hudsonville high school course framework · rhombus, or square. slope formula distance formula...

HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

COURSE/SUBJECT Geometry B

KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS

POLYGONS AND QUADRILATERALS

SIMILARITY

RIGHT TRIANGLES ANDTRIGONOMETRY

EXTENDING PERIMETER, CIRCUMFERENCE,AND AREA

SPATIAL REASONING

CIRCLES

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Look for and express regularity in repeated reasoning.

CHAPTER PACING

LESSON #

STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY CONCEPT

Polygons andQuadrilaterals

6-1 G1.5.2 Classify Polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons.

Find the sum of the interior angle measures of a convex decagon.

regular polygon interior angle exterior angle concave convex

6-2, 6-3 G.CO.11 Prove properties of parallelograms;opposite sides & opposite angles arecongruent, and diagonals bisect eachother.

JKLM is a parallelogram. Find the measure of JK, LM, <L and <M.

Parallelogram properties. diagonals bisect

6-4 G.CO.11 Prove that rectangles areparallelograms with congruentdiagonals.

Find the measure of GJ and HK.

Rectangle properties.

CHAPTER PACING

LESSON #


6-5 G.GPE.4

G.GPE.4

I can connect a property of a figure tothe tool needed to verify that property.

I can use coordinates and the right toolto prove or disprove a claim about afigure (using slopes, midpoint, anddistance formula)

Use the diagonals to determine whether a parallelogram with the given vertices is a rectangle, rhombus, or square.

slope formula distance formula perpendicular

6-6 G1.4.1 Use properties of kites and trapezoids to solve problems.

Find the measure of each numbered angle in the kite below.

kite properties trapezoid properties base, leg, midpoint isosceles

CHAPTER LESSON STANDARD CHAPTER LEARNING TARGETS EXAMPLE KEY PACING # CONCEPT

Similarity Relationships

7-1 G.SRT.2 Be able to write and solve ratios and proportions

4 x 7 = 14

ratio proportion extremes means cross product

7-2 G.SRT.2 Using similarity transformations (dilations), determine if two triangles aresimilar by showing all correspondingangles congruent and all correspondingsides are proportional.

Identify the pairs of congruent angles and corresponding sides.

similar similar polygons similarity ratio

G.C.5 I I can define similarity and know that itpreserves angle measures and makes lengths proportional

7-3 G.SRT.3

G.SRT.5

Establish the AA criteria as a sufficient condition for two triangles to be similar.

Use triangle similarity (AA, SSS, & SAS) to solve problems.

Explain why two triangles are similar and write a similarity statement.

AA SSS SAS Reflexive Symmetric Transitive

CHAPTER PACING

LESSON #


7-4 G.SRT.4

G.SRT.5

Prove a line parallel to one side of atriangle divides the other two sides proportionally (Triangle Proportionality Thm).

Prove that if a line divides two sides of a triangle proportionally, it is parallel to thethird side (Converse of the TriangleProportionality Thm).

Use the Pythagorean Thm to provetriangles similar (geometric means).

Use properties of similar triangles (sidesplitting) to solve problems.

Find the length of each segment.

Triangle Proportionalit y

Converse

Two-Transversal

Triangle Angle Bisector

7-5 G.SRT.5 Use similar triangles with indirectmeasurements to solve problems.

Converting units of measure (square feetto square miles)

indirect measurement

scale drawing

scale

7-6 G.SRT.1 Define & perform dilations with a givencenter & scale factor on a figure in thecoordinate plane.

graph the image after the given scale factor.

J(-2,0) K(-1,-1) L(-3,-2) with a scale factor 3

dilation

scale factor

CHAPTER PACING

LESSON #


Right Trianglesand Trigonometry

8-1 G.SRT.6 Apply similarity relationships in righttriangles to solve problems.

Find u, w, v in the triangle. Pythagorean Theorem Similarity between right triangles.

