Download 10407_Pre_Algebra_90

Course Title:
Pre-Algebra 9 - 12
Date Adopted: June 1990
Department: Mathematics
UC/CSU Requirement: No
Pre-Requisite:
Fulfills CSF Requirement: No
Eighth Grade Placement
Test Scores
Length of Course: Two Semesters
Fulfills H/S Graduation
Credit As:
Required X Elective
Semester Units/Credits: 5
Grade Level: 9 - 12
I.
Course Description
This course maintains and strengthens skills previously developed and increases
the student's ability to solve abstract and practical problems, especially those
involving multiple steps. The student is introduced to new topics in number theory
and elementary algebra in preparation for Algebra I.
II.
Rationale
It is essential for the student to be proficient in arithmetic and its use in solving
problems, to be acquainted with fundamental concepts of algebra, and to be
comfortable solving problems on paper, with a calculator, and mentally.
III.
Goals, Objectives, and Performance Indicators
1.0 GOAL:
The student will be able to understand basic ideas and
terminology concerning sets.
1.1
Obj:
The student will define and identify terms relating to sets
and use proper set notation.
***1.1.1:
Given the terms: set, subset, intersection, union,
equivalent, equal, empty, null disjoint, the student
will know the definitions.
***1.1.2:
Given any set named in rule form, the student will
rename the set by writing it in list form.
Given a set of at most four members, the student
will list all or an indicated number of subsets of the
given set.
***1.1.3:
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1.2
***1.1.4:
Given two sets, the student will indicate whether the
sets are equal, equivalent, or neither.
***1.1.5:
Given two sets, the student will indicate whether the
sets are disjoint or intersecting.
***1.1.6:
Given at least two sets, the student will write their
union.
***1.1.7:
Given at least two sets, the student will write their
intersection.
Obj:
The student will identify the subsets of the set of real
numbers (naturals, wholes, integers, rationals, and
irrationals) and determine to which subsets any real
number belongs.
**1.2.1:
Given two or more sets, the student will show the
relationship of the sets using the appropriate
symbols of set notation.
*1.2.2: Given any set of numbers, the student will describe or list
the members of the set.
2.0 GOAL:
The student will be able to find the sum, difference, product, or
quotient of rational numbers, choosing an appropriate method of
calculation.
2.1
Obj:
The student will add rational numbers.
*2.1.1: Given at least two integers, the student will find the sum.
*2.1.2: Given at least two rational numbers, the student will write
the sum.
*2.1.3: Given any two integers, the student will demonstrate the
use of a number line to find the sum.
2.2
Obj:
The student will subtract rational numbers.
**2.2.1:
Given any expression involving subtraction of
rational numbers, the student will rewrite the
sentence as addition.
*2.2.2: Given any two rational numbers, the student will find the
difference.
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2.3
Obj:
The student will multiply rational numbers.
*2.3.1: Given any two integers, the student will find the product.
2.4
*2.3.2:
Given any two rational numbers, the student will
state whether the product is positive, negative, or
zero.
*2.3.3:
Given any two rational numbers, the student will
find the product.
Obj:
The student will divide rational numbers.
**2.4.1:
Given..., the student will give the reciprocal
multiplicative inverse for any rational number.
**2.4.2:
Given any two integers, the student will find the
quotient.
*2.4.3: Given any two rational numbers, the student will state
whether the quotient is positive, negative, or zero.
2.5
2.6
**2.4.4:
Given any two rational numbers, the student will
find the quotient accurately to a given place value.
**2.4.5:
Given a number, the student will test for divisibility
by 2, 3, 4, 5, 6, 9, and 10.
Obj:
The student will simplify numerical expressions, using the
order of operations.
**2.5.1:
Given any numerical expression without symbols of
inclusion, the student will use the order of
operations to simplify it.
**2.5.2:
Given any numerical expression with symbols of
inclusion, the student will use the order of
operations to simplify it.
Obj:
The student will evaluate algebraic expressions.
*2.6.1: Given an expression in one variable and replacement
value, the student will evaluate the expression.
**2.6.1:
Given an expression in two or more variables and
replacement values, the student will evaluate the
expression.
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2.7
Obj:
The student will find the absolute value of any rational
value.
*2.7.1: Given any integer, the student will write the absolute
value.
