Download 10449_Geometry_Support_ADOPTION_4-2-08

Course Description
A. COVER PAGE
1. Course Title
9. Subject Area
Geometry Support
a-History/Social Science
2. Transcript Title / Abbreviation
b-English
Geometry Support
c-Mathematics (elective credit)
3. Transcript Course Code / Number
10449
d-Laboratory Science
4. School
e-Language other than English
PHS, LHS
f-Visual & Performing Arts
5. District
X g- Elective
Antelope Valley Union High School District
6. City
10. Grade Level(s)
10th
Lancaster, California
11. Seeking “Honors” Distinction?
7. School / District Web Site
www.avdistrict.org
Yes
8. School Course List Contact
X No
12. Unit Value
0.5 (half year or semester equivalent)
Name: Matthew Winheim
X 1.0 (one year equivalent)
Title/Position: Coordinator,
Curriculum, Instruction and
2.0 (two year equivalent)
Other: _______________________________
Intervention
Phone:
948- 7655
Ext.: 315
E-mail:
[email protected]
13. Was this course previously approved by UC?
Yes
X
No
If yes, check all that apply:
Course reinstated after removal within 3 years. Year removed from list? ________
Same course title?
Yes
No
If no, previous course title? __________________________________
Identical course approved at another school in same district. Which school ? ____________________
Same course title?
Yes
No
If no, course title at other school? __________________________________________________
Alternative course title for course with identical content at this school
Title of previously-approved identical course: ________________________________________
Advanced Placement (AP) or International Baccalaureate (IB) course
Approved UC College Prep (UCCP) Initiative course
Approved P.A.S.S. course
Approved ROP/C course. Name of ROP/C? ______________________________________________
X Other. Explain: Not applying for a-g credit
14. Is this a re-submission of a course that was previously NOT approved by UC?
Is this course modeled after an UC-approved course from another school outside your district?
Yes
Yes
X
X
No
No
If so, which school(s)? ______________________________________________________________________
Geometry Support ADOPTION 4-2-08
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15. Pre-Requisites

Students received at least one passing grade of C or better in Algebra 1.
16. Co-Requisites

Students must be concurrently enrolled in Geometry.
17. Brief Course Description
This is a tutorial math class for sophomore students who are concurrently enrolled in a Geometry class. The course
will provide students:

An opportunity to spend more time on extended topics from their Geometry class to provide enrichment in
course content and necessary support to students at rick of failing the course.

Time to strengthen their prequisite Algebra 1 skills.

Time to prepare for the CAHSEE (which will be taken in March.)
B. COURSE CONTENT
Please refer to instructions
18. Course Goals and/or Major Student Outcomes

Students will improve their mathematical abilities.

Students will improve their Algebra 1 abilities.

Students will receive tutoring in Geometry.