8-2 G.SRT.6

G.SRT.7

G.SRT.9

Use characteristics of similar figures to justify and define trigonometric ratios.

Use sine & cosine ratios for acute angles in right triangles when giventwo side lengths.

Use the sine function to find the length of the triangle’s altitude.

Find cos A of the triangle.

Find x using trigonometry.

SOH, CAH, TOA

8-3 G.SRT.8 Use sine, cosine, tangent, & their inverses to solve for unknown side lengths and angle measures of a righttriangle.

Find the measure of angle P. Inverse sin, cos, and tan.


8-4 G.SRT.8 Solve application problems involvingright triangles, including angle ofelevation & depression, navigation,and surveying.

An air traffic controller at an airport sights a plane at an angle of elevation of 41degrees. The pilot

Angle of elevation Angle of depression

reports that the plane’s altitude is 4000 ft. What is the horizontal distance between the plane and the airport?

8-5 G.SRT.10 Prove the Laws of Sines and Cosines Find the measure of angle R Law of Sines is and use them to solve problems. using the Law of Cosines. similar to

solving G.SRT.11 Derive the Law of Sines by drawing

the altitude & establishingrelationships to the original triangle;including solving real world problems.

proportions.

Law of Cosines is similar to solving 8 = 4 -

G.SRT.11 Use the Law of Cosines to solve real world problems.

2x

8-6 G.SRT.11 Solve real world problems including vectors.

The vector <7, 9> represents the velocity of a

Vector Component

helicopter. What is the form direction of this vector to Magnitude the nearest degree? Direction

Equal vectors Parallel vectors

CHAPTER PACING

LESSON #


ExtendingPerimeter, Circumference,and Area

9-1 G.SRT.9

G.GMD.1

Traditional area formula of a triangleA = 1/2 *b*h

I can calculate the area of the base for prisms and pyramids

Find the area of a triangle with base 7 inches and height 10 inches.

Find

Height is always perpendicular to the base.

Working with formulas.

9-2 G.CO.1

G.C.5

G.GMD.1

G.GMD.1

Precisely define circles.

I can calculate the area of a circle.

I can calculate the area of the base for a cylinder or a cone.

I can explain how to generate theformula A = ½ x apothem x perimeter for a regular polygon and calculatethe area of a regular polygon.

Find the area of a circle with radius 5 cm.

Find the area of a regular octagon with side length 10 inches.

Pi Center of a circle Radius Diameter Apothem Central Angle

9-3 G.MG.2 Calculating area of composite figures. Calculate the area of the shaded ring in the target.

Add or subtract areas of shapes.

CHAPTER PACING

LESSON #


9-4 G.GPE.7 I can use the coordinates of the vertices of triangles and rectangles graphed in the coordinate plane tocompute area.

Calculate the area of the irregular figure.

Irregular shapes are most common in the real world.

9-5 Describe the effect of changing onedimension on perimeter and area.

Describe the effect of changing bothdimensions on area.

Converting units of measure.

Describe the effect of each change on the perimeter and area if only the height is doubled.

Describe the effect of each change on the area if the base and height are doubled.

Square feet to square miles.

9-6 S.CP.2 I can calculate the probability of an event.

Find the probability of hitting the bullseye on the target.

Geometric probability

CHAPTER PACING

LESSON #


SpatialReasoning

10-1 G.GMD.1

G.GMD.4

G.MG.1

I can identify the bases for prisms,cylinders, pyramids, and cones.

I can identify the shapes of 2D cross sections of 3D objects.

Represent real-world objects as geometric figures.

Classify each figure. Name the vertices, edges, and bases.

face edge vertex prism cylinder pyramid cone cube net cross section

CHAPTER PACING

LESSON #


10-2 G.MG.1 Draw representations of three-dimensional figures.

Recognize a three-dimensional figurefrom a given representation.

