Download 10411_Introductory_Geometry_90

Course Title:
Introductory Geometry
Date Adopted: June 1990
Department:
Mathematics
UC/CSU Requirement: No
Pre-Requisite:
Completion of Algebra I
or consent of Instructor
Fulfills CSF Requirement: No
Length of Course: Two Semesters
Semester Units/Credits: 5
Grade Level:
I.
Fulfills H/S Graduation
Credit As:
Required X Elective
10 - 12
Course Description
Introductory Geometry is a course dealing with the organization of known facts into
formal mathematical structures, the study of various relationships and the
measurement of geometric figures, and review of basic algebraic skills and concepts
including manipulation of algebraic expressions and sentences will also be emphasized.
II.
Rationale
Introductory Geometry aids in the development of certain patterns of good reasoning
and thinking processes. The manipulation and problem solving techniques of
various figures and diagrams have great application to the geometric shapes found
around us.
III.
Goals, Objectives, and Performance Indicators
1.0 GOAL: The student will be able to express relationships between points,
lines, and planes.
1.1
Obj:
The student will be able to define these terms: lies on, lies
in, contains, intersects, intersection space, colinear,
coplanar, segment, ray, midpoint of a segment, and
bisector of a segment.
1.1.1:
Given a diagram, the student will match appropriate
terms to parts of the diagram.
1.1.2:
Given a list of terms from Objective 1.1, the student
will write definitions.
Intro.Geometry - June 1990
1
1.1.3:
1.2
Obj:
Given a set of problems, the student will include
correct terminology in the solutions.
The student will use the terms point, line, and plane.
1.2.1:
Given a list of terms including point, line, and
plane,
the student will single these terms out as
undefined.
1.2.2:
Given a diagram, the student will match point, line
and plane to appropriate parts of the diagram.
2.0 GOAL: The student will be able to classify angles.
2.1
2.2
Obj:
The student will be able to define and use these terms:
angle, half-plane, adjacent angles, vertical angles,
congruent angles, acute angle, right angle, obtuse angle,
complementary angle, supplementary angle, bisector of an
angle, perpendicular lines, perpendicular to a plane, and
perpendicular bisector.
2.1.1:
Given a diagram of various angles and the list of
terms above, the student will be able to match the
terms to the appropriate parts of the correct angles.
2.1.2:
Given the list of terms above, the student will be
able to write definitions.
2.1.3:
Given a problem, the student will use proper
terminology and symbols in its solution.
Obj:
The student will name and identify an angle and its parts
using appropriate terminology.
2.2.1:
2.2.2:
2.2.3:
Given an angle, the student will name the angle
using the angle symbol and (a) a letter for the
vertex,
(b) a number for the vertex where permitted, and/or
(c) three letters.
Given a drawing of an angle, the student will
identify
it as an acute, obtuse, or right angle.
Given a diagram of an angle, the student will label
the sides, vertex, interior, and exterior.
Intro.Geometry - June 1990
2
3.0 GOAL: The student will be able to recognize and use the special angular
relationships between pairs of lines and between lines and
planes.
3.1
3.2
3.3
Obj:
The student will define and use the terms: parallel lines,
parallel planes, transversal, corresponding angles, interior
angles, exterior angles, alternate interior angles, and
alternate exterior angles.
3.1.1:
Given a diagram and the list in Obj. 3.1, the student
will correctly match the terms to parts of the
diagram.
3.1.2:
Given the same list of terms, the students will be
able to define them using precise terminology.
3.1.3:
Given a problem, the student will use proper
terminology and symbols in its solution.
Obj:
The student will recognize the angle relationships that
exist when two lines are cut by a transversal.
3.2.1:
Given a pair of parallel lines cut by a transversal
with angles numbered, the student will correctly
identify the numbered angles' relationships.
3.2.2:
Given parallel lines cut by a transversal with angles
numbered, the student will be able to determine
which pairs of angles are congruent and which
pairs
are supplementary.
3.2.3:
Given parallel lines cut by a transversal with angles
numbered and some of the measures given, the
student will be able to find the measures of the
unknown angles.
