Math 413, Mathematics for the Middle Grades
(2:45-4:00 TuTh, C-10)

Syllabus: Here is the syllabus.

Online resources:
Homework: Remember that you do not have to turn in the HW. However you should keep up with it. This is why we have target dates. You should have completed your HW by the target date and have it in a form that you would be confident relying on at the next exam. You can of course come back to it and revise it afterwards.

Assigned
Target date
Exercises
9/4
9/11
Fostering Algebraic Thinking Ch. 1
Write up three different solutions to the Golden Apples problem on p. 7 in Fostering Algebraic Thinking
9/11

Fostering Algebraic Thinking Ch. 1 No new homework this week. But take a look at problem of the fortnight. Just follow the link below. It should appear on the website anytime.
9/18
9/25
Fostering Algebraic Thinking Ch. 1 Write up a solution to the Locker Problem with 200 lockers on p. 10 in Fostering Algebraic Thinking. Make sure you carefully explain why the lockers that end up open are exactly the ones whose number is a perfect square. This means you also need to explain why those lockers whose number is not a square end up closed. Which locker(s) changed the most? Why? How did you find them?
9/25
10/2
Fostering Algebraic Thinking Ch. 2
Write up a solution for the Crossing the River problem on p. 11 in Fostering Algebraic Thinking. Be sure to justify each claim carefully, especially the result for A adults and C children.
10/2

Fostering Algebraic Thinking Ch. 2
Homework holiday. Prepare for the upcoming exam.
10/9
10/16
Fostering Algebraic Thinking Ch. 2
Write up a solution to the Cuisenaire train problem. How many different trains of length n can you build if you distinguish between the front and the back of the train? Justify your answer. How many trains of length n can you build out of exactly k rods? Explain why.

For the following problem, we will cover the material on Thu. Suppose you have postage stamps in 7-cent and 9-cent denominations. What is the largest postage you cannot make by combining such stamps? Can you find a convincing reason why any larger postage can be made? Notice that this question is slightly different from the question in the text.
10/16
10/23
Fostering Algebraic Thinking Ch. 2
Do the Crawling Snail problem on p. 31 and the Sums of Consecutive Numbers problem on p. 37. Make sure you carefully justify your solutions to both problems.
10/23
10/30
Fostering Algebraic Thinking Ch. 2
Make up an Age Problem like the one on p. 32-33 with your own age. Then solve the problem to make sure that the result is indeed your age. Can you use numbers other than 3, 5, and 7 to divide by?

Carefully write up the solution of the Sneaking Up the Line problem on p. 35.

In solving the Cutting Edge Problem, we gave an algorithm for cutting up a triangle into pieces and reassembling a rectangle from those pieces. In the first step of this algorithm, we cut the triangle into two pieces, from which we can assemble a parallelogram. Prove that this is really possible to do. That is, you need to show that if you follow steps 1-3 on p. 39 in the book, then the resulting geometric figure is really a parallelogram.
10/30
11/6
Fostering Algebraic Thinking Ch. 2
Write up a detailed solution of the Lots of Squares problem.

In the Gum Problem, explain how Jack makes two mistakes which cancel each other to give the correct answer. How could Jack fix his argument? In part 2, explain why the information given is insufficient to determine what fraction of the class is absent. Can you give upper and lower bounds on the fraction of the class that is absent?

Review the Euclidean algorithm and the definition of greatest common divisor. You don't have to write anything down, just be prepared because we will use these concepts in the next class or two.
11/6
11/13
Thinking Mathematically Introduction and Ch 1 pp 1-10
Read pp 1-32 in "How to solve it" by G. Polya. This is the handout I gave you in class today. If you weren't there, you can find copies on my office door.

Other than the reading, this is a homework holiday. Prepare for the upcoming exam.
11/13
11/21 (Wed!)
Thinking Mathematically Introduction and Ch 1 pp 1-10
This week's assignment is to be turned in by 7 PM on Wed 11/21. You can submit it to me in person, or put it in the envelope outside my office.
11/20
11/27
Thinking Mathematically Introduction and Ch 1 pp 11-25
Read the handout from "Knowing and Teaching Elementary Mathematics" by Liping Ma. This is the handout I gave you in class today. If you weren't there, you can find copies on my office door.

Write up detailed solutions of the Warehouse and Paper Strip problems in Thinking Mathematically, inluding careful explanations of the mathematical reasons for your conclusions.
11/27
12/4
Thinking Mathematically Introduction and Ch 1 pp 11-25
This week's assignment is to be turned in by 7 PM on Tue 12/4. You can submit it to me in person, or put it in the envelope outside my office.

Write up detailed solutions to the Palindromes and Patchwork problems in Thinking Mathematically, inluding careful explanations of the mathematical reasons for your conclusions. These are for your own homework notes, you don't have to turn them in.

The problem of the fortnight: The Mathematics Department in San Diego posts a new fun problem every two weeks.  If you'd like to submit a solution, give it or e-mail it to me, so that I can fax them all together to San Diego. Winners receive prizes.

Numb3rs: The movie for class on Thu, 9/13 is an episode of Numb3rs called Pandora's Box. You can watch it online here if you have a broadband internet connection. The computers on campus all have broadband internet, but you'll need to find one that has headphones. The movie will appear in a pop-up window, so make sure you allow pop-ups. If for some reason the link above doesn't work, just go to CBS Innertube and follow the links All Shows -> Primetime -> Numb3rs -> Full Episodes: Numb3rs.

Exam solutions:
• First hourly exam pdf
• Second hourly exam pdf
• Final exam pdf
Useful links: The links below lead to sites with encyclopedias of math terms.  You can use them to find definitions, examples, and some theorems.
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