(Instructor: Steffen Lempp)

- Lecture Notes (free download for educational/non-profit purposes only)
- the following Singapore Math textbooks:
- Primary Mathematics Textbook 5A (U.S. Edition) (You may
have this book already from your Math 130 class; do
**not**buy this book if you don't have it; copies of the few pages we need will be provided for free in class, or you can download them below!) - Primary Mathematics Textbook 6A (U.S. Edition) (You may have this book already from your Math 130 class)
- New Elementary Mathematics Textbook 1 (Syllabus D) (You may have this book already from your Math 131 class)
- New Elementary Mathematics Textbook 2 (Syllabus D)
- New Elementary Mathematics Textbook 3A (Syllabus D)
- New Syllabus Additional Mathematics Textbook
(Do
**not**buy this book, copies of the few pages we need will be provided for free!)

- Primary Mathematics Textbook 5A (U.S. Edition) (You may
have this book already from your Math 130 class; do

There will be **no** credit for late homework except
in case of illness or family emergency.

**HW # 1 DUE 1/26**: Primary 5A, p. 25, # 1, 4, 7, 10 (using bar diagrams) and p. 60, # 2, 4, 6, 8 (in two ways, using both methods on page 58); Lecture Notes, p. 4, # 1.1**HW # 2 DUE 2/4**: Lecture Notes, p. 8, # 1.3, 1.4; NEM 1, p. 25, # 5-7 and p. 27, # 1, 5; Primary 6A, p. 29, # 3, 6 and p. 33, # 2, 6 and p. 38, # 4, 6 and p. 60, # 7, 10 and p. 68, # 8, 10 (all using bar diagrams!)**HW # 3 DUE 2/9**: Primary 6A, p. 82, # 2, 4, 7 (using pictures as in text); 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 2/16**: Lecture Notes, p. 23, # 2.1; NEM 1, p. 139, # 4dg, 5, 7, 10, 13 and p. 174, # 10, 13 and p. 181, # 17, 21; NEM 2, p. 117, # 4, 6, 8, 9 (GST = general sales tax)**HW # 5 DUE 2/23**: Lecture Notes, p. 33, #2.2 and p. 35, #2.4 and 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 3A, p. 77, # 1df, 3abc, 4bd, 6bd, 8**HW # 6 DUE 3/2**: NEM 2, p. 53, # 4, 6, 10 (literal = linear) and p. 78, # 17, 37 and p. 141, # 6, 12 (by elimination method) and p. 148, # 10, 20 and p. 151, # 11, 18, 20, 21**HW # 7 DUE 3/9**: Lecture Notes, p. 61, # 3.1-3.2; NEM 2, p. 159, # 1 and p. 163, # 3dfhj and p. 164, # 4dhl, 5-7**HW # 8 DUE 3/23**: NEM 3A, p. 47, # 4, 18, 22 and p. 50, # 5, 10, 12, 14 and p. 55, #3-5 (**Typo**for # 22 on p. 49: Second inequality should read "2x+1 < x+2")**HW # 9 DUE 3/30:**NEM 2, p. 122, # 3, 5, 9, 10; NEM 3A, p. 102, # 2, 10, 12 and p. 106, # 1bfj, 2 and p. 109, # 2, 6, 8, 12, 14**HW # 10 DUE 4/6:**NEM 2, p. 28, # 3dhl, 4bdh and p. 31, # 2bdf and p. 33, # 6dhlpt; NEM 3A, p. 114, # 6, 10, 16, 17; also solve:- |.5x+4| > 2.5
- |4(x-5)| ≤ 3
- |x-1| < 2x+5

**HW # 11 DUE 4/13:**NEM 2, p. 65, # 1hlpt and p. 66, # 3, 7, 11, 14; NEM 3A, p. 31, # 1dh, 2dh and p. 39, # 12, 15, 17, 20; Lecture Notes p. 98, # 5.1 and p. 99, # 5.2 (Note: Solve all NEM 2 quadratic equations by factorization!)**HW # 12 DUE 4/20:**NEM 2, p. 133, # 3 and p. 135, # 1, 2, 4, 5; NEM 3A, p. 34, # 1bf, 2lptz, 4bd and p. 41, # 2, 4 and p. 129, # 5 and p. 138, # 1, 5; also solve:- 2x
^{2}< 5x-1 - -x
^{2}+5 ≥ 2x

- 2x
**HW # 13 DUE 4/27:**Lecture Notes, p. 125, # 6.1, Add'l Math, p. 78, # 1d, 2df, 4df and p. 81, # 1dg, 3bd, 5 and p. 83, #1c, 2f, 3c (note that in the Singapore math books, "index" = "exponent", and "surd" = "algebraic expression involving roots")**HW # 14 DUE 5/6:**Add'l Math, p. 87, # 1e, 2b, 3di and p. 91, # 2cd, 4cf and p. 97, # 2dgh, 6, 8, 10 and p. 100, # 2, 5, 7 and p. 103, # 2ace, 4, 9, 13

The comparison I am looking for is how the **mathematical concepts**
are introduced. I'm not necessarily looking for a value judgment from you,
which one you like better, but mainly for an investigation of how the
presentation of the topic differs from a mathematical point of view.
E.g., is the concept defined differently? Are the examples by which it is
introduced very different? Etc.?

Your project will consist of a short (joint) paper (of 2-3 pages), with copies of the relevant "other" schoolbook pages attached, and a short presentation (10-15 minutes) in class about this comparison of topics. You can use an overhead projector or copied handouts if you prefer. (I'll help you get an overhead projector if you need one.) Presentations will start in mid-April. I suggest that each group meet with me briefly a few days before your presentation for feedback.

Here is a list of possible topics (with reference to treatment in my Lecture Notes):

- How are the properties of arithmetic (commutative law, etc.)
**first**presented? (Cf. Proposition 1.2. Presentation by NC and KH on April 29.) - How is the slope of a line defined? (How is it motivated that one can
define the slope as
**one single**number? (Cf. section 2.4. Presentation by CM and JR on May 2.) - How is solving two linear equations in two unknowns presented? (Cf. section 2.5. Presnetation by SS and KVD on May 4.)

- Singapore Primary Math 5A: Pages 22-25
- Singapore Primary Math 5A: Pages 56-64
- Additional Mathematics: Pages 75-84
- Additional Mathematics: Pages 85-94
- Additional Mathematics: Pages 95-104

Calculators of any kind are discouraged for any part of this course and will not be allowed during exams.

**Midterm Exam 1:**Monday, February 28, 7:15-8:15 p.m., B139 Van Vleck Hall**Midterm Exam 2:**Monday, April 4, 7:00-8:00 p.m., B139 Van Vleck Hall**Final exam:**Tuesday, May 10, 10:05-12:05, B139 Van Vleck Hall

- Steffen Lempp's Math Education Page (including a lot of information on math courses for UW elementary and special education majors)
- Errata List for all Singapore math books
- Mathematics-Science Dual Minor For Elementary and Special Education Students
- $500 scholarship of the Brookhill Foundation
- James Milgram: "The Mathematics Pre-Service Teachers Need to Know" (see especially chapter 8 on algebra)
- Hung-Hsi Wu: "Introduction to School Algebra"
- GeoGebra (free mathematics software for teaching geometry, algebra and calculus in middle school and high school)
- Middle School Mathematics PRAXIS Test
- Wikipedia entry on "algebra" and its history

The other two math courses for this minor, Math 136 and Math 138, will focus on precalculus and early calculus; and on probability, statistics and combinatorics, respectively.

Note that in spring semester 2011 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.)

- 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 (@math.wisc.edu">lemppmath.wisc.edu)