*2.7.2: Given any rational number, the student will write the
absolute value.
3.0 GOAL:
The student will be able to recognize the various forms for
representing rational numbers.
3.1
Obj:
The student will demonstrate an understanding of place
value of the decimal number system.
*3.1.1: Given any decimal number, the student will be able to
identify the place value of any digit.
*3.1.2: Given a decimal numeral, expressed in digits or words,
the student will write it in the other form.
**3.1.3:
3.2
Given any decimal, the student will write the
number in expanded notation using exponents.
Obj:
The student will apply knowledge of place value to round
any decimal numeral to a given place value.
*3.2.1: Given any decimal, the student will round the numeral to
the indicated place value.
*3.2.2: Given any rational number, the student will express the
number as a decimal rounded to the indicated place
value.
*3.2.3: Given any problem using decimal numeral, the student
will round to the appropriate place when making an
estimate.
3.3
Obj:
The student will recognize the various forms for
representing a rational number and will convert among
fraction, decimal, and percent equivalents.
**3.3.1:
Given any terminating decimal, the student will
write the number in simplified fractional form.
**3.3.2:
Given any repeating decimal, the student will write
the number in simplified fractional form.
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*3.3.3: Given any fraction, the student will convert to both
decimal and percent.
*3.3.4: Given any fraction, the student will convert to both
decimal and percent.
*3.3.5: Given any percent, the student will convert to both
fraction and decimal.
*3.3.6: Given any fraction, the student will determine if its
decimal will be repeating or terminating.
3.4
3.5
Obj:
The student will write any numerical expression in
simplest form by choosing the appropriate numbers (in
decimal or fraction form) to use in the situation.
**3.4.1:
Given any numerical expression involving rational
numbers, the student will translate the expression
into an equivalent expression (using decimal form
or using fraction form) which suits the given
situation.
**3.4.2:
Given a problem, the student will determine the
most appropriate form of numbers to use.
Obj:
The student will use the order relations to compare
rational numbers.
*3.5.1: Given at least two fractions, the student will write them in
increasing or decreasing order.
**3.5.2:
3.6
Obj:
Given at least two rational numbers in any form, the
student will change the numbers to the same form
and write the numbers in increasing or decreasing
order.
The student will draw and label a number line, and locate
rational numbers.
**3.6.1:
Given a unit distance, the student will draw and
label a number line, indicating the origin and a clear
scale.
*3.6.2: Given points on a number line, and their coordinates, the
student will assign the coordinates to the points.
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*3.6.3: Given any rational number, a student will label the
corresponding point on a number line.
*3.6.4: Given a set of numbers, the student will order those
numbers and locate them on the number line.
4.0 GOAL:
The student will be able to identify and use properties of rational
numbers and apply the properties to simplify numerical
calculations.
4.1
Obj:
4.2
4.3
The student will recognize and/or give examples of the
following: closure, commutative, associate, identity and
inverse properties of addition.
**4.1.1:
Given any rational number, the student will write its
additive inverse.
***4.1.2:
Given a numerical or algebraic example of one of
the properties, the student will indicate the property
being demonstrated by the examples.
***4.1.3:
Given a property, the student will given an example
using numbers and/or variables demonstrating that
property.
Obj:
The student will recognize and/or give examples of the
following: closure, commutative, associative, identity and
inverse properties of multiplication.
**4.2.1:
Given any rational number, the student will write its
multiplicative inverse.
**4.2.2:
Given a numerical or algebraic example of one of
the properties, the student will indicate the property
being demonstrated by the example.
***4.2.3:
Given the property name, the student will give an
example using numbers and/or variables
demonstrating that property.
Obj:
The student will recognize and/or give examples of the
distributive property.
**4.3.1:
Given an example, the student will identify the
distributive property being illustrated.
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*4.3.2: Given an expression of the form ax + bx, the student will
apply the distributive property.
*4.3.3: Given the property name, the student will give an example
using numbers and/or variables.
*4.3.4: Given an expression of the form x(z + b), the student will
use the distributive property to simplify.
4.4
Obj:
The student will recognize and/or give examples of the
multiplicative property of 0 and 1.
*4.4.1: Given an example of these properties, the student will fill
in the missing parts.
*4.4.2: Given the name of the property, the student will give and
example demonstrating that property.
