Download Course Title: Transition to College Math Course Number: 38010

APS
DISTRICT HIGH SCHOOL MATHEMATICS CURRICULUM FRAMEWORK
Course Title: Transition to College Math
Course Number: 38010
Department: Mathematics
ADS Number: 20354131
Prerequisites:
Successful completion of Algebra II
Length of Course: One Year
Credit/PRI Area: .50 per Semester/Math
Grade Level(s): 11 - 12
Important Notes: This course is not open to students who have completed Algebra II with a grade of B or better. This is a course for college-intending students who have
already attempted high school courses in Algebra I and Geometry with unsatisfactory results .
This course requires student access to a graphing calculator.
COURSE DESCRIPTION: In Transition to College Math the student approaches the basic concepts and techniques from Algebra I and Geometry through numerical
computation in concrete problem settings. Graphing is used to strengthen numerical intuition and to give concrete representation of functional relationships. The goal is to
increase the readiness of the student to do college-level work in mathematics, and therefore, to open career options to him/her that might otherwise remain closed.
Although references in parentheses following each performance standard align with the National Council of Teachers of Mathematics Standards (NCTM), the State of New
Mexico Mathematics Standards (NM), and the Albuquerque Public Schools Mathematics Standards (APS), it is expected that by the time the student takes this course, he/she has
already met or exceeded the standards.
TRANSITION TO COLLEGE MATH
10.1.10
Albuquerque Public Schools 03/04
STRATEGIES:
The “Illustrations” column in the Program of Studies provides exemplars of the performance standards, strategies, and best practices suggested by mathematics teachers in the
Albuquerque Public Schools (APS).
ASSESSMENTS:
Assessments may include: authentic and performance-based assessment, cooperative learning, teacher observations, checklists, test and exams, formal and informal writing, small
group and full class discussions, oral and multimedia presentations, individual and group projects, demonstrations, and portfolios. Assessments are based on appropriate rubrics.
SUGGESTED TEXTBOOKS AND INSTRUCTIONAL MATERIALS:
 Current state adopted mathematics textbooks
 Supplemental materials
 Graphing calculators
 Computer software
SUGGESTED TITLES/AUTHORS WEB SITES:
 Rubistar4teachers.com
 Nctm.org
Approved by HSCA:
TRANSITION TO COLLEGE MATH
10.2.10
Albuquerque Public Schools 03/04
STRAND I: GLOBAL MATHEMATICS PROCESSES
CONTENT STANDARD: The student understands and uses mathematical processes.
BENCHMARK: The student uses problem solving, reasoning and proof, communication, connections, and representations as appropriate in all mathematical experiences.
GRADE
11, 12
PERFORMANCE STANDARDS
ILLUSTRATIONS
NOTE: Illustrations include suggested activities for attaining each
performance standard. A check for () refers to a key feature to look for
while assessing student performance.
1. Prepares mathematically for future careers (APS – I. 14).
2.
Uses graphing technology throughout the curriculum (APS – I.9;
NM – IC.2).
3.
Applies the “rule of four” (i.e., represents mathematics graphically,
symbolically, verbally, numerically) (APS – All of Strand I, III.20L).
4.
Uses reasoning and problem-solving strategies to solve new problems
[APS – I.3; NM – IIA (5-7)].
5.
Makes connections among mathematical concepts (APS – I.12;
NM – IA.6).
6.
Relates applications to mathematical language in equation or inequality
presentations and solves for the stated unknown (APS – I.9;
NM – IB.13).
7.
Develops resourcefulness and perseverance in problem solving
(APS - I.1).
8.
9.
No. purchased (x)
100
105
115
130
200
400

Works in teams to share ideas, to develop and coordinate group
approaches to problems, to share with each other, and to communicate
findings (APS – I.4, I.8).
Recognizes when to use previously learned strategies to solve new
problems (APS – I.2; NM – IC.1, IID.2).
TRANSITION TO COLLEGE MATH
1 - 9. The student follows through the steps to determine quantity discounts and
profits for the sale of a manufactured product.
 Often businesses give a discount on products to encourage large sales.
A clock radio company gives Wal-Shop Stores a $0.15 discount on
each radio over 100 that they purchase. The regular wholesale price
on orders less than 100 is $90.00. If they buy more than 100, the price
for each radio decreases. Complete the chart below.