Obj:
The student will distinguish between parallel lines and
intersecting lines.
3.3.1:
Given several pairs of lines, the student will be able
to identify which are parallel, which interact, and
which do neither.
3.3.2:
Given a typical classroom, the student will be able
to identify parallel, perpendicular, and intersecting
lines.
Intro.Geometry - June 1990
3
4.0 GOAL: The student will be able to state and apply relationships
regarding angles of polygons.
4.1
4.2
4.3
Obj:
The student will classify polygons and define and use
terms regarding angles and segments.
4.1.1:
Given a set of polygons, the student will be able to
classify them using terms such as regular, convex,
triangle, quadrilateral, pentagon, hexagon, octagon,
and decagon.
4.1.2:
Given a drawing of a polygon, the student will be
able to correctly label the parts using the correct
terms.
4.1.3:
The student will be able to correctly define the
correct terms for the parts of a polygon.
Obj:
The student will know the classifications of triangles
according to sides and angles.
4.2.1:
Given a set of triangles, the student will be able to
use lengths of sides to classify the triangles as
scalene, equilateral, or isosceles.
4.2.2:
Given a set of triangles, the student will be able to
use the measures of angles to classify the triangles
as right, acute, obtuse, or equiangular.
Obj:
The student will know and be able to apply the formulas
for the sum of the measures of the interior and exterior
angles of convex polygons.
4.3.1:
Given a convex polygon, the student will be able to
write the correct formula for the sum of the interior
angles.
4.3.2:
Given a convex polygon, the student will be able to
use the correct formula to solve for the missing
angles.
4.3.3:
Given a triangle, the student will be able to write
formulae for measures of exterior and remote
interior angles.
4.3.4:
Given a triangle, the student will be able to use
Intro.Geometry - June 1990
4
formulae to solve for missing angles.
4.3.5:
Given a convex polygon, the student will be able to
write the sum of the exterior angles or solve for
missing angles.
5.0 GOAL: The student will be able to understand the relations between
triangles and their parts, including triangle inequalities,
corresponding and congruencies, and congruencies of triangles.
5.1
Obj:
5.1.1:
Given a triangle, the student will identify the sides
and angles that are included and the sides and
angles that are opposite.
5.1.2:
Given a right triangle, the student will know the
hypotenuse and legs.
5.1.3:
Given an isosceles triangle, the student will know
which is the base and which is the legs.
5.1.4:
5.2
The student will be able to define these terms: included
and opposite sides and angles; legs and base of an
isosceles triangle; altitudes and medians of all triangles.
Obj:
Given a triangle, the student will be able to identify
the altitudes and medians.
The student will be able to define and identify the six pairs
of corresponding angles and sides, corresponding
triangles and congruent triangles.
5.2.1:
Given a pair of corresponding triangles, the student
will know the corresponding parts.
5.2.2:
Given a pair of congruent triangles, the student will
know the corresponding angles and sides.
5.2.3:
Given two statements about two triangles, the
student will be able to indicate whether or not a
congruency for triangles exists.
6.0 GOAL: The student will be able to understand and utilize characteristics
and properties of various quadrilaterals.
6.1
Obj:
The student will know the definition of the following terms:
parallelogram, rectangle, square, rhombus, trapezoid,
bases, legs, isosceles trapezoid, and median of a
trapezoid.
Intro.Geometry - June 1990
5
6.2
6.1.1:
Given a set of quadrilaterals and the list of terms
above, the student will be able to match the
appropriate terms to the quadrilaterals.
6.1.2:
Given a list of terms from the objective, the student
will be able to write the definitions.
Obj:
The student will be able to compare and contrast special
quadrilaterals according to their properties.
6.2.1:
Given a chart of the special properties of
quadrilaterals, the student will be able to identify
those properties which apply to a given
quadrilateral.
6.2.2:
Given a quadrilateral in which the measures of
certain sides and angles are known, the student will
be able to find the unknown angles or sides.
7.0 GOAL: The student will be able to understand and apply properties of
similar polygons.