*4.4.3: Given a numerical or algebraic example of this property,
the student will indicate the property being
demonstrated.
4.5
4.6
Obj:
The student will recognize and/or give examples of the
addition and multiplication properties of equality.
**4.5.1:
Given a numerical or algebraic example of these
properties, the student will indicate the property
being demonstrated.
**4.5.2:
Given a property, the student will give an example
using numbers and/or variables demonstrating that
property.
Obj:
The student will identify properties and definitions used in
each step of a given solution of a linear equation.
**4.6.1:
Given a list of steps, the student will identify each
property.
*4.6.2: Given a solution to a linear equation, the student will
indicate the property being illustrated.
5.0 GOAL: The student will be able to find the square roots of whole
numbers, fractions, and decimals, whose square roots are
rational and will be able to estimate square roots with integral
imperfect square radicands as a check of results obtained with
calculators.
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5.1
Obj:
The student will understand and use terminology relating
squares and square roots.
*5.1.1: Given expressions written as radicals, the student will
identify the radicand and radical sign in the
expression.
*5.1.2: Given a number, the student will determine if the number
is rational or irrational.
*5.1.3: Given two rational numbers, the student will verify that
one number is a root of another.
5.2
Obj:
The student will estimate and evaluate irrational square
root.
*5.3.1: Given any rational number, the student will locate it
between two perfect squares.
6.0 GOAL: The student will be able to use prime factorization to find factors,
greatest common factor, and least common multiple of a set of
whole numbers.
6.1
Obj:
The student will find the greatest common factor of two or
more whole numbers.
*6.1.1: Given any whole number greater than one, the student will
determine if the number is prime or composite.
*6.1.2: Given the prime factorization of two or more whole
numbers, the student will find the least common
multiple.
7.0 GOAL: The student will be able to use exponential notation with integral
exponents.
7.1
Obj:
The student will evaluate numerical expressions involving
integral exponents.
*7.1.1: Given any number, the student will raise it to a given
power.
*7.1.2: Given two or more factors with like bases and using the
product of powers property, the student will find the
product.
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7.2
Obj:
The student will convert whole numbers between base-ten
notation and scientific notation.
*7.2.1: Given two or more factors that are powers of 10, the
student will solve using mental calculations.
**7.2.2:
Given any number, the student will write it in
scientific notation.
**7.2.3:
7.4
Obj:
Given any number written in scientific notation, the
student will write it as a decimal number.
The student will multiply numbers represented in scientific
notations.
**7.4.1:
Given two decimal numbers, the student will
multiply; and then convert factors and product to
scientific notation to see the relationship.
**7.4.2:
Given two numbers written in scientific notation,
the student will multiply in that form.
8.0 GOAL: The student will be able to choose an appropriate unit of
measure and use the necessary formulas to find the
circumference or perimeter, areas of polygons and circles, and
the volumes and surface areas of selected solids.
8.1
Obj:
The student will calculate and label with appropriate units
the perimeter of any polygon or circumference of any
circle.
*8.1.1: Given the radius or diameter of a circle in integers,
fractions or decimal numbers, the student will
calculate the circumference.
*8.1.2: Given the circumference of a circle, the student will
calculate the radius or diameter.
*8.1.3: Given the lengths of all sides of a polygon, the student will
calculate the perimeter of the figure.
*8.1.4: Given the lengths of some of the sides of a polygon where
enough information is included to deduce the
lengths of the remaining sides, the student will
calculate the perimeter of the figure.
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*8.1.5: Given the perimeter of a polygon and the lengths of all but
one of the sides, the student will calculate the
length of the remaining side.
***8.1.6:
Given a word problem which involves finding the
perimeter of polygons and/or circumference of
circles or combinations of circles and polygons, the
student will calculate the quantity requested.
8.2
Obj:
The student will calculate and label with appropriate units
the area of circles and polygons.
*8.2.1: Given the radius or diameter of a circle, the student will
calculate the area of the figure.
8.3
**8.2.2:
Given the area of a circle, the student will calculate
the radius or diameter to the nearest whole number.
***8.2.3:
Given the circumference of a circle, the student will
calculate the area of the circle.
***8.2.4:
Given a complex figure with some dimensions, the
student will deduce the lengths of the remaining
sides and will calculate the area of the figure.
