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MATHEMATICS: GEOMETRY

GRADES: 10 - 12

 

Cumulative Progress Indicators

Major Outcome

Strategies/Activities Resources with Text Reference

Assessments

4.2.A.1

4.5.A.1

 

 

 

 

 

Students will be able to:

  • identify and represent undefined terms – point, line, plane – by their appropriate geometric symbols.

  • Text: Geometry, AGS Publishing

    • Chapter 1

  • Red Binder – Instructional Strategies

 

See “Assessment”

4.5.A.1

4.5.B.1

4.5.B.2

4.5.A.1

4.5.B.1

4.5.B.2

Students will be able to:

  • define and illustrate geometric terminology and use appropriate symbols of the following topics: angles, triangle, parallel lines, perpendicular lines, quadrilaterals, other polygons, circles, 3-dimensional figures, networks, vectors, areas, volumes, symmetry, tessellations, and transformations.

  • Text: Geometry, AGS Publishing

    • Chapter 1

  • Geometer’s Sketchpad

  • Activity: “Seattle Shapes” (students can classify shapes in any method they choose with appropriate justification)

See “Assessment”

4.5.A.1

4.5.D.2

Students will be able to:

  • make and test conjectures.

  • Text: Geometry, AGS Publishing

    • Chapter 2

  • This objective is addressed in sections throughout the text.

See “Assessment”

4.2.6.A.1

4.2.8A.1

Students will be able to:

  • use a compass and straightedge to perform the basic constructions of:

  • duplicating segments and angles

  • perpendiculars

    • perpendicular bisectors

    • perpendiculars

  • angle bisectors

  • parallel lines

  • triangles and quadrilaterals

  • Text: Geometry, AGS Publishing

    • Chapter 3

  • Geometer’s Sketchpad

  • Activity: Patty Paper Constructions

See “Assessment”

 

 

4.2.A.3

4.2.A.4

4.2.E.1

4.5.B.2

4.5.D.3

Students will be able to:

  • construct proofs.

  • Congruent triangles

    • SSS

    • SAS

    • ASA

    • SAA

  • Line segments and angles – CPCTC

  • Text: Geometry, AGS Publishing

    • Chapters 3 and 4

See “Assessment”

4.2.A.3

4.3.7.A.1

4.2.8.A.1

4.2.8.A.4

4.2.D.2

4.5.B.1

4.5.B.2

4.5.D.3

4.5.E.1

Students will be able to:

  • apply geometric relationships of angles to solve problems within the following topics:

  • Angles

    • complementary

    • supplementary

    • bisected

    • vertical

    • linear pair

    • right

  • Triangles

    • triangle inequality

    • exterior angle equals sum of remote interior angles

    • sum of interior angles is 180

    • special triangles

      • Isosceles triangle – base angles are equal

      • Equilateral triangle – angles equal

      • Right triangle

        • Sum of two acute angles is 90

        • Trigonometric ratios

  • Text: Geometry, AGS Publishing

    • Chapter 3

  • Geometer’s Sketchpad

  • Activity: “Saws and Ladders”

See “Assessment”

 

4.2.A.3

4.2.7.A.1

4.2.8.A.1

4.2.8.A.4

4.2.D.2

4.5.B.1

4.5.B.2

4.5.D.3

4.5.E.1

Students will be able to:

  • Parallel lines:

  • Alternate interior angles are equal.

  • Alternate exterior angles are equal.

  • Angles on the same side of a transversal are supplementary.

  • Corresponding angles are equal.

  • Perpendicular lines:

  • Form right angles

  • Form equal adjacent angles

  • Form four equal angles

  • Polygons:

  • Sum of interior angles: (n-2) 180

  • Sum of exterior angles: 360

  • Regular polygons

    • One interior angle: (n-2) 180

n

    • One exterior angle: 360/n

  • Special quadrilaterals:

  • Parallelogram

    • Opposite angles are equal.

    • Consecutive angles are supplementary.

  • Rectangle:

    • All parallelogram angle relationships

    • Four right angles

  • Rhombus

    • All parallelogram angle relationships

    • Diagonals bisect a pair of opposite angles.