Draw all six orthographic views of the following object.

orthographic view

isometric drawing

10-3 G.2.2.1 Apply Euler’s formula to find thenumber of vertices, edges, and faces of a polyhedron.

Develop and apply the distance andmidpoint formulas in three dimensions.

Find the length of the diagonal of a 4 ft by 8 ft by 12 ft rectangular prism.

polyhedron

space

distance formula 3-D

midpoint formula 3-D

10-4 G.1.8.1 Calculating formulas (circumference,area, perimeter, & volume) of three-dimensional figures.

Find the lateral area and surface area of the following:

lateral face lateral edge right prism oblique prism altitude surface area lateral surface right cylinder oblique cylinder

CHAPTER PACING

LESSON #


10-5 G.1.8.1 Calculating formulas (circumference,area, perimeter, & volume) of three-dimensional figures.

Find the lateral area and surface area of a regular square pyramid with base edge length 5 in. and slant height 9 in.

vertex of a pyramid

slant height

axis of a cone

10-6 G.GMD.1

G.GMD.3

G.MG.1

I can calculate the volume of prisms and cylinders.

I can defend the statement, “The formula for the volume of a cylinder is basically the same as the formula for the volume of a prism.”

I can calculate the volume of a cylinderand use the volume formula to solve problems.

Calculating formulas (circumference,area, perimeter, & volume) of three-dimensional figures.

Calculating volume of compositefigures.

Find the volume of each prism:

volume of prisms and cylinders

CHAPTER PACING

LESSON #


10-7 G.GMD.3

G.MG.1

I can calculate the volume of a pyramid and use the volume formulato solve problems.

I can calculate the volume of a cone and use the volume formula to solve problems.



Find the volume of a hexagonal pyramid with a base area of 25 ft 2 and a

height of 9 ft.

Volume of a Cone/Pyramid

10-8 G.GMD.3

G.MG.1

I can calculate the volume of a sphereand use the volume formula to solve problems.



Find the volume of a sphere with surface area 144π m2 .

Volume and surface are of spheres


Circles 11-1 G.C.2

G.C.4

I can identify chords and tangents.

I can recognize that the radius of acircle is perpendicular to the tangentwhere the radius intersects the circle.

I can define and identify a tangentline.

Chords

Secants

Tangent lines

Point of tangency

11-2 G.C.2 I can identify inscribed angles. Central angle

G.C.3

I can describe the relationshipbetween a central angle and the arc it intercepts.

Major/minor arcs

Arc addition I can apply the Arc Addition Postulateto solve for missing arc measures.

11-3 G.CO.1

G.C.5

G.C.5

Precisely define distance around acircular arc (arc length).

I can define a sector of a circle.

I can calculate the area of a sector using the ratio of the intercepted arc measure and 360 degrees multipliedby the area of the circle.

Find the area of the shaded region above.

Sector

Arc length

Area and circumference of a circle


11-4 G.C.2

G.C.3

I can describe the relationshipbetween an inscribed angle and thearc it intercepts.

I can recognize that an inscribedangle whose sides intersect theendpoints of the diameter of a circleis a right angle.

I can prove that opposite angles in aninscribed quadrilateral aresupplementary.

Find the measure of angle RST and the measure of arc SU.

Inscribed angle

Intercepted arc

Diameter of a circle

11-5 G.C.2 I can identify circumscribed angles.

I can describe the relationshipbetween an inscribed angle and thearc it intercepts.

I can describe the relationshipbetween a circumscribed angle andthe arcs it intercepts. Find the value of x in the

figure above.

Circumscribed angle

Arcs of circles

11-7 G.GPE.1 I can identify the center and radius ofa circle given its equation.

I can use the distance formula or Pythagorean theorem, thecoordinates of a circles center, andthe circles radius to write the equation of a circle

Find the equation of the circle with center (5, -2) and radius 8.

Center of circle

Radius of circle

Distance

hudsonville high school course framework · rhombus, or square. slope formula distance formula...

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