Students will study the CAHSEE Math Standards.
19. Course Objectives


Course teachers will coordinate with Geometry teachers to create math lessons that will assist students in both
the Geometry content and math skills necessary to master that content.
Students will be given instruction and assignments covering the CAHSEE Math Standards.
20. Course Outline
California Standards Covered (Geometry and the standards assessed on the CAHSEE):
Listed below.
21. Texts & Supplemental Instructional Materials
Geometry; Reasoning, Measuring and Applying. McDougall Littell
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22. Key Assignments
Assignments will come from any of the supplemental materials available in the district approved text supplemental
materials and any teacher developed materials that are appropriate in supporting student learning in the core
Geometry class.
Additional assignments pertaining to CAHSEE content as will be of use in this course as appropriate.
23. Instructional Methods and/or Strategies
Primary instruction methods:
- Modeling
- Cooperative learning
- One-on-one tutoring
Other Strategies:
- Breaking topics into small pieces
- Regular, systematic formative assessments
- Using worksheets which give good amounts of practice for
each part of a new standard.
The instructional methods to be used in this course includes re-teaching key concepts, practice activities for current
concepts, and pre-teaching upcoming concepts by laying a foundation for upcoming skills development. These
methods need to coincide with the individual site’s map for Geometry instruction as derived from and coinciding
with the AVHSD curriculum pacing for Geometry. This course is not a study hall. Rather, it is a platform on which
teachers have the resource of an additional period of time for use with their site’s Geometry students that are in
need of support in order to successfully complete the course with a passing mark.
Additional strategies may include instruction on study skills, test taking strategies, organizational management,
note taking, time management, motivational activities, team building, character development, and goal setting: all
with reference to and in support of student success in Geometry and in high school.
24. Assessment Methods and/or Tools
- Regular formative assessments to gage student learning and to assist in lesson planning.
- Practice summative assessments covering several topics/standards.
- Time will be given for assignments to be completed in class.
C. HONORS COURSES ONLY
Please refer to instructions
25. Indicate how this honors course is different from the standard course.
D. OPTIONAL BACKGROUND INFORMATION
Please refer to instructions
26. Context for Course (optional)
Many students who receive grades of D or F in one semester of Algebra 1 during a regular school year are not
successful in Geometry. This course offers students the opportunity to continue to refine their abilities to apply
mathematic problem solving techniques from Algebra while they engage in activities addressing skills and
standards in support of the core curriculum for Geometry.
Students who passed only one semester of Algebra 1 or just passed two semesters of Algebra 1 having less that C’s
in both semesters will be at-risk of not successfully completing Geometry. However, with this support class, and
concurrent enrollment in a Geometry class, students can be successful.
27. History of Course Development (optional)
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California Geometry Standards Covered
The geometry skills and concepts developed in this discipline are useful to all students. Aside from learning these skills
and concepts, students will develop their ability to construct formal, logical arguments and proofs in geometric settings
and problems.
1.0 Students demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and
inductive and deductive reasoning.
2.0 Students write geometric proofs, including proofs by contradiction.
3.0 Students construct and judge the validity of a logical argument and give counterexamples to disprove a statement.
4.0 Students prove basic theorems involving congruence and similarity.
5.0 Students prove that triangles are congruent or similar, and they are able to use the concept of corresponding parts of
congruent triangles.
6.0 Students know and are able to use the triangle inequality theorem.
7.0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of
quadrilaterals, and the properties of circles.
8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface
area of common geometric figures.
9.0 Students compute the volumes and surface areas of prisms, pyramids, cylinders, cones, and spheres; and students commit to
memory the formulas for prisms, pyramids, and cylinders.
10.0 Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms,
and trapezoids.
11.0 Students determine how changes in dimensions affect the perimeter, area, and volume of common geometric figures and
solids.
12.0 Students find and use measures of sides and of interior and exterior angles of triangles and polygons to classify figures and
solve problems.
13.0 Students prove relationships between angles in polygons by using properties of complementary, supplementary, vertical,
and exterior angles.
14.0 Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine distance and find missing lengths of sides of right triangles.
16.0 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.
17.0 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.
18.0 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.
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