    • Perpendicular diagonals form four right angles.

 

 

  • Text: Geometry, AGS Publishing

    • Chapters 3 - 6

 

See “Assessment”

 

4.2.A.3

4.2.7.A.1

4.2.8.A.1

4.2.8.A.4

4.2.D.2

4.5.B.1

4.5.B.2

4.5.D.3

4.5.E.1

Students will be able to:

  • Square:

  • All parallelogram, rectangle, and rhombus angle relationships

  • Trapezoid:

  • Angles whose vertices are endpoints of one leg are supplementary.

  • Isosceles trapezoid:

  • All trapezoid angle relationships

  • Angles in each pair of base angles are equal.

  • Circles:

  • Angle vertex at center of circle

    • Measure of central angles equals measure of its intercepted arc.

  • Angle vertex on circle

    • Measure of inscribed angle equals half measure of intercepted arc.

    • Measure of angle formed by a tangent and a chord equals half the measure of the intercepted arc.

  • Angle vertex in the interior of circle

    • Measure of angle formed by two chords equals half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

  • Angle vertex in the exterior of the circle (optional)

    • Measure of angle formed by two secants, a tangent and secant, or two tangents equals half the difference of the measures of the intercepted arcs.

  • Text: Geometry, AGS Publishing

    • Chapters 3 - 6

 

  • See “Assessment”

 

4.2.A.3

4.2.B.4

4.2.E.1

4.2.E.2

Students will be able to:

  • Apply geometric relationship of segment length to solve problems within the following topics:

  • Triangles

  • Triangle inequality

  • Perimeter

  • Sides opposite equal angles are equal.

  • Segment joining midpoints of two sides equals half of the third side.

  • Similar triangles

  • Definition of similar triangles sets up proportions.

  • A line through the interior of a triangle parallel to one side divides the other two sides proportionally.

  • The bisector of an angle of a triangle divides the opposite side into segments proportional to the adjacent sides of the triangle.

  • The perimeters, altitudes, and medians of two similar triangles are proportional to any pair of corresponding sides.

  • The area of two similar triangles have the same ratio as the square of any two corresponding sides.

  • Special triangles

  • Isosceles triangle

    • The median, altitude, and angle bisector from the vertex angle coincide.

  • Right triangles

    • Pythagorean theorem

    • 30-60-90 theorem

    • 45-45-90 theorem

    • trigonometric ratios

 

  • Text: Geometry, AGS Publishing

    • Chapters 3 - 10

 

  • See “Assessment”

 

4.2.A.3

4.2.B.4

4.2.E.1

4.2.E.2

Students will be able to:

  • Parallel lines

  • If three parallel lines intersect two transversals, then the transversals are divided proportionally.

  • Polygons

  • Perimeter

  • Similar polygons

    • Definition of similar polygons; set up proportions

    • The area of two similar polygons have same ratio as the squares of measures of any two corresponding sides.

  • Regular polygon

  • Apothem – radius of inscribed circle

  • Radius – radius of circumscribed circle

  • Side

  • Special quadrilaterals

  • Parallelogram

    • opposite sides are equal

    • diagonals bisect each other

  • Rectangle

    • all parallelogram side relationships

    • diagonals are equal

  • Rhombus

    • all parallelogram side relationships

    • all sides are equal

  • Square

    • all parallelogram, rectangle, and rhombus side relationships

  • Trapezoid

    • median equals half the sum of the bases

  • Text: Geometry, AGS Publishing

    • Chapters 3 - 10

 

  • See “Assessment”

 

4.2.A.3

4.2.B.4

4.2.E.1

4.2.E.2

Students will be able to:

  • Isosceles trapezoid

  • All trapezoid side relationships

  • Legs are equal

  • Diagonals are equal

  • Circles

  • Diameter equals two times radius

  • In same or congruent circles, equal arcs have equal chords

  • In same or congruent circles, chords equidistant from the center are equal

  • Diameter perpendicular to a chord bisects the chord

  • Two tangent segments from the same exterior point of a circle are equal

  • A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

 

  • Text: Geometry, AGS Publishing

    • Chapters 3 - 10

 

  • See “Assessment”

4.2.A.2

4.2.E.1

4.5.F.4

Students will be able to:

  • Apply geometric relationships of arcs and circumference to solve problems within the following topics:

  • Measure of arcs in same or in congruent circles are equal when:

    • central angles are equal.

