Download Scope_and_Sequence-Geometry (CPM)

San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 1
CA
Content
CPM Chapter
Pacing Standard
Support Resources
(Standard Component)
and Section
Number
o The following standards are embedded throughout the text as regular parts of solutions to problems (see
www.cpm.org/pdfs/standards/GC_CA_Content_Correlations.pdf)
o Students should focus on justifying why statements are true during the first semester.
o Students should focus on formalizing their justifications so that they become proofs during the second
semester.
Embed
1.0*
• Students demonstrate understanding by identifying and giving examples of undefined terms, Embedded in lessons
and exercises.
axioms, theorems, and inductive and deductive reasoning.
Embed
2.0*
• Students write geometric proofs, including proofs by contradiction.
Embed
3.0*
• Students construct and judge the validity of a logical argument and give counterexamples to
disprove a statement.
Weeks
8.0*
1.1.1 – 1.1.5
• Students solve problems involving perimeter and area of common
1 -3
1.2.1 – 1.2.5
geometric figures.
1.3.1.
– 1.3.3
10.0*
• Students compute areas of polygons, including rectangles.
11.0
• Students determine how changes in dimensions affect the perimeter and
area of common geometric figures.
12.0*
• Students find and use measures of sides and of interior angles of
triangles and polygons to classify figures.
22.0*
• Students know the effect of rigid motions on figures in the coordinate
plane and space, including rotations, translations, and reflections.
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 1
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 1
Pacing
Weeks
4-5
Weeks
6-7
Weeks
8-10
CA
Standard
Number
4.0*
7.0*
•
•
12.0*
13.0
•
•
1.0*
•
6.0
8.0*
•
•
10.0*
•
14.0**
15.0
•
•
4.0*
5.0
•
•
Content
(Standard Component)
CPM Chapter
and Section
Support Resources
Appendix A
Students prove (justify) basic theorems involving congruence.
2.1.1 – 2.1.5
Students prove (justify) and use theorems involving the properties of
parallel lines cut by a transversal.
Students find measures of interior and exterior angles of triangles.
Students prove (justify) relationships between angles in polygons
(triangles) by using properties of complementary, supplementary,
vertical, and exterior angles.
2.2.1 – 2.2.4
Students demonstrate understanding by identifying and giving examples
2.3.1 – 2.3.3
of axioms and theorems.
Appendix B
Students know and are able to use the triangle inequality theorem.
Students know, derive, and solve problems involving the perimeter and
area of common geometric figures.
Students computer areas of polygons, including rectangles, scalene
triangles, equilateral triangles, parallelograms, and trapezoids.
**Students prove the Pythagorean Theorem (geometrically).
Students use the Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles.
Week 9 - 10 Benchmark #1(emphasizes: 7.0, 8.0,10.0, 13.0, 15.0, 22.0)
3.1.1 – 3.1.4
Students prove (justify) basic theorems involving similarity.
3.2.1 – 3.2.6
Students prove that triangles are similar.
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 2
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 1
Pacing
Week
11
Weeks
12-14
Week
15
Week
16
Weeks
17-18
CA
Standard
Number
18.0*
Content
(Standard Component)
CPM Chapter
and Section
Support Resources
•
4.1.1 – 4.1.5
Students know the definitions of the basic trigonometric functions
defined by the angles of a right triangle.
19.0*
• Students use trigonometric functions to solve for an unknown length of
a side of a right triangle, given an angle and a length of a side.
18.0*
5.1.1 – 5.1.4
• Students know the definitions of the basic trigonometric functions
5.2.1 – 5.2.2
defined by the angles of a right triangle.
5.3.1 – 5.3.3
19.0*
• Students use trigonometric functions to solve for an unknown length of
5.3.5
a side of a right triangle, given an angle and a length of a side.
20.0
• Students know and are able to use angle and side relationships in
problems with special right triangles, such as 30-60-90 triangles and 4545-90 triangles.
5.0
6.1.1 – 6.1.4
• Students prove that triangles are congruent.
• Students are able to use the concept of corresponding parts of congruent
triangles.
7.0*
7.1.1 – 7.1.4
• Students use theorems involving properties of circles.
8.0*
• Students solve problems involving perimeter, circumference and area of
common geometric figures.
12.0*
• Students use measures of sides and of interior angles of polygons to
classify figures and solve problems.