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20.0 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.
21.0 Students prove and solve problems regarding relationships among chords, secants, tangents, inscribed angles, and inscribed
and circumscribed polygons of circles.
22.0 Students know the effect of rigid motions on figures in the coordinate plane and space, including rotations, translations,
and reflections.
California State Board of Education
1430 N Street, Suite #5111
Sacramento, CA 95814
http://www.cde.ca.gov/be/st/ss/mthgeometry.asp
CAHSEE Standards Covered
Grade 6—Statistics, Data Analysis, and Probability
1.0
Students compute and analyze statistical measurements for data sets:
1.1 Compute the range, mean, median, and mode of data sets.
2.0
Students use data samples of a population and describe the characteristics and
limitations of the samples:
2.5 Identify claims based on statistical data and, in simple cases, evaluate the validity of the claims.
3.0
Students determine theoretical and experimental probabilities and use these to make
predictions about events:
3.1 Represent all possible outcomes for compound events in an organized way (e.g., tables, grids, tree
diagrams) and express the theoretical probability of each outcome.
3.3 Represent probabilities as ratios, proportions, decimals between 0 and 1, and percentages between 0 and
100 and verify that the probabilities computed are reasonable; know that if P is the probability of an event,
1- P is the probability of an event not occurring.
3.5 Understand the difference between independent and dependent events.
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Grade 7—Number Sense
1.0
Students know the properties of, and compute with, rational numbers expressed in a
variety of forms:
1.1 Read, write, and compare rational numbers in scientific notation (positive and negative powers of 10)
with approximate numbers using scientific notation.
1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and
take positive rational numbers to whole-number powers.
1.3 Convert fractions to decimals and percents and use these
representations in estimations, computations, and applications.
1.6 Calculate the percentage of increases and decreases of a quantity.
1.7 Solve problems that involve discounts, markups, commissions, and profit, and compute simple and
compound interest.
2.0
Students use exponents, powers, and roots, and use exponents in working.
2.1 Understand negative whole-number exponents. Multiply and divide expressions involving exponents
with a common base.
2.2 Add and subtract fractions by using factoring to find common denominators.
2.3 Multiply, divide, and simplify rational numbers by using exponent rules.
2.4 Use the inverse relationship between raising to a power and extracting the root of a perfect square
integer; for an integer that is not square, determine without a calculator the two integers between which its
square root lies and explain why.
2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance
of the number from zero on a number line; and determine the absolute value of real numbers.
Grade 7—Algebra and Functions
1.0
Students express quantitative relationships by using algebraic terminology,
expressions, equations, inequalities, and graphs:
1.1 Use variables and appropriate operations to write an expression, an equation, an inequality, or a system
of equations or inequalities that represents a verbal description (e.g., three less than a number, half as
large as area A).
1.2 Use the correct order of operations to evaluate algebraic expressions such as
3(2 x  5) 2 .
1.5 Represent quantitative relationships graphically and interpret the meaning of a specific part of a graph
in the situation represented by the graph
2.0
Students interpret and evaluate expressions involving integer powers and simple
roots:
2.1 Interpret positive whole-number powers as repeated multiplication and negative whole-number powers
as repeated division or multiplication by the multiplicative inverse. Simplify and evaluate expressions that
include exponents.
Geometry Support ADOPTION 4-2-08
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2.2 Multiply and divide monomials; extend the process of taking powers and extracting roots to monomials
when the latter results in a monomial with an integer exponent.
3.0
Students graph and interpret linear and some nonlinear functions:
3.1 Graph functions of the form y= nx2 and y= nx3 and use in solving problems.
3.3 Graph linear functions, noting that the vertical change (change in y-value) per unit of horizontal change
(change in x-value) is always the same and know that the ratio (“rise over run”) is called the slope of a
graph.
3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet
to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of a line
equals the quantities.
4.0
Students solve simple linear equations and inequalities over the rational numbers:
4.1 Solve two-step linear equations and inequalities in one variable over the rational numbers, interpret the
solution or solutions in the context from which they arose, and verify the reasonableness of the results.
4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
Grade 7—Measurement and Geometry
1.0
Students choose appropriate units of measure and use ratios to convert within and
between measurement systems to solve problems:
1.1 Compare weights, capacities, geometric measures, times, and temperatures within and between
measurement systems (e.g., miles per hour and feet per second, cubic inches to cubic centimeters).
1.2 Construct and read drawings and models made to scale.
1.3 Use measures expressed as rates (e.g., speed, density) and measures expressed as products (e.g., persondays) to solve problems; check the units of the solutions; and use dimensional analysis to check the