10.3.10

Price for each radio
with discount
$90.00
$90.00 – 5(0.15) = ?
$90.00 – 15(0.15) = ?
$90.00 = ?
$90.00 – 100(0.15) = ?
$90.00 = ?
Amount owed to
manufacturer
$9000 = (100 x $90)
?
= (105 x $89.25)
?
= (115 x $
)
?
= (130 x $
)
?
= (200 x $
)
?
= (400 x $
)
What would be some of the factors used to determine the
manufacturing cost of the radio? List as many factors of the
manufacturing costs as you can. Discuss your list with classmates and
add to your own if possible.
Complete the following table for the cost of manufacturing radios at
$60 each.
Albuquerque Public Schools 03/04
GRADE
11, 12
PERFORMANCE STANDARDS
ILLUSTRATIONS
Company produces
100 radios
105 radios
115 radios
130 radios
200 radios
400 radios



TRANSITION TO COLLEGE MATH
10.4.10
Cost to produce
100 x $60 = ?
105 x $60 = ?
x $60 = ?
?
?
?
Amount owed by Wal-Shop –
Cost to produce = Profit
$9000 – 6000 = $3000
$9371.25 – 6300 = $3071.25
What do you notice about the amount that Wal-Shop pays to the
manufacturer for 400 radios in the first table compared to the “cost to
produce” the 400 radios in the second table? Does the clock radio
company make any profit on 400 radios?
Predict what happens to the company’s profit if 405 radios are sold to
Wal-Shop at the discounted rate. Make another row on the tables if
necessary.
Graph P(x) = 45x - .15x2 on a graphing calculator. This is the
function which describes profit for this problem. Find the maximum
profit (vertex). Explain how this relates to the tables and the
predictions that you made for the profits. Does this company need to
set a limit on the number of radios that can receive a discount? Why?
 all required components
 use of technology
 effective communication
 collaboration
 problem-solving strategies
 real-world connections
 reasonable predictions
Albuquerque Public Schools 03/04
STRAND II: NUMBER SENSE AND OPERATIONS
CONTENT STANDARD: The student demonstrates number sense through experiences with meaningful mathematical problems that focus on number meaning, number
relationships, place value concepts, relative effects of operations, and multiple representations to communicate sound mathematical thinking.
BENCHMARK: The student understands rational, real, and complex numbers and uses a variety of means, including technology, as appropriate, to solve problems in these
number systems.
GRADE
11, 12
PERFORMANCE STANDARDS
ILLUSTRATIONS
Using a variety of examples such as 7 - -16, the student identifies the real
and the imaginary parts.
 correct identification of parts
1.
Identifies and defines terms and symbols basic to complex numbers
(APS – II.1L; NM – 1F.S.).
1.
2.
Uses models (e.g., Venn diagrams) to show similarities and differences
among real/imaginary numbers (APS – II.2L; NM – 1F.S.).
2. The student draws a Venn diagram illustrating the real number system and
the imaginary numbers. On a real number line, he/she indicates that no
points exist for the complex numbers.
 graphic organizer
 accuracy
3.
Develops fluency in operations with real numbers using mental
computations or paper-and-pencil calculations (for simple cases) and
technology (for more complicated cases) (APS – II3.L; NM – IC.2).
4.
Uses order of operations and the commutative, associative, and
distributive axioms to evaluate and simplify numeric and algebraic
expressions (APS – V.9E; NM – IA.2).
3, 4. The student is presented with multiple opportunities to demonstrate
his/her computational skills. These opportunities vary in level of difficulty
so that the student builds mental, as well as technical skills. A suggested
example: 1.5 – 2(0.3 + 10)2 – 100(0.5)
 accuracy
 strategy used
5.
Simplifies radicals with numerical radicands and estimates their values
both mentally and with the use of a calculator (APS – V.18E;
NM - IA.11, IA.12).
6.
Develops estimation techniques (APS – II.10E; NM – IC.2).
TRANSITION TO COLLEGE MATH
10.5.10
5, 6. The student estimates the 48. Does 24 seem reasonable? Why or why
not? The student checks his/her estimate with a calculator. He/She then
simplifies the 48 and verifies using a calculator that the simplified answer
is equal to 48.
 reasonable estimation
 accuracy in simplifying the radical
 effective communication
Albuquerque Public Schools 03/04
GRADE
11, 12
PERFORMANCE STANDARDS
7.
