HS.A.8 Apply geometric theorems to verify properties of circles.CC2.3.HS.A.9 Extend the concept of similarity to determine arc lengthsand areas of sectors of circles.CC2.3.HS.A.13 Analyze relationships between two-dimensional andthree-dimensional objects CC2.3.HS.A.14 Apply geometric concepts to model and solve real world problems.CC2.3.HS.A.12 Explain volume formulas and use them to solve problems..G.2.3.2.1 Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?).CC2.3.HS.A.13 Analyze relationships between two-dimensional and three-dimensional objects.

Honors Geometry Learning Map (updated 3/13)