**8.2.5:
Given a word problem involving area, the student
will calculate the area to solve the problem.
**8.2.6:
Given a word problem involving area that has
multiple parts, the student will correctly calculate
the area and incorporate that value into the other
parts of the problem to arrive at a solution.
Obj:
The student will calculate the volumes and surface areas
of rectangular and triangular prisms, cylinders, and other
solids and label with appropriate units.
**8.3.1:
Given the radius or diameter of a sphere, the radius
or diameter and height of a cylinder, the length,
width, and height of a rectangular solid, or the base,
height, and length of a prism, where dimensions are
given as integers, fractions or decimals, the student
will calculate the volume and surface area.
9.0 GOAL: The student will be able to use and demonstrate knowledge of
geometric vocabulary relating to lines, angles, and plane and
solid figures.
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9.0
Obj:
The student will identify, name, and draw rays, angles,
lines, line segments and planes.
*9.1.1: Given a description or sketch of a line, angle, ray, line
segment, or plane the student will correctly identify
each.
*9.1.2: Given the geometric symbol, the student will identify it as
the symbol for ray, angle, line, or line segment.
*9.1.3: Given two points, the student will draw a line, a line
segment or ray.
*9.1.4: Given two lines, the student will write the symbolic
description of each.
*9.1.5: Given an angle, line, ray, or line segment, the student will
write the symbolic description of each.
*9.1.6: Given a set of angles, the student will classify each as
acute, right, obtuse, or straight, without the aid of a
protractor.
*9.1.7: Given an angle or a measure of an angle, the student will
state its complement or supplement, or its measure.
*9.1.8: Given at least two parallel lines and a transversal, the
student will identify angles formed by them as
supplementary, vertical, adjacent, or congruent,
alternate
interior,
alternate
exterior,
or
corresponding.
9.2
Obj:
The student will identify, name, and draw these plane
geometric figures:
circles, triangles, various
quadrilaterals, and polygons of more that form sides.
*9.2.1: Given sketches of plane geometric figures, the student
will identify them by names.
*9.2.2: Given a written description of a plane geometric figure,
the student will identify the figure described by
name.
**9.2.3:
Given the name of a geometric figure, the student
will state its essential characteristics.
*9.2.4: Given a circle, the student will identify specified parts of
it.
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*9.2.5: Given a geometric figure, the student will tell whether or
not it is a polygon.
*9.2.6: Given the name of a polygon or the number o f sides of a
polygon, the student will give its number of sides or
name it.
*9.2.7: Given a triangle, with sides of equal length marked, the
student will classify it as scalene, isosceles, or
equilateral.
9.3
**9.2.8:
Given a triangle, the student will classify it as acute,
obtuse, or right.
**9.2.10:
Given the measure of two of the angles of a triangle,
the student will find the measure of the third angle
by subtracting the sum of the two given angles from
180x.
**9.2.11:
Given a right triangle and the lengths of two of the
three sides, the student will find the length of the
third side using the Pythagorean Theorem, showing
the work involved.
**9.2.12:
Given a triangle and the length of each of its sides,
the student will use a Pythagorean relationship to
determine whether or not it is a right triangle.
Obj:
The student will identify, name, and draw solid geometric
figures.
**9.3.1:
Given the name of a geometric solid (cube,
rectangular prism, pyramid, cylinder, cone, or
sphere), the student will sketch a drawing of the
solid.
**9.2.2:
Given a sketch of a geometric solid, the student will
give its names.
**9.2.3:
Given a sketch of a geometric solid, the student will
identify and/or determine its number of vertices,
edges, and faces.
**9.3.4:
Given the sketch of a geometric solid (cube,
rectangular prism, pyramid, cylinder or sphere), the
student will identify its base(s) and height.
Pre-Algebra (9 - 12) - June 1990
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10.0 GOAL: The student will be able to demonstrate a knowledge of ways to
express functions and relationships.
10.1
10.2
Obj:
The student will demonstrate an understanding of the
concept of a relation and of a function.
***10.1.1:
Given the definition of a function and a relation, the
student will state and apply the definition.
***10.1.2:
Given a set of ordered pairs, the student will state
whether the set is a function or a relation.
***10.1.3:
Given an equation, the student will determine if the
equation describes a function or a relation.