ILLUSTRATIONS
Develops intuitive notions of functional relationships (e.g., linear,
quadratic, exponential) (APS – V.4L, V.7L, V.10L; NM – IB.3, IB.5,
IC.1).
TRANSITION TO COLLEGE MATH
10.6.10
7. The student graphs f(x) = x + 2, (x + 2) 2, and f(x) = 2x on the same
coordinate plane using a graphing utility. He/She then notes in a sentence or
two any similarities and/or differences seen in the graphs. Where does each
graph intercept the x-axis? If any graph does not intercept the x-axis, how
could you explain it? The student then tests other sets of functions to
reinforce assumptions.
 graphing representations
 use of technology
 clear and concise explanations
 insights
Albuquerque Public Schools 03/04
STRAND III: GEOMETRY, SPATIAL SENSE, AND MEASUREMENT
CONTENT STANDARD: The student demonstrates an understanding of concepts, properties, and relationships of geometry and measurement through experiences with
meaningful mathematical problems that focus on identifying, describing, classifying, visualizing, comparing, estimating, and measuring various
aspects of shapes and objects.
BENCHMARK: The student probes theorems, explores and tests several logical reasoning methods, and uses trigonometric relationships and Cartesian coordinates to represent
objects in the plane. The student uses formulas for solving measurement problems and uses scaling as appropriate.
GRADE
11, 12
PERFORMANCE STANDARDS
ILLUSTRATIONS
1.
Uses and applies commonly used geometric symbols (APS – III.1E).
1.
Given line AB, the student represents line AB, segment AB, ray AB, and the
and the measure of segment AB using geometric symbols.
 accuracy
 completion of required components
2.
States and applies the properties of congruent and similar figures and
solids (APS – III.2E; NM – IID.1).
2. The student is given a congruency statement, such as ∆ABC  ∆XYZ.
He/She identifies and lists the corresponding parts.
 accuracy
 completion of required components
3.
Uses the distance and midpoint formulas as it applies to points, lines,
segments, and circles (APS – III.3E; NM – IIB.2).
3. The student computes both the distance between and the midpoint of the
segment with endpoints A(3,-5) and B(-2,-1).
 accurate solutions
 appropriate formulas
4.
Draws and constructs representations of two- and three-dimensional
geometric objects using a variety of tools (APS – III.4E;
NM – IIA.1, IIA.4).
5.
Solves problems involving right triangles using the Pythagorean
Theorem (APS – III.5E; NM – IID.4).
4. The student constructs a square using a compass and straight edge.
 correct construction techniques
 use of appropriate tools
 completion of required components
5. The student calculates the length of the diagonal of a 6 cm x 8 cm rectangle
using the Pythagorean Theorem.
 accurate solution
5, 11. The student finds the area of an isosceles triangle with base of 8 cm and
legs of 10 cm.
 correct application of formulas
 accurate solution
TRANSITION TO COLLEGE MATH
10.7.10
Albuquerque Public Schools 03/04
GRADE
11, 12
PERFORMANCE STANDARDS
6.
ILLUSTRATIONS
Uses concepts and techniques of coordinate geometry and trigonometry
to solve problems (APS – III.10L, III.12L, III.13L; NM – IID.5, IID.6).
6, 9. The student solves the following problem with documentation of
work provided. A sketch must be included.
A ladder that is 20 feet long is leaning against the side of a building. If the
angle formed between the ladder and the ground is 75, how far is the bottom
of the ladder from the base of the building?
 representation
 accurate solution
 justification of work
7.
Uses algebraic sentences to express geometric relationships
(APS – V.11E; NM – IA.6).
7,10. The student finds the value of x.



8.
Uses concepts and techniques of coordinate geometry to graph points and
lines and writes the equations of lines with specified properties
(APS – V.3E; NM – IIB.1).
9.
Employs trigonometric ratios to find parts of triangles (APS – III.12L;
NM - IID.5, IID.6).
correct equation
accurate solution
understanding of proportionality
8. The student writes an equation for a line that passes through (-2,8) and (1,2)
and verifies his/her work.
 correct equation
 documentation of work
 accuracy
10. Solves problems involving proportion, percent, and mixtures
(APS – II.8E; NM – ID.2).
11. Applies standard formulas for finding area and determines the area of
nonstandard shapes by decomposition (APS – III.6E; NM – IIA.2).
