Math 135: Algebraic Reasoning for Teaching Mathematics
(Instructor: Steffen Lempp)
NEW SCHOLARSHIP:
The Brookhill Foundation now supports
Math
135 students as well as students taking the new
math/science minor for elementary and special education majors
by a new scholarship!
CLASS POLICIES:
Handout stating class
policies
- Lecture Notes (free download for
educational/non-profit purposes only)
- the following Singapore Math textbooks:
HOMEWORK:
Homework will be assigned on Wednesdays at the beginning of lecture and due the
following Wednesday at the beginning of class.
There will be no credit for late homework except
in case of illness or family emergency.
- HW # 1 DUE 1/30: Primary 5A, p. 25, # 1, 4, 7, 10 (using
bar diagrams) and p. 60, # 2, 4, 6, 8 (using bar diagrams in at least two
different ways)
- HW # 2 DUE 2/6: Lecture Notes, p. 4, # 1.1 and p. 8,
# 1.2, 1.3; NEM 1, p. 25, # 5-7 and p. 27, # 1, 5
- HW # 3 DUE 2/13: Primary 6A, p. 29, # 3, 6 and
p. 33, # 2, 6 and p. 38, # 2, 4, 6 (all using bar diagrams!);
NEM 1, p. 141, # 2dfh, 4dfh and p. 147, # 2dfh, 4dfh (In the last two
exercises, explain each step carefully by a rule or a definition!)
- HW # 4 DUE 2/20: Primary 6A, p. 60, # 4, 7, 10 and
p. 68, # 5, 8, 10 (all using bar diagrams!) and p 82, # 2, 4, 7 (using
pictures as in text); NEM 1, p. 139, # 4dg, 5, 7, 10, 13, 15
- HW # 5 DUE 2/27: Lecture Notes, p. 34, #2.2 and
p. 35, 2.4; NEM 1, p. 174, # 3, 6, 10, 13; p. 181, # 13, 17, 21;
NEM 3A, p. 77, # 1df, 3abc, 4bd, 6bd, 8
- HW # 6 DUE 3/5: Lecture Notes, p. 41, # 2.5;
NEM 1, p. 158, # 3dhl and p. 161, # 12, 24 and p. 166, # 4, 10, 17, 20
(with the method of this section, i.e., using only one variable!);
NEM 2, p. 117, # 4, 6, 8, 9 (GST = general sales tax)
- HW # 7 DUE 3/12: NEM 2, p. 53, # 4, 6, 10 (literal =
linear) and p. 78, # 17, 37 and p. 130, # 4 and p. 141, # 6, 12 (by
elimination method) and p. 148, # 10, 20 and p. 151, # 12, 18, 20
- HW # 8 DUE 3/26: Lecture Notes, p. 61, # 3.1-3.2;
NEM 2, p. 90, # 31, 33 and p. 151, # 11, 17, 21 and p. 159, # 1-3
and p. 163, # 3dfhj
- HW # 9 DUE 4/2: NEM 2, p. 164, # 3dhl, 4dhl, 5-7;
NEM 3A, p. 47, # 2, 4, 10, 18, 22 and p. 50, # 5, 7, 10, 12, 14 and
p. 55, # 3-5
- HW # 10 DUE 4/9: NEM 3A, p. 102, # 2, 10, 12 and
p. 106, # 1bfj, 2 and p. 109, # 2, 6, 8, 12, 14
- HW # 11 DUE 4/16: NEM 2, p. 122, # 2, 3, 5, 6, 9, 10
- HW # 12 DUE 4/23: NEM 3A, p. 114, # 4, 6, 10, 16, 17, 22;
also solve:
- |.5x+4| > 2.5
- |4(x-5)| ≤ 3
- |x-1| < 2x+5
- HW # 13 DUE 4/30: NEM 2, p. 28, # 2dhl, 3dhl, 4bdh and
p. 31, # 2bdf and p. 33, # 6dhlpt and p. 65, # 1hlpt and
p. 66, # 3, 7, 11, 14; NEM 3A, p. 31, # 1dh, 2dh and
p. 34, # 1bf, 2lptz, 4bd and p. 39, # 12, 15, 17, 20 (Note: Solve all NEM 2
quadratic equations by factorization!)
- HW # 14 DUE 5/7: NEM 2, p. 133, # 3 and
p. 135, # 1, 2, 4, 5; NEM 3A, p. 41, # 2, 4 and p. 129, # 5 and
p. 138, # 1, 5; also solve:
- 2x2 < 5x-1
- -x2+5 ≥ 2x
COPIED PAGES FROM OTHER SINGAPORE PRIMARY MATH BOOKS:
For copyright reasons, the links below are password protected.
Please get your user name and password from me by
email if you have forgotten it.
Use of these links will be monitored, and unauthorized use is prohibited.
EXAMS:
Makeup exams will be scheduled only with the instructor's
consent, and only in case of illness or family emergency or conflict with
another required class. In the latter case, please let me know as soon as
possible!
Calculators of any kind are discouraged for any part of this course and
will not be allowed during exams.
- Midterm Exam 1: Thursday, February 28,
6:30 p.m. - 7:30 p.m., B139 Van Vleck Hall
- Midterm Exam 2: Thursday, April 3,
6:30 p.m. - 7:30 p.m., B139 Van Vleck Hall
- Final exam: Monday, May 12, 9:30 a.m. - 11:30 a.m.,
room B129 Van Vleck Hall(NOTE CHANGED EXAM TIME)
MISCELLANEOUS USEFUL LINKS:
PURPOSE OF THIS NEW COURSE:
This course is the first of three new courses of the math component of the new
Mathematics-Science Dual Minor for all Elementary Education
and Special Education majors wishing to enhance their content preparation in
mathematics and science. This new minor is particularly suitable for those
Elementary Education majors seeking Middle Childhood-Early Adolescence
certification and intending to teach mathematics and science in middle school.
The other two math courses for this minor, Math 136 and Math 138, to be first
offered in fall 2008 and spring 2009, will focus on precalculus and early
calculus; and on probability, statistics and combinatorics, respectively.
Note that in spring semester 2008 only, Math 135 can also be taken in place of
Math 132 by students already admitted into the Elementary Education or
Special Education program.
Math 135 focuses on the mathematical content needed to teach pre-algebra
and algebra in upper-level elementary and middle school.
The core instructional goals of Math 135 are:
- problem-solving;
- making mathematically grounded arguments about the strengths and weaknesses
of a range of solution strategies (including standard techniques)
- examining the rationale behind middle-school students' mathematical work
and how it connects to prior mathematical understanding and future
mathematical concepts
- flexible use of multiple representations such as graphs, tables, and
equations (including different forms)
- using functions to model real-world phenomena
- modeling real-world problems ("word problems") as mathematical problems and
then interpreting the mathematical solution in the real-world context
- symbolic proficiency (solving equations and inequalities, simplifying
expressions, factoring, etc.)
The mathematical content topics of Math 135 include:
- Review: basic properties of the real numbers
- Linear Functions: proportional relationships, linear equations and systems
of linear equations, linear inequalities
- Quadratic Functions: different forms of quadratic equations, factoring
quadratic polynomials, completing the square and quadratic formula,
graphing quadratic functions, quadratic inequalities, brief discussion of
polynomial functions
- Exponential Functions: understanding the difference between additive and
multiplicative growth, exponential rules, exponential growth and decay,
brief discussion of logarithmic functions
Prepared by
Steffen Lempp
(lempp@math.wisc.edu)