7.1
Obj:
7.1.1:
7.2
7.3
Obj:
The student will be able to define and use these terms:
ratio, proportion, and similar polygons.
Given the list of terms from the objective, the
student will know and be able to use the definitions.
The student will be able to apply the properties of
proportions to transform a proportion.
7.2.1:
Given an incomplete proportion, the student will
know how to find the missing term of a proportion.
7.2.2:
Given two or more proportions, the student will
know how to find equivalent proportions.
Obj:
The student will be able to apply similarity of polygons to
solve problems for missing sides or perimeters, and to
determine whether two or more polygons are similar.
7.3.1:
Given the lengths of certain sides of similar
polygons, the student will find the other sides.
7.3.2:
Given the lengths of the sides of a pair of polygons,
the students will state whether or not the polygons
Intro.Geometry - June 1990
6
are similar.
8.0
8.1
8.2
8.3
GOAL:
Obj:
The student will be able to define and use these terms:
radical, Pythagorean theorem, faces, edges, vertices,
tangent, sine, and cosine.
8.1.1:
Given a list of terms from the above objective, the
student will be able to write definitions.
8.1.2:
The student will be able to reduce a list of radicals
to simplified form.
Obj:
The student will be able to explore right triangles by
algebraic applications of the Pythagorean theorem and its
converse.
8.2.1:
Given the lengths of two sides of a right triangle,
the
student will know how to find the length of the third
side.
8.2.2:
Given the lengths of the sides of a triangle, the
student will know how to determine if it is a right
triangle.
Obj:
8.3.1:
8.4
The student will be able to understand and apply
properties of right triangles.
Obj:
The student will explore and apply properties of special
right triangles.
Given the length of one side of a 30-60-90 triangle,
the student will be able to find the lengths of the
remaining sides.
The student will be able to apply these trigonometric
ratios: sine, cosine, and tangent.
8.4.1:
Given the measure of an acute angle and one side
of a right triangle, the student will be able to solve
for the remaining sides.
8.4.2:
Given the length of two sides of a right triangle, the
student will be able to apply the appropriate ratio to
solve for the acute angles and remaining side.
Intro.Geometry - June 1990
7
9.0 GOAL: The student will be able to understand and apply the properties
of circles.
9.1
9.2
Obj:
The student will be able to define and use these terms:
circle, center, interior, exterior, radius, chord, diameter,
secant,
concentric
circles,
sphere,
inscribed,
circumscribed, tangent, point of tangency, common
tangent, common internal tangent, common external
tangent, externally tangent, internally tangent, central
angle, minor arc, semicircle, major arc, congruent circles,
congruent arcs, arc of a chord, distance, inscribed angle,
intercept, tangent segment, secant segment, and external
segment.
9.1.1:
Given the diagram of a circle with its associated
lines and segments, the student will be able to
correctly identify terms listed in the objective.
9.1.2:
Given the terms listed in the objective, the student
will be able to define the terms using precise
terminology.
9.1.3:
Given a problem, the student will be able to
use proper terminology and symbols in its
solution.
Obj:
The student will be able to solve problems involving
circles, lines, and segments associated with circles.
9.2.1:
Given a circle and its associated lines and
segments, the student will know how to apply
theorems relating to diameters, radii, chords,
secants, and tangents to find measures of
segments and angles.
9.2.2:
Given a circle and its associated lines and
segments, the student will know how to apply
theorems relating to measures of arcs and
relating to angles to find the measures of
arcs.
10.0 GOAL: The student will develop proficiency in finding areas and/or
volumes of polygons, circles, and solids.
10.1
Obj:
The student will be able to define and use these terms:
polygonal region, altitude, base, area, center, radius,
apothem, central angle of a regular polygon,
Intro.Geometry - June 1990
8
circumference of a circle, pi, arc length, and sector and
segment of a circle.
10.2
10.1.1:
Given a diagram of a polygon and/or a circle, the
student will be able to identify applicable terms
from the list in Objective 10.1.