reasonableness of the answer.
2.0
Students compute the perimeter, area, and volume of common geometric objects
and use the results to find measures of less common objects. They know how
perimeter, area and volume are affected by changes of scale:
2.1 Use formulas routinely for finding the perimeter and area of basic two-dimensional figures and the
surface area and volume of basic three-dimensional figures, including rectangles, parallelograms,
trapezoids, squares, triangles, circles, prisms, and cylinders.
2.2 Estimate and compute the area of more complex or irregular two- and three-dimensional figures by
breaking the figures down into more basic geometric objects.
2.3 Compute the length of the perimeter, the surface area of the faces, and the volume of a threedimensional object built from rectangular solids. Understand that when the lengths of all dimensions are
multiplied by a scale factor, the surface area is multiplied by the square of the scale
factor and volume is multiplied by the cube of the scale factor.
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2.4 Relate the changes in measurement with a change of scale to the units used (e.g., square inches, cubic
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feet) and to conversions between units (1square foot = 144 square inches or [1 ft ] = [144 in ], 1 cubic
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3
inch is approximately 16.38 cubic centimeters or [1 in ] = [16.38 cm ]).
3.0
Students know the Pythagorean theorem and deepen their understanding of plane
and solid geometric shapes by constructing figures that meet given conditions and
by identifying attributes of figures:
3.2 Understand and use coordinate graphs to plot simple figures, determine lengths and areas related to
them, and determine their image under translations and reflections.
3.3 Know and understand the Pythagorean theorem and its converse and use it to find the length of the
missing side of a right triangle and the lengths of other line segments and, in some situations, empirically
verify the Pythagorean theorem by direct measurement.
3.4 Demonstrate an understanding of conditions that indicate two geometrical figures are congruent and
what congruence means about the relationships between the sides and angles of the two figures.
Grade 7—Statistics, Data Analysis, and Probability
1.0
Students collect, organize, and represent data sets that have one or more variables
and identify relationships among variables within a data set by hand and through
the use of an electronic spreadsheet software program:
1.1 Know various forms of display for data sets, including a stem-and-leaf plot or box-and-whisker plot;
use the forms to display a single set of data or to compare two sets of data.
1.2 Represent two numerical variables on a scatterplot and informally describe how the data points are
distributed and any apparent relationship that exists between the two variables (e.g., between time spent on
homework and grade level).
Grade 7—Mathematical Reasoning
1.0
Students make decisions about how to approach problems:
1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information,
identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical
question or problem posed.
2.0
Students use strategies, skills, and concepts in finding solutions:
2.1 Use estimation to verify the reasonableness of calculated results.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic
and algebraic techniques.
2.4 Make and test conjectures by using both inductive and deductive reasoning.
3.0
Students determine a solution is complete and move beyond a particular problem by
generalizing to other situations:
3.3 Develop generalizations of the results obtained and the strategies used and apply them to new problem
situations.
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Algebra I
2.0
Students understand and use such operations as taking the opposite, finding the reciprocal, and taking a
root, and raising to a fractional power. They understand and use the rules of exponents.
3.0
Students solve equations and inequalities involving absolute values.
4.0
Students simplify expressions before solving linear equations and inequalities in one variable, such as
3(2x – 5)+ 4(x – 2) = 12.
5.0
Students solve multistep problems, including word problems, involving linear equations and linear
inequalities in one variable and provide justification for each step.
6.0
Students graph a linear equation and compute the x- and y-intercepts (e.g., graph 2 x + 6
y = 4). They are also able to sketch the region defined by linear inequality (e.g., they
sketch the region defined by 2x + 6y < 4).
7.0
Students verify that a point lies on a line, given an equation of the line. Students are able
to derive linear equations by using the point-slope formula.
8.0
Students understand the concepts of parallel lines and perpendicular lines and how their
slopes are related. Students are able to find the equation of a line perpendicular to a given
line that passes through a given point.
9.0
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.
10.0
Students add, subtract, multiply, and divide monomials and polynomials. Students solve
multistep problems, including word problems, by using these techniques.
15.0
Students apply algebraic techniques to solve rate problems, work problems, and percent
mixture problems.
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Written by:
Matthew Winheim
Reviewed by:
Bob Patton
Murray Miller
Kathy Echegary
Paulette Arispe
Christine Wilkins
Lance Pierson
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