***10.1.4:
Given a word description of a relation, the student
will write an equation which symbolizes that
relation.
***10.1.5:
Given a word description of a relation, the student
will write an equation which symbolizes that
relation.
Obj:
The student will graph simple relations and functions in all
quadrants of the coordinate plane.
*10.2.1:
Given a Cartesian coordinate system, the student
will identify the origin, x-axis, y-axis, and quadrants
I - IV.
*10.2.2:
Given an ordered pair, the student will correctly
identify the abscissa and ordinate.
Given a set of ordered pairs, the student will
correctly set up a Cartesian coordinate system and
plot the points.
*10.2.3:
***10.2.4:
Given a relation and its domain, the student will
graph the relation.
***10.2.5:
Given the graph of a simple function and sufficient
information, the student will represent the function
as a set of ordered pairs.
11.0 GOAL: The student will be able to translate a phrase written in words
into algebraic symbols, simplify the resulting expression
and evaluate once the values of the unknowns are given.
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11.1
11.2
Obj:
The student will translate word phrases into algebraic
expressions.
**11.1.1:
Given an algebraic expression the student will
describe in words what the symbols mean.
**11.1.2:
Given a phrase in words, the student will assign
variables and write the phrase in mathematical
symbols.
Obj:
The student will simplify algebraic expressions.
**11.2.1:
Given an algebraic expression involving two or
more terms, such as ax + by + cx + dy, where a, b, c,
and d are real numbers, the student will identify
which of the terms are like and combine like terms.
**11.2.2:
Given an algebraic expression such as xa(xb), where
a and b are real numbers, the student will use the
laws of exponents to simplify the expression.
**11.2.3:
Given an algebraic expression involving the product
of two or more monomials, such as axy(bxy), where
a and b area real numbers, the student will simplify
the product.
**11.2.4:
Given an expression of the type ax + b(x + y) + cy,
where a, b, and c are real numbers, the student will
simplify the expression using the distributive
property.
***11.2.5: Given an expression of the type ax + b(x + y) + cy, and
simplification of the expression, the student will
justify each step by stating the appropriate
property, theorem or definition.
12.0 GOAL: The student will be able to solve and/or graph simple linear
equations, proportions, and inequalities written with
integer, fraction, or decimal coefficients.
12.1
Obj:
The student will use ratios and proportions to solve for the
unknown in a variety of problems including those
involving percent.
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12.2
*12.1.1:
Given a ratio written in any form, the student will
express the ratio in an equivalent form in simplest
terms.
*12.1.2:
Given a proportion with terms written as rational
numbers, the student will find the value of the
unknown by the means-extremes method and
solving the resulting equation.
*12.1.3:
Given a simple percent problem, the student will
solve the problem using a proportion.
Obj:
The student will use properties of real numbers to simplify
linear equations to the form ax + b = c, and solve the
equation, where a, b, and c are integers and solutions
obtained are rational numbers.
**12.2.1:
Given a linear equation of the form ax = c, the
student will solve the equation algebraically.
**12.2.2:
Given a linear equation of the form x + b = c, the
student will solve the equation algebraically.
**12.2.3:
12.3
Obj:
Given a linear equation of the form ax + b = c, the
student will solve the equation algebraically.
The student will solve simple inequalities and display
solution sets on the number line.
**12.3.1:
Given an inequality of the form x < a or x > a, the
student will graph the solution set using real
numbers or integers.
***12.3.2: Given an inequality of the form x< a or x > a, the student
will graph the solution set using real numbers or
integers.
**12.3.3:
Given a graph on the number line, the student will
determine whether or not it is the solution set to a
given inequality.
***12.3.4: Given an inequality which can be written in the form ax + b
> c or ax + b < c, the student will solve the
inequality and graph its solution set.
12.4
Obj:
The student will solve practical problems using equations.
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**12.4.1:
Given a word problem that can be translated into a
proportion, the student will designate a variable,
write a proportion and solve it algebraically.
**12.4.2:
Given a word problem involving percents, the
student will write a proportion and solve it.
**12.4.3:
Given a word problem, the student will write an
equation which represents the word problem.
**12.4.4:
Given a word problem, the student will designate a
variable, write an equation and solve for the
unknown.
*
Essential
**
Expected
***
Extended
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