Assignment information will be posted here as the semester unfolds. A number such as A.B.c refers to problem or practice exercise c at the end of section A.B.

You only need to turn in the Problems; the Practice Exercises are suggestions for your study, and may be discussed in class. Remember to type your homework and bring a printed copy to class!

The homework template I mentioned in class is available here. A little minicourse on latex is available here, and here's a list of beautiful examples of latex typesetting (or related *tex typesetting). Let Niles know if you're interested in more!

Past Homework

Homework 1 due Friday, 01/16

Practice Exercises (do not turn in): 10.2.4, 10.4.5
Problems (type, print, and turn in): 10.1.4, 10.1.8, 10.2.4, 10.2.10
Bonus problem: Carefully explain part 4 of Activity 10D, and its relationship to part 2.

Homework 2 due Wednesday, 01/21

Practice Exercises (do not turn in): 10.5.4, 10.5.8, 9.1.1, 9.1.5
Problems (type, print, and turn in): 10.4.1, 10.5.3, 10.5.11, 10.5.19

Homework 3 due Monday, 01/26

Practice Exercises (do not turn in): 9.1.5, 9.2.5
Problems (type, print, and turn in): 10.5.11, 9.1.4, 9.1.9, 9.2.9

Homework 4 due Friday, 01/30

Practice Exercises (do not turn in): 9.3.1, 9.3.4, 9.4.2, 9.5.3
Problems (type, print, and turn in): 9.3.3, 9.3.5, 9.3.7, 9.4.5
Additional problem: Use the parallel postulate (and triangle congruence) to explain why the diagonals in a rhombus bisect the interior angles. Go on to explain why diagonals in a rhombus are perpendicular bisectors.

Homework 5 due Monday, 02/02

Problems (type, print, and turn in): 9.5.8, 9.5.10, 9.5.16, 9.6.1, 9.6.5
Additional problem: moved to HW 6.
Additional problem 2: Consider the sequence formed by ones digits of powers of 2. What is the pattern, and what is the ones digit of 2¹⁰⁰?

Homework 6 due Friday, 02/06

Problems (type, print, and turn in): 9.6.7, 9.6.13, 9.7.2, 9.7.5, 9.7.10, 9.7.12
Additional problem: Explain why a quadrilateral having opposite angles equal must be a parallelogram. Then use this to explain why a quadrilateral having opposite sides equal must be a parallelogram.

Homework 7 due Friday, 02/13

Type and turn in at least four problems from each group on the review sheet.

Extra Credit due Monday, 02/16

Find a general expression for the terms in a quadratic sequence whose first terms are
\[ c, (c + b), (c + b + a), \ldots \] It might be easiest to first try this for specific values of \(c\), \(b\), and \(a\). Email Niles if you'd like a hint.

Extra Credit due Monday, 02/16

Follow the steps in this article to make a cool Islamic art pattern with compass and straightedge!

Homework 8 due Friday, 02/20

Problems: 11.1.4, 11.3.4, 11.4.5, 11.4.9, 11.4.21

Homework 9 due Monday, 02/23

Problems: 12.1.4, 12.2.4, 12.3.2, 12.3.7, 12.4.9, 12.5.3

Homework 10 due Friday, 02/27

Problems: 14.5.6, 14.5.16, 12.6.2, 12.6.4
Additional Problem: Use a ruler to carefully estimate the square constant (permieter/diagonal).

Homework 11 due Monday, 03/02

Problems: 12.7.3, 12.8.4, 12.8.12, 12.9.1, 12.9.6

Homework 12 due Friday, 03/06

Problems: 13.1.3, 13.1.4, 13.1.8, 13.2.9, 13.2.14

Homework 13 due Monday, 03/09

Problems: 13.3.11, 13.3.22, 13.4.1, 14.1.4, 14.1.5
Additional problem: Draw a pattern which, when cut out and folded up, makes an oblique rectangular prism.

Homework 14 due Friday, 03/13

Type up and turn in 12 problems of your choosing from chapters 11 and 12.

Homework 15 due Monday, 03/23

Problems 14.1.8 — 14.1.13.
You can use this link to download graph paper.

Writing Assignment due Monday, 03/23

See guidelines and suggested topics in class email or here. I've opened a dropbox in our Carmen course for you turn your papers in. Please submit your document in pdf and use a filename that begins with your last name.

Here is a video illustrating Archimedes Method for finiding the volume of the sphere.

Homework 16 due Friday, 03/27

1. Draw objects that have the following combinations of symmetries:

• horizontal and vertical reflection symmetry
• rotation symmetry, but no reflection symmetry
• both reflection and rotation symmetry
• translation and reflection symmetry, but no rotation symmetry
• glide-reflection symmetry and rotation symmetry

2. Use geogebra.org or another tool of your choosing to do activity 14 F. Print a nice-looking pattern that you create in this way.

3. Problem 14.2.8

Homework 17 due Monday, 03/30

• Why doesn't ASS give a triangle congruence? See the text, or Activity 14I, "triangle T"
• Describe what happens when you combine a reflection and a rotation (for example, on an octagon)
• Construct a square and an octagon as in Activity 14M.
• Look up the Newark Earthworks, and appreciate the Octagon!