Week 17 & 18 BENCHMARK #2(emphasizes 4.0, 5.0, 18.0, 19.0, 20.0)
1.0*, 2.0*, 3.0*, 4.0*, 5.0, 6.0, 7.0*, 8.0*, 10.0*, 11.0, 12.0*, 13.0, 15.0, 18.0*, 19.0*, 20.0, 22.0*
Review and take Final Exams
END OF SEMESTER 1
Assessment Resources
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 3
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
CA
Content
CPM Chapter
Pacing Standard
Support Resources
(Standard Component)
and Section
Number
o The following standards are embedded throughout the text as regular parts of solutions to problems (see
www.cpm.org/pdfs/standards/GC_CA_Content_Correlations.pdf)
o Students should focus on justifying why statements are true during the first semester.
o Students should focus on formalizing their justifications so that they become proofs during the second
semester.
Embed
1.0*
• Students demonstrate understanding by identifying and giving examples of undefined terms, Embedded in lessons
and exercises.
axioms, theorems, and inductive and deductive reasoning.
Embed
2.0*
• Students write geometric proofs, including proofs by contradiction.
Embed
3.0*
• Students construct and judge the validity of a logical argument and give counterexamples to
disprove a statement.
Weeks
4.0*
7.2.1 – 7.2.6
• Students prove basic theorems involving congruence.
1-2
5.0
• Students are able to use the concept of corresponding parts of congruent
triangles.
7.0*
• Students prove and use theorems involving properties of quadrilaterals.
12.0*
• Students find and use measures of sides of interior and exterior triangles
and polygons to classify figures and solve problems.
13.0
• Students prove relationships between angles in polygons (triangles and
quadrilaterals) by using properties of complementary, supplementary,
vertical, and exterior angles
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 4
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
Pacing
Week 3
Weeks
4-5
Week 6
CA
Standard
Number
7.0*
12.0*
•
•
17.0*
•
8.0*
•
10.0*
11.0
•
•
12.0*
•
13.0
•
7.0*
8.0*
•
•
Content
(Standard Component)
Students prove and use theorems involving properties of quadrilaterals.
Students find and use measures of sides of interior and exterior triangles
and polygons to classify figures and solve problems.
Students prove theorems by using coordinate geometry, including the
midpoint of a line segment, the distance formula, and various forms of
equations of lines.
Students know, derive, and solve problems involving the perimeter and
area of common geometric figures.
Students compute areas of polygons.
Students determine how changes in dimensions affect the perimeter and
area of common geometric figures.
Students find and use measures of sides and of interior and exterior
angles of polygons to classify figures and solve problems.
Students prove relationships between angles in polygons by using
properties of exterior angles.
Students prove and use theorems involving the properties of circles.
Students know, derive, and solve problems involving the perimeter,
circumference and area of common geometric figures.
CPM Chapter
and Section
Support Resources
7.3.1 – 7.3.3
8.1.1 – 8.1.5
8.2.1 – 8.2.2
8.3.1 – 8.3.3
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 5
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
CA
Standard
Number
8.0*
•
9.0
•
11.0
•
Week 8
16.0*
•
Weeks
9-10
7.0*
21.0*
•
•
Weeks
11-13
8.0*
•
9.0
•
21.0*
•
Pacing
Week 7
Content
(Standard Component)
CPM Chapter
and Section
Support Resources
9.1.1 – 9.1.5
Students know, derive, and solve problems involving the volume, lateral
area, and surface area of common geometric figures.
Students compute the volumes and surface areas of prisms and
cylinders.
Students determine how changes in dimensions affect the volume of
solids.
Week 8 - 10 Benchmark #3 (emphasizes 8.0, 9.0, 10.0, 12.0, 17.0)
9.2.1 – 9.2.4
Students perform basic constructions with a straightedge and compass,
such as angle bisectors, perpendicular bisectors, and the line parallel to a
given line through a point off the line.
10.1.1 – 10.1.5
Students prove and use theorems involving the properties of circles.
10.3.1
Students prove and solve problems regarding relationships among
chords, tangents (right angle to diameter/radius),and inscribed angles.
11.1.1 – 11.1.5
Students know, derive, and solve problems involving the volume, lateral
11.2.1 – 11.2.3
area, and surface area of common geometric figures.
Appendix C
Students compute the volumes and surface areas of pyramids, cones and
spheres.
Students prove and solve problems regarding relationships among
chords, tangents, secants and inscribed and circumscribed polygons of
circles.
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 6
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
Pacing
Week
14
CA
Standard
Number
Content
(Standard Component)
1.0*
•
2.0*
3.0*
•
•
4.0*
5.0
•
•
7.0*
•
8.0*
•
10.0*
•
12.0*
•
13.0
•
CST Review
Students demonstrate understanding by identifying and giving examples
of undefined terms, axioms, theorems, and inductive and deductive
reasoning.