10.1.2:
Given the list of terms from Objective 10.1, the
student will be able to define the terms using
precise terminology.
10.1.3:
Given a problem, the student will be able to use the
correct terminology in the solution.
Obj:
The student will solve problems involving polygons,
circles, and solids.
10.2.1:
Given a polygon, the student will be able to find
areas and segments relating to the polygon, using
the appropriate formulae.
10.2.2:
Given a circle, the student will be able to find the
circumference, area, radius, diameter, arc length,
area of a sector, and measure of a segment using
the appropriate formulae.
10.2.3:
Given a circle circumscribed about one of various
polygons, the student will be able to compute the
circumference, radius, and/or apothem.
11.0 GOAL: The student will be able to perform basic geometric
constructions using compass and straightedge.
11.1
Obj:
The student will be able to perform basic geometric
constructions.
11.1.1:
The student will be able to perform the following
constructions:
a.
a segment congruent to a given segment.
b.
an angle congruent to a given angle.
c.
an angle bisector.
d.
a perpendicular to a line segment.
e.
a perpendicular bisector of a line segment.
f.
a perpendicular to a line at a given point on
that line.
g.
a perpendicular to a line at a given point
outside the line.
Intro.Geometry - June 1990
9
11.1.2:
Given a compass and a straightedge, the student
will be able to perform the following advanced
constructions:
a.
a line parallel to a given line through a given
point.
b.
a midpoint of an arc.
c.
the division of a segment into a given number
of congruent segments.
12.0 GOAL: The student will demonstrate proficiency in the use of
coordinate geometry.
12.1
12.2
12.3
Obj:
The student will be able to define and use these terms:
ordered pair, graph, x-axis, y-axis, origin, coordinate axes,
coordinate system, slope, x coordinate, and y coordinate.
12.1.1:
Given the set of terms from the Objective, the
student will be able to draw a coordinate plane and
label the parts.
12.1.2:
Given a set of terms from the objective, the student
will be able to define the terms using precise
terminology.
Obj:
The student will be able to use appropriate formulae to
solve problems involving distance, midpoint, and slope of
a line.
12.2.1:
Given the coordinates of two points, the student will
be able to use appropriate algebraic formulae to
derive the length, midpoint, and slope of the line
segment connecting them.
12.2.2:
Given a set of lines, the student will be able to
identify the slope of each as positive, negative,
zero, or undefined.
Obj:
The student will be able to solve problems involving
equations of lines and graphing of lines.
12.3.1:
Given a linear equation, the student will be able to
graph the equation.
12.3.2:
Given a linear equation, the student will be able to
transform the equation to standard form and to
slope intercept form.
Intro.Geometry - June 1990
10
12.3.3:
Given two points, a point and the slope, or a point
and an intercept, the student will know how to write
the equation and graph the line.
12.3.4:
Given the equation of two lines, the student will be
able to algebraically solve for the intersection of the
two lines.
12.3.5:
Given a slope and two points, the student will find
the equation of the line having the given slope and
find the midpoint of the segment joining the two
points.
13.0 GOAL: The student will be able to understand and use basic forms of
logic.
13.1
13.2
Obj:
The student will be able to define and use these terms:
statements, statement variables, truth table, truth value,
negation of a statement, conjunction, disjunction,
statement forms, double negation, contradiction,
contrapositives, biconditional, conditional, converse,
inverse, and incorrect reasoning from the converse.
13.1.1:
Given a list of terms from the Objective, the student
will be able to match these terms to a list of definitions.
13.1.2:
Given a list of terms from the Objective, the student
will be able to give an example of each term.
13.1.3:
Given a statement, the student will be able to
rephrase it in the conditional form, the converse
form, the inverse form, and the contrapositive form.
Obj:
The student will be able to construct truth tables and use
them to determine whether or not statements are logically
equivalent.
13.2.1:
Given statement forms of various degrees of
difficulty, the student will be able to construct truth
tables.
13.2.2:
Given statement forms, the student will be able to
construct truth tables to determine whether or not
the statement forms are logically equivalent.