    • chords are equal.

    • intercepted by parallel lines.

    • intercepted by equal inscribed angles.

    • diameter perpendicular to a chord bisects its arcs.

  • Circumference: 2πr or πd

  • Length of arc: m (2πr)

360

 

  • Text: Geometry, AGS Publishing

    • Chapters 10

 

  • See “Assessment”

 

4.2.E.2

4.5.F.4

Students will be able to:

  • Solve problems involving perimeter, area, and volume of geometric figures using formulae:

  • Perimeter of polygons - sum of all sides

  • Area of a plane figure

    • Triangle: ½ bh

    • Rectangle: bh

    • Square: s2

    • Parallelogram: bh

    • Trapezoid: ½ (b1 + b2) h

    • Regular polygoin: ½ asn or ½ aP

  • Circle

    • Πr2

  • Sector of a circle: m (2πr)

360

  • Irregular figures

 

  • Surface area

  • Prism: sum of the areas of the faces

  • Pyramid: sum of the areas of the faces

  • Cylinder: 2πr2 + 2πrH

  • Cone: πrl + πr2

  • Sphere: 4πr2

 

  • Text: Geometry, AGS Publishing

    • Chapters 9, 11

 

  • See “Assessment”

4.2.E.2

4.5.F.4

Students will be able to:

  • Volume

  • Prism: BH

  • Pyramid: (1/3) BH

  • Cylinder: BH

  • Cone: (1/3) BH

  • Sphere: (4/3) πr3

 

  • Text: Geometry, AGS Publishing

 

  • See “Assessment”

 

4.2.C.1

Students will be able to:

  • Apply the principles of coordinate geometry to determine properties of geometric figures.

  • Midpoint formula

  • Slope

    • Formula

    • Parallel and perpendicular lines

  • Distance formula

 

  • Text: Geometry, AGS Publishing

    • Chapter 4

 

  • See “Assessment”

4.2.B.1

4.2.B.2

4.2.B.3

4.2.B

Students will be able to:

  • Identify, illustrate, and apply the principles of transformations, symmetry, and tessellations to the solutions of problems.

  • Symmetry

 

 

  • Text: Geometry, AGS Publishing

    • Chapter 26

  • See “Assessment”

4.2.B.1

4.2.B.2

4.2.B.3

4.2.B

Students will be able to:

  • Transformations

  • Reflections

    • Image across a line

    • Translation: two reflections across parallel lines

    • Glide reflection: a translation flowed by a reflection across a line that is perpendicular to the lines of translation

  • Rotation: two reflections over two intersecting lines

  • Dilations

    • Identify mapping equal to preimage

    • Contraction: similar to preimage

    • Expansion: similar to preimage

  • Tessellations

 

  • Text: Geometry, AGS Publishing

 

  • See “Assessment”

Assessment

 

 

The purpose of assessments is to determine student understanding, performance attitude and application of skills. Assessments can be:

  • Diagnostic: telling teachers what the student needs to learn.

  • Formative: telling us how well the student is doing as work progresses, and

  • Summative: telling us how well the student did at the end of a unit/task.

 

It is important to assess student work at all stages of development through a variety of methods that may include:

  • Standardized Achievement Tests: provide data that establish student levels of performance.

  • Teacher generated tests/quizzes: (selected response and/or construction response) – the data will provide information regarding the extent of student learning. High school courses are required to administer course specific school-wide mid-termed final examinations.

  • Authentic assessment: performance tasks and projects that demonstrate student level of application and competency.

  • Student Self and Peer Assessment: students reflect on, make a judgment and then report on their own or a peer’s behavior and performance.

  • Portfolio: collection of student work that exhibits the student’s efforts, progress and achievement.

 

Information from a variety of assessments should be used to improve instruction, focus student attention on strengths and weaknesses, improve program planning, and serve as the data for reports to students and other concerned individuals.

 

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