Students write geometric proofs, including proofs by contradiction.
Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
Students prove basic theorems involving congruence and similarity.
Students prove that triangles are congruent or similar, and they are able
to use the concept of corresponding parts of congruent triangles.
Students prove and use theorems involving the properties of parallel
lines cut by a transversal, the properties of quadrilaterals, and the
properties of circles.
Students know, derive, and solve problems involving perimeter,
circumference, area, volume, lateral area, and surface area of common
geometric figures.
Students compute areas of polygons, including rectangles, scalene
triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.
Students find and use measures of sides and of interior and exterior
angles of triangles and polygons to classify figures and solve problems.
Students prove relationships between angles in polygons by using
properties of complementary, supplementary, vertical, and exterior
angles.
CPM Chapter
and Section
Support Resources
Geometry Connections Extra Practice
Geometry Extra Practice Topics
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 7
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
14.0*
Pacing
Week
14
(cont.)
•
CA
Standard
Number
15.0
•
16.0*
•
17.0*
•
18.0*
•
19.0*
•
20.0
•
21.0*
•
22.0*
•
Students prove the Pythagorean theorem.
Content
(Standard Component)
Students use the Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles.
Students perform basic constructions with a straightedge and compass,
such as angle bisectors, perpendicular bisectors, and the line parallel to a
given line through a point off the line.
Students prove theorems by using coordinate geometry, including the
midpoint of a line segment, the distance formula, and various forms of
equations of lines and circles.
Students know the definitions of the basic trigonometric functions
defined by the angles of a right triangle. They also know and are able to
use elementary relationships between them. For example, tan(x) =
sin(x)/cos(x), (sin (x))2 + (cos (x))2 = 1.
Students use trigonometric functions to solve for an unknown length of
a side of a right triangle, given an angle and a length of a side.
Students know and are able to use angle and side relationships in
problems with special right triangles, such as 30°, 60°, and 90° triangles
and 45°, 45°, and 90° triangles.
Students prove and solve problems regarding relationships among
chords, secants, tangents, inscribed angles, and inscribed and
circumscribed polygons of circles.
Students know the effect of rigid motions on figures in the coordinate
plane and space, including rotations, translations, and reflections.
CPM Chapter
and Section
Support Resources
Geometry Connections Extra Practice
Geometry Extra Practice Topics
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 8
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
Pacing
Weeks
15-16
CA
Standard
Number
Content
(Standard Component)
1A 2.0*
•
1A 4.0*
•
1A 5.0*
•
1A 6.0*
•
1A 9.0*
•
1A 11.0
•
1A 14.0*
•
Pre-Algebra 2 Skill Review
Students understand and use such operations as taking the opposite,
finding the reciprocal, taking a root, and raising to a fractional power.
They understand and use the rules of exponents.
Students simplify expressions prior to solving linear equations and
inequalities in one variable, such as 3(2x-5) + 4(x-2) = 12.
Students solve multistep problems, including word problems, involving
linear equations and linear inequalities in one variable and provide
justification for each step.
Students graph a linear equation and compute the x- and y- intercepts
(e.g., graph 2x + 6y = 4). They are also able to sketch the region defined
by linear inequality (e.g., they sketch the region defined by 2x + 6y < 4).
Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically. Students
are able to solve a system of two linear inequalities in two variables and
to sketch the solution sets.
Students apply basic factoring techniques to second-and simple thirddegree polynomials. These techniques include finding a common factor
for all terms in a polynomial, recognizing the difference of two squares,
and recognizing perfect squares of binomials.
Students solve a quadratic equation by factoring or completing the
square.
CPM Chapter
and Section
Support Resources
Geometry Connections Extra Practice
Algebra Extra Practice Topics
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 9
Secondary Education
Revised 8/23/2012
San Bernardino City Unified School District
Scope and Sequence
High School Geometry – CPM
Semester 2
1A 21.0*
•
Students graph quadratic functions and know that their roots are the xintercepts.
Pacing
CA
Standard
Number
Weeks
17-18
Standards 1.0 – 22.0
Review and take Final Exams
Content
(Standard Component)
CPM Chapter
and Section
Support Resources
BENCHMARK #6
Assessment Resources
END OF SEMESTER 2
Mathematics Framework for California Public Schools, California Department of Education, © 2006
Geometry Connections, Version 3.0, CPM Educational Program, © 2008
1A = Algebra 1 Standard
* Key Standard
** Not an essential standard component.
Page 10
Secondary Education
Revised 8/23/2012