Intro.Geometry - June 1990
11
14.0 GOAL: The student will be able to understand and apply in proofs the
basic postulates, theorems, and definitions in geometry and
where applicable, will complete two-column proofs including the
given, the proof, the figure, the statements, and the reasons
using the proper symbols and terminology.
14.1
14.2
14.3
Obj:
The student will review and utilize postulates and
theorems of equality and inequality where applicable in
proofs.
14.1.1:
Given an algebraic statement, the student will be
able to identify the postulate or theorem of equality
or inequality that supports the statement.
14.1.2:
Given a short algebraic proof, the student will be
able to provide the reasons.
Obj:
The student will be able to complete/develop two-column
proofs concerning angle addition; special angles;
bisectors; perpendicular lines; and parallel lines.
14.2.1:
Given a statement to prove regarding betweeness of
segments, the student will be able to complete a
two-column proof.
14.2.2:
Given a statement to prove involving the protractor
postulate and/or the angle addition postulate, the
student will be able to complete a two-column
proof.
14.2.3:
Given a statement to prove concerning angle
bisectors and complementary, supplementary,
vertical congruent, and right angles, the student will
be able to complete a two-column proof.
14.2.4:
Given a statement to prove concerning
perpendicular and parallel lines, the student will be
able to complete a two-column proof.
Obj:
The student will be able to complete/develop proofs
concerning measures of angles in triangles and triangle
congruency.
14.3.1:
Given a statement to prove concerning exterior and
interior angles of a triangle, the student will be able
to develop two-column proofs.
Intro.Geometry - June 1990
12
14.4
14.3.2:
Given two or more non-right triangles, the student
will be able to prove the triangles congruent using
SSS, SAS, ASA and AAS.
14.3.3:
Given two or more right triangles, the student will
recognize that right triangle methods apply and will
be able to prove the triangles congruent using HL.
14.3.4:
Given two or more triangles, the student will be able
to prove that specific angles or sides are congruent
by proving the triangles congruent.
14.3.5:
Given a statement concerning isosceles triangles,
the student will be able to prove congruency using
isosceles triangle theorems.
Obj:
The student will be able to apply congruent to develop
proofs concerning quadrilaterals.
14.4.1:
Given sides, angles, and/or diagonals of a
quadrilateral, the student will be able to prove that it
is a square, rhombus, or a rectangle (as
appropriate).
14.4.2:
Given a statement concerning a rectangle,
parallelogram, rhombus, trapezoid, or square, the
student will be able to complete a two-column proof
concerning congruence of angles and/or sides.
15.0 GOAL: The student will be able to demonstrate proficiency in
performing binary and uniary operations on rational
numbers.
15.1
Obj:
The student will draw and label a number line, and match
any rational number with a point on the line.
15.1.1:
Given a line, the student will establish a number line
by identifying an origin and a scale.
15.1.2:
Given points on a number line and their
coordinates, the student will assign the coordinates
to the points.
15.1.3:
Given any rational number, the student will label the
corresponding point on a number line.
Intro.Geometry - June 1990
13
15.1.4:
Given a rational number in either fraction or
decimal form, the student will convert the
number to the other form.
15.1.5:
15.2
15.3
Obj:
Given a set of numbers, the student will order the
numbers and locate them on the number line.
The student will find the absolute value of any rational
number.
15.2.1:
Given the phrase, "absolute value," the student will
state the definition.
15.2.2:
Given any rational, the student will write the
absolute value.
15.2.3:
Given any numerical expression involving absolute
value, the student will state the definition.
Obj:
The student will add, subtract, multiply, and divide rational
numbers.
15.3.1:
Given any two integers, the
student will
demonstrate the use of a number line to find the
sum.
15.3.2:
Given any numerical expression involving
subtraction of rational numbers, the student will
rewrite the expression using addition.
15.3.3:
Given the relationship between subtraction and
addition of integers, the student will cite examples
and demonstrate the relationship on the number
line.
15.3.4:
Given any two rational numbers, the student will
state whether the sum, product, or quotient is
positive, negative, or zero.