TRANSITION TO COLLEGE MATH
10.8.10
Albuquerque Public Schools 03/04
STRAND IV: PATTERNS, FUNCTIONS, AND ALGEBRAIC CONCEPTS
CONTENT STANDARD: The student demonstrates an understanding of algebraic skills and concepts through experiences with meaningful mathematical problems that focus
on discovering, describing, modeling, and generalizing patterns and functions, representing and analyzing relationships, and finding and
supporting solutions.
BENCHMARK: The student represents patterns with relations and functions, investigates rates of change, and symbolically manipulates numbers.
GRADE
11, 12
PERFORMANCE STANDARDS
ILLUSTRATIONS
1.
Expresses and investigates relationships algebraically (NM – IA.6).
1, 3, 4. The student writes and solves an equation describing the following
situation: Twice a number is decreased by 9, and this sum is
multiplied by 4. The result is 8 less than 10 times the number. What is
the number?
 accuracy
2.
Finds the sum, difference, product, quotient, and powers of rational
numbers, expressions, and equations (APS – V.20E,V.21E;
NM – IA.15, IA.17).
2. The student simplifies the following expressions:
a) Simplify 4x2a + 1
b) solve for a: c + m
y2
a²
x
a
2 - 2__
y-a
 accuracy
=
3.
Identifies and uses common algebraic symbols and terms (APS – V.7E).
4.
Solves linear equations and inequalities in one variable (APS – V.12E;
NM – IC.4, ID.2).
5.
Solves systems of linear equations in two variables by algebraic and
graphical methods (APS – V.5L, V.13L; NM – IC.4, IC.5).
5. The student solves by graphing and then gets an exact solution
algebraically. The student verifies his/her work.
2y – 2x = 8
y + x = -2
 graphical representation
 documentation of work
 accuracy
6.
Simplifies algebraic expressions containing positive, negative, and
fractional exponents (NM – IA.4).
6. The student simplifies:
a) -3⁰
b) (-2x) -2 xy⁰ y²(x) -2
2
-27
(x²y) -2 xyxy -2
 accuracy
 ability to work with exponents
TRANSITION TO COLLEGE MATH
10.9.10
c
Albuquerque Public Schools 03/04
GRADE
11, 12
PERFORMANCE STANDARDS
7.
ILLUSTRATIONS
Translates word problems into algebraic equations or systems and solves
them (APS – V.11E; NM – IC.1, IC.9).
7. The student sets up a chart, writes an equation, and solves: Six hundred
grams of barium was mixed with 2400 grams of other chemicals to form
3000 grams of the compound. If 9000 grams of the compound was
needed, how much barium was required?


skillful translation of words to symbols
accuracy
8.
Finds the sum, difference, product, and quotient of polynomial
expressions (APS – V.15.E; NM – IA.17).
8. The student simplifies the following polynomials:
a) Multiply: (2x + 4)(3x2 - 2x -10) b) Divide: 5x2 - 1 by x – 2
 accuracy
9.
Evaluates polynomial expressions (NM – IA.17).
9. The student evaluates: ax – a(a – x) if a = ? and x = ? (various values can
be used).
 accuracy
10. Factors polynomials over the rational numbers (APS – V.16E;
NM – IA.14).
10. The student factors 10x4 - 7x3y + x2y2.
 accuracy
11. Uses factoring to write a rational expression in simplest form
(APS – V.19E; NM – IA.15).
11, 12. The student simplifies: x2² + x – 20 • x2² + 10x + 16
x2 - x – 2
x2 + 3x – 40
 accuracy
 factoring skills
12. Determines the values for which a rational expression is undefined
(APS – V.17L).
13. Solves quadratic equations by factoring, quadratic formula, graphing and
numerical methods (APS – V.13E; NM – IB.12).
14. Analyzes the nature of solutions to quadratic equations using the
discriminant ( APS – V.11L).
TRANSITION TO COLLEGE MATH
10.10.10
13. The student solves algebraically and graphically
a) 2x + x2 - 5 = 0
b) x2 = -5x2+ 50x
 multiple representations of the solution
 accuracy
14. The student uses the discriminant to determine the type of solutions for
a) x2 = -4x + 2
b) -2x = -3x2 – 8
 determination of roots
Albuquerque Public Schools 03/04