Download Honors/Standard Geometry Pacing Guide 2016

Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 1
Unit 1: Geometric Figures
Standards
Week
Pre-Test
Week 1
Aug. 1-5
G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and theorems).
Understand the differences among supporting evidence, counterexamples, and actual proofs.

Know undefined terms and use them to create new definitions.

Identify different logic systems, discuss history of them, and discuss how geometric systems formed.
G.T.8: Develop the distance formula using the Pythagorean Theorem. Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems. Find measures of the
sides of polygons in the coordinate plane; apply this technique to compute the perimeters and areas of polygons in real-world and mathematical problems.

Plot points on a line or graph and find the distance between two points and the midpoint of a segment.

Use line segments to make shapes and find area and perimeter.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and theorems).
Understand the differences among supporting evidence, counterexamples, and actual proofs.
G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric
notation.
Week 2
Aug. 8-12
G.PL.5: Explain and justify the process used to construct, with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric
software, etc.), congruent segments and angles, angle bisectors, perpendicular bisectors, altitudes, medians, and parallel and perpendicular lines.
G.T.8: Develop the distance formula using the Pythagorean Theorem. Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems. Find measures of the
sides of polygons in the coordinate plane; apply this technique to compute the perimeters and areas of polygons in real-world and mathematical problems.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric
notation.

Continue using geometric notation, introduce notation for perpendicular and parallel lines.
Week 3
Aug. 15-19
G.QP.2: Prove that given quadrilaterals are parallelograms, rhombuses, rectangles, squares or trapezoids. Include coordinate proofs of quadrilaterals in the coordinate plane.

Create definitions for various quadrilaterals to use in coordinate proofs.
G.QP.5: Deduce formulas relating lengths and sides, perimeters, and areas of regular polygons. Understand how limiting cases of such formulas lead to expressions for the circumference and
the area of a circle.

Create formulas to find area and perimeter of shapes created.
Unit 1 Assessment
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Indianapolis Public Schools
Curriculum and Instruction
Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 1
Unit 2: Reasoning and Proofs
Standards
Week
Week 4
Aug. 22-26
G.LP.1: Understand and describe the structure of and relationships within an axiomatic system (undefined terms, definitions, axioms and postulates, methods of reasoning, and
theorems). Understand the differences among supporting evidence, counterexamples, and actual proofs.

Start connecting if-then statements to the concept of arguments. Make explicit that Geometry can be thought of as an axiomatic system with if-then statements forming the basis
of all future concepts.
G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric
notation.

Build on previous work by including and identifying inside of proofs.
G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements.

Know the different forms of statements and decide which are true.
PS.3: Construct viable arguments and critique the reasoning of others.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric
notation.

Build on previous definitions and introduce new ones as needed.
Week 5
Aug. 29-Sept. 2
G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements.

Build on previous work by including and identifying inside of proofs.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs, and flow
charts formats.

Expose students to a variety of proofs framing them as arguments.
Week 6
Sept. 7-9
(3 days)
Labor Day &
District PD
Week 7
Sept. 12 & 13
(2 days)
PS.3: Construct viable arguments and critique the reasoning of others.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
G.LP.2: Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric
notation.

Build on previous definitions and introduce new ones as needed.
G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements.

Build on previous work by including and identifying inside of proofs.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs, and flow
charts formats.

Decide on a type of proof(s) your class will be using throughout semester and use them to organize arguments.
PS.3: Construct viable arguments and critique the reasoning of others.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Benchmark 1 Window Opens –10th grade only
Unit Assessment
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Indianapolis Public Schools
Curriculum and Instruction
Honors/Standard Geometry
Pacing Guide 2016-2017
Quarter 1
Unit 3: Parallel and Perpendicular Lines
Standards
Week
G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements.

Apply these techniques to definitions and theorems of parallel and perpendicular lines.
Week 7
Continued
Sept. 14-16
(3 days)
G.PL.3: Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are supplementary; and
points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment.

Know and apply definitions of angle relationships.

Explore real-world examples of angle relationships.
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Benchmark 1 Window Closes
G.LP.3: State, use, and examine the validity of the converse, inverse, and contrapositive of conditional (“if – then”) and bi-conditional (“if and only if”) statements.
G.LP.4: Develop geometric proofs, including direct proofs, indirect proofs, proofs by contradiction and proofs involving coordinate geometry, using two-column, paragraphs, and flow
charts formats.
Week 8
Sept. 19-23
(4 days)
PIT
G.PL.3: Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent, alternate exterior angles are congruent, and corresponding angles are congruent; when a transversal crosses parallel lines, same side interior angles are supplementary; and
points on a perpendicular bisector of a line segment are exactly those equidistant from the endpoints of the segment.

Continue building on work from previous week.

Explore real-world examples of angle relationships.
G.PL.4: Know that parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Determine if a pair of lines are parallel, perpendicular, or neither by
comparing the slopes in coordinate graphs and in equations. Find the equation of a line, passing through a given point that is parallel or perpendicular to a given line.

Focus on slope and rate of change.

Focus on creating equations of lines from a variety of entry points (two points, x and y intercepts, point and a slope, standard form...)

Students could create a guide for ISTEP+10 for equations of linear functions based on this unit.

PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Corrective Instruction – based on data from Benchmark 1 and other formative assessments
Week 9
Sept.26-30
Unit Assessment
PS: 1, 2, 3, 4, 5, 6, 7, and 8+ (Focus instruction using the Process Standards)
Process Standards for Mathematics (PS):
1. Make sense of problems
and persevere in solving
them.
2. Reason abstractly and
quantitatively.
3. Construct viable
arguments and critique the
reasoning of others.
4. Model with
mathematics.
5. Use appropriate tools
strategically.
6. Attend to precision.
7. Look for and make use
of structure.
Fall Break, Oct 3-17
End of First Quarter
Indianapolis Public Schools
Curriculum and Instruction
8. Look for and express
regularity in repeated
reasoning.