15.3.5:
Given the rules for the sign of the product of two
integers, the student will justify these rules by
proof, examples, or logical explanation.
15.3.6:
Given any two integers, the student will find the
sum, difference, product, and quotient.
Intro.Geometry - June 1990
14
15.4
15.3.7:
Given any two rational numbers, the student will
find the sum, difference, product, and quotient.
15.3.8:
Given any two rational numbers, the student will
find the quotient accurate to a given place value.
Obj:
The student will calculate square and cube roots.
15.4.1:
Given the rational numbers a and b, the student will
determine if a is the square root of b.
15.4.2:
Given any whole number, the student will
approximate the square root of that number to the
nearest hundredth, using a calculator.
16.0 GOAL: The student will be able to recognize and use the properties of
numbers.
16.1
16.2
Obj:
The student will recognize and/or give examples of the
following: commutative, associative, identity, and inverse
properties of addition.
16.1.1:
Given any real number, the student will write its
additive inverse.
16.1.2:
Given a numerical or algebraic example of one of
the properties (commutative, associative, identity,
and inverse) of addition, the student will indicate
the name of the property being demonstrated in the
example.
16.1.3:
Given a property name (commutative, associative,
identity, and inverse property of addition), the
student will give an example using numbers and/or
variables to demonstrate that property.
Obj:
The student will recognize and/or give examples of the
following: commutative, associative, identity and inverse
properties of multiplication.
16.2.1:
Given any non-zero real number, the student will
write its multiplicative inverse.
16.2.2:
Given a numerical or algebraic example of one of
the properties (commutative, associative, identity,
and inverse) of multiplication, the student will
Intro.Geometry - June 1990
15
indicate the name of the property being demonstrated by the example.
16.2.3:
16.3
16.4
16.5
Obj:
Given a property name (commutative, associative,
identity, and inverse property of multiplication), the
student will give an example using numbers and/or
variables to demonstrate that property.
The student will recognize and/or give examples of the
distributive property.
16.3.1:
Given an expression written as a sum, the student
will apply the distributive property and change it to
a product.
16.3.2:
Given an expression written as a product, the
student will apply the distributive property and
change it to a sum.
16.3.3:
Given a numerical or algebraic example of the
distributive property, the student will indicate the
name of the property being demonstrated by the
example.
16.3.4:
Given the distributive property name, the student
will be given an example using numbers and/or
variables to demonstrate that property.
Obj:
The student will recognize and/or give examples of the
following: reflexive, symmetric and transitive properties
of equality.
16.4.1:
Given a numerical or algebraic example of one of
the properties (reflexive, symmetric, and transitive)
of equality, the student will indicate the name of the
property being demonstrated.
16.4.2:
Given a property name (reflexive, symmetric, and
transitive) of equality, the student will give an
example using numbers and/or variables to
demonstrate that property.
Obj:
The student will recognize and/or give examples of the
substitution principle.
Intro.Geometry - June 1990
16
16.6
16.7
16.8
16.5.1:
Given a numerical or algebraic example of the
substitution principle, the student will name the
principle.
16.5.2:
Given the name "substitution principle," the student
will give an example using numbers and/or
variables to demonstrate the principles.
Obj:
The student will recognize and/or give examples of the
multiplication properties of 0 and 1.
16.1.1:
Given the name of a property (property of 0 or 1),
the student will give an example using number
and/or variables to demonstrate that property.
16.1.2:
Given a numerical or algebraic example of the
multiplication property of 0 or 1, the student will
indicate the name of the property being illustrated.
Obj:
The student will recognize and/or give examples of the
addition and multiplication properties of equality.
16.7.1:
Given any linear equation and an equivalent
equation derived through use of either the addition
or multiplication property of equality, the student
will name the property that was used.
16.7.2:
Given the name of the addition or multiplication
property of equality, the student will give an
example illustrating that property.
Obj:
The student will identify properties and definitions used in
each step of a given solution of a linear equation.
16.8.1:
Given a list of definitions and/or properties and a
set of examples, the student will match these two
sets.