Homework 18 due Friday, 04/03

Problems: 14.3.6, 14.3.7, 14.4.7

Homework 19 due Monday, 04/06

Problems: 14.5.19, 14.5.21, 14.5.24, 14.6.4, 14.6.7

Homework 20 due Friday, 04/10

Turn in your work on the review sheet problems.

Writing assignment due Monday, 04/13

Revisit your writing assignments and make sure that you've clearly attributed content from your references. See email for more details.

Extra Credit due Monday, 04/13

An equilateral triangle has 6 symmetries: 3 reflections and 3 rotations (including the "identity", which rotates by 0 or 360 degrees). Make a "multiplication table" which shows what you get by combining each pair. You will need to be very careful about the order that you combine them in, as combining symmetries is not necessarily commutative.

A square has 8 symmetries total. Make a "multiplication table" which shows what you get by combining each pair. For this to be feasible, you will want to see how understanding just a few combinations can allow you to deduce the others. This will allow you to notice and use patterns in the multiplication table to complete it.

After you have thought about this for a while, you should take a look at the Wikipedia article about the dihedral group. If you look before you've really thought about this, it may be too overwhelming!

Homework 21 due Friday, 04/17

Problems 15.1.7, 15.1.9
One of 15.2.2, 15.2.3, 15.2.4
One of 15.2.5, 15.2.6, 15.2.7
Problems 15.3.7, 15.3.9, 15.3.13

Homework 22 due Monday, 04/20

Problems 16.1.2, 16.1.5, 16.2.3, 16.3.6
Additional problem: What is the exact theoretical probability that 5 out of 10 coin flips will be heads?

Homework 23 due Friday, 04/24

Problems 16.3.17, 16.3.18, 16.4.12, 16.4.15

Your final grade will be based on written homework, written and oral in-class participation, quizzes, midterms, and a final exam. The precise breakdown is as follows:

• In-class participation: 12%
• Homework: 5%
• Writing Assignments: 4%
• Quizzes: 14%
• Midterm exams: 15% each, for a total of 45%
• Final exam: 20%

The two lowest quiz and homework grades will be dropped. If your final exam score is higher than one of your midterms, then that grade will replace the lowest midterm grade.

Participation

Thoughout this semester we will be focused on the how and why of elementary mathematics. This means that you will be responsible both for knowing the content and for knowing how to explain the content. We will practice this in a variety of ways, and much of this practice will take place in class.

Teaching mathematics requires listening carefully to students, assessing their ideas, and responding in ways that make sense. Our class participation is designed to practice these essential skills. You will have opportunities on a daily basis to listen to your fellow classmates explain ideas and ask questions. You will be asked to respond with your ideas and with additional questions. Together we will see how and why mathematics works! Participating in this course includes all of the following:

• Show interest in mathematical ideas.
• Show interest in different ways of approaching mathematical ideas.
• Listen carefully to different ways of solving a problem.
• Carefully evaluate a proposed method of solution.
• State whether you agree or (respectfully) disagree with a statement.
• Show interest in learning with and from others.

Homework and Quizzes

Homework and Quizzes will be scored using the rubric below. Scores are based both on mathematical correctness and quality of explanations. Homework should be typed and presented as you would an essay. If necessary, you may draw diagrams by hand on separate pages. Quizzes will be hand-written during the first 10 or 15 minutes of class.

The homework is intended to give you time to develop your explanations and understanding of the content. You are encouraged to work with your classmates on this, but you must write your own explanations. Homework is designed to help you learn, and not as an assessment tool. Therefore grades for homework will be recorded on a complete/incomplete basis (scores of 3 and higher are complete). The numerical scores are given only for your information.

The weekly quizzes are opportunities to evaluate your current grasp of the material. They will be very short and based on previous homework problems or class activities. Quiz grades will be recored as scored.

The descriptions on the rubric below are meant as a guide to help answer the question What constitutes a good explanation of mathematics? This is a subtle and challenging question—one that is worthy of considerable time and energy. As you write your explanations, consider the distinction between Procedure and Conceptual Meaning. A complete explanation addresses both of these, but the conceptual meaning is essential. Explanations that address procedure only are a disservice to students and do not support their future learning. They are also much less interesting!

Quizzes and exams will follow this scale; Niles will use these for comments on homework too, although homework grades are recorded on a complete/incomplete basis. Homework will be considered complete if the average score is R (3) or higher.

G++

Exemplary

Excellent work that exceeds the assignment guidelines.

G+

Good plus (10)

Correct procedure with an explanation that effectively addresses relevant definitions and concepts.

G

Good (9)

Correct procedure with nearly complete explanation.

Em/G

Emerging/Good (8)

Well-developed but incomplete explanation.
Procedural errors are minor or nonexistant.

Em+

Emerging plus (7)

Emerging explanation that shows understanding.
Procedural errors are minor or nonexistant.

Em

Emerging (6)

Explanation that mentions core definitions or conceptual meaning relevant to the question.
Possibly some non-minor procedural errors.

R/Em

Relevant/Emerging (5)

Work that has merit but also has significant shortcomings in the procedure and/or explanation.

R

Relevant effort (3)

Work that shows relevant effort but is seriously flawed.

NC

No credit (0)

No work submitted, or no relevant effort shown.