17.0 GOAL: The student will be able to evaluate algebraic phrases and give
solution sets of linear algebraic sentences.
17.1
Obj:
The student will recognize variables and replacement sets,
and will evaluate expressions.
17.1.1:
Given an open expression and a replacement set,
the student will find the value of the expression
replacement.
Intro.Geometry - June 1990
17
17.1.2:
17.2
17.3
Obj:
Given a verbal expression in one unknown, the
student will designate a variable and translate it into
an open expression.
The student will find and graph the solution sets of an
open sentence.
17.2.1:
Given an equation or inequality, and a finite
replacement set, the student will determine the
solution set and graph it on the number line.
17.2.2:
Given a sentence involving absolute value, the
student will write an equivalent compound sentence
and graph the solution set.
Obj:
The student will identify equivalent open sentences by
comparing solution sets.
17.3.1:
Given any two equations and a replacement set, the
student will determine if that set is the intersection
of the two equations.
18.0 GOAL: The student will be able to define, identify, and factor
polynomials and perform basic operations with
polynomials.
18.1
18.2
Obj:
The student will use proper terminology and name
polynomials by degree or by number of terms.
18.1.1:
Given any monomial, the student will identify the
coefficient and degree.
18.1.2:
Given any polynomial, the student will correctly
name it, both by degree and by the number of terms.
18.1.3:
Given any polynomial, the student will write it in
descending order of degree.
18.1.4:
Given any polynomial, the student will name any
like terms and simplify the polynomial.
Obj:
The student will add, subtract, multiply or divide algebraic
expressions.
18.2.1:
Given two polynomials, the student will find the
sum or difference.
Intro.Geometry - June 1990
18
18.3
18.2.2:
Given any monomial raised to a power, the student
will simplify.
18.2.3:
Given any two monomials, the student will find the
product.
18.2.4:
Given any two binomials, the student will find the
product.
18.2.5:
Given any binomial, the student will find the square.
18.2.6:
Given any two polynomials with at most three
terms, the student will find the product.
18.2.7:
Given any two monomials, the student will write the
quotient and simplify.
18.2.8:
Given a polynomial and a monomial, the student will
find the quotient and write the answer in simplest
form.
18.2.9:
Given a polynomial and a binomial, the student will
find the quotient and write the answer in simplest
form.
18.2.10:
Given two radical expressions, the student will
change each to a suitable form and add or subtract.
18.2.11:
Given two radical expressions, the student will find
the product or quotient in simplest form.
18.2.12:
Given two rational expressions with like
denominators, the student will add or subtract.
18.2.13:
Given two rational expressions with unlike
denominators, the student will add or subtract.
18.2.14:
Given two or more rational expressions, the student
will find the product and the quotient in simplest
form.
Obj:
The student will identify radical expressions and will write
radicals in simplest form.
18.3.1:
Given any algebraic expression, the student will
identify whether or not it is radical.
Intro.Geometry - June 1990
19
18.3.2:
18.3.3:
18.3.4:
Given any radical expression, the student will name
the radicand, root, and index.
Given a radical expression, the student will identify
whether or not the radicand has a perfect-square
factor.
Given a radical expression, the student will write
the expression in simplest form.
19.0 GOAL: The student will be able to solve linear equations and
inequalities in one variable and graph the solutions on the
number line.
19.1
19.2
Obj:
The student will recognize and use the addition property
of equality.
19.1.1:
Given a list of properties, definitions and theorems
written in words or in algebraic symbols, the
student will identify the addition property of
equality.
19.1.2:
Given equations of the form x + a = b and
x + a + b =c, where a, b, and c are elements of the
set of rational numbers, the student will use the
addition property to solve the equation.
Obj:
The student will recognize and use the multiplication
property of equality.
19.2.1:
Given a list of properties, definitions and theorems
written in words or in algebraic symbols, the
student will identify the multiplication property of
equality.
19.2.2:
Given equations of the form ax = b and
ax + bx = c, where a, b, and c are elements of the
set of rational numbers, the student will solve
equations.
Intro.Geometry - June 1990
20