Write up solutions for two different ways to solve the handshake problem. A complete write up should explain how to add one more person to a group, and how to find the number of handshakes for 10 people in a group. If possible, include images that might be helpful for fellow students to follow your thought process. To go the extra mile, explain how to find the number of handshakes for 20 or 100 people.

Oct 1st/2nd (depending on section)

1. Create a one page guide to your X-mania number system (you may use your group’s system, or another system of your choosing). Make it clear how your system relates to the manipulatives (a.k.a. “artifacts”). Include examples of the numbers 1 thru 20 in your new number system, along with numbers equivalent to 87, 200, and 3144.
2. Jimmy is a curious & bright student in your class. He asks you (a) where the number “zero” came from and (b) why we need it. Short on time (or unsure of a good answer) you say “I’ll find out and tell you next time.” Using the internet or books, create a response appropriate for a grade school classroom. This should be typed and in your own words. Site any sources you find helpful. [Try not to spend more than 30 to 40 minutes on this questions. The majority of your effort should be on the first question.]

Oct 6th/7th (depending on section)

Create a method for adding together multidigit base 5 numbers. Show your method on the two examples 23five + 14five, 234five + 312five, then two more examples of your own choosing. Focus on visual models and recording how you performed the tasks. (Due Day 4)

HW list: Please submit homework as one pack, stapled together in the order listed below.

* Textbook Exercises and Problems should be short answers (often a number or picture). Writing and Discussion questions should have paragraph answers. Workbook exercises are generaly short answers or pictures.

• TB: Exercises and Problems 3.1 (p138): 2-18 even, 28, 37 (for some of the numeration systems, you'll need to read the section)
• TB: Writing and Discussion 3.1 (p141) #1. (This should be typed or written in excellent handwriting.)
• TB: Read p 145-147: "Number Properties." Create a study guide (about 1 page) which explains and gives examples of the properties: Closure, Identity, Associativity, and Commutativity. These properties are true for addition with whole numbers. Do you think they're true for subtraction, multiplication, and division of whole numbers? Justify your answer for each operation and property.
• WB: 3.1 #1-7.
• WB: 3.2 #1-6 (started in class Wed/Thurs)

Oct 13th/14th (depending on section)

• TB: Exercises and Problems 3.2 (p158): 3-8, 10, 12, 14-18, 20, 22, 35, 36
• TB: Exercises and Problems 3.3 (p180): 5, 7-10, 13, 15, 16, 42, 43, 52, 53
• WB: 3.3 (p60): 1, 3, 5, 6 (will be worked on in class on Monday/Tuesday, Oct 20/21st)

Oct 22nd/23rd

Topics covered will include alternate bases (including base 5), addition, subtraction, and multiplication, in base 5 and other bases. Properties: identity, commutivity, associativity, closure. You do not have to memorize Egyptian / Babylonian / Mayan number systems. If questions are asked about these systems, the symbols will be given.

(This may not be an exhaustive list.)

This is your only homework for the weekend. Take you time and make your final draft beautiful and easy to read.

• WB 3.4: 1- 6 (only 1-4 were begun in class, finish thru 6)
• TB: Exercises and Problems 3.4 (p203): 2, 4, 8, 10, 13-14, 15, 17-19, 27-30 (read about the equal quotients and compatible numbers methods in the chapter before starting 27-30)
• Time Lapse Long Division

• Story Problem Worksheet - Handed out in class on Monday/ Tuesday (Available outside my office door)
• WB: 1.3 (p15), #1-9. You will need additional paper to explain #4-9. Show multiple steps as you manipulate the algebra pieces
• WB: 2.1 (p24) #4-7.

  No textbook sections for this homework.

HW due Monday or Thursday, depending on section.

No homework will be due on Monday/Tuesday (Nov 17th/18th) of Week 8. Next assignment will be due on Monday/Tuesday of Week 9. (This is Thanksgiving Week and Test Day)

In week 7, we finished Venn Diagrams and Started Ch 4.

Draft 2 of Long Division: If you earner lower than 7/10 on the long division time lapse project and are unsatisfied with your grade, you may resubmit this part of the homework. Please make sure your new version is clear, easy to follow, and in beautiful handwriting (or typed). You must staple your original time lapse project to the back of the new version. (Please attach only the time lapse part, not the rest of HW 5.) Due date: Monday/Tuesday of Week 8.

• Divisibility worksheet (Done in class)
• TB: Exercises and Problems 4.1 (p229): 3-6, 13-24
• TB 4.1 (p232): Writing and Discussion #2
• TB: Exercises and Problems 4.2: (p248) 1, 3, 7, 9, 11, 13, 15, 20, 21, 22, 24, 25, 26, 27
• WB 4.2 (p87): 1-9

at the 2nd midterm.

Midterm on Monday/Tuesday

Test topics will include:
• Division Models
• Long Division
• Story Problems / Problem solving
• Algebra
• Venn Diagrams & set notation
• Divisibility
• Factoring & LCMs & GCFs

Take home portion of Second Midterm. Due start of Week 10.

Thanksgiving: No class on Thursday.

Wednesday evening class will meet.

Intended Plan: Your turn to teach: Small groups will be assigned review topics or challenge topics which they will teach during the last week. These groups will be formed and begin prepping on Monday/Tuesday of Week 9, on the test day. Groups may need to meet outside of class. Additional time will be available to any groups wanting to meet during Wednesday's class (4:40 - 6:30). (This includes any Tuesday groups who want the extra time, since Thanksgiving will take over Thursday's slot)

Possible topics to teach include the following review topics. Consider which ones you'd be interested in by Wed/Thurs this week. I will attempt to create groups based on your preferences of topics. (If scheduling to work with your group outside of class is more important, groups can be based on that as well, if you can create a consensus on your topic.)

1. Subtraction models (3 of them)
2. Multiplication models and/or link between area model and algorithm
3. Division models (2 of them)
4. Long division via sharing model
5. Algebra via manipulatives
6. Set notation & Venn diagrams
7. Divisibility tests for 3 and 9
8. Divisibility tests for 2, 5 and 4.
9. GCFs and LCMs via factor trees
10. GCFs and LCMs via workbook method
11. Other ideas?

    Or you can pick a non-review area such as

12. Divisibility test for 11
13. Tests for even / odd in other bases. ex) What do even numbers look like in base 4, base 5, etc?
14. Other ideas?

Guidelines for teaching project:

• If you are doing a review topic, you can choose to teach it as you would to grade schoolers, or to adults. If you are exploring a non-review area, you may need to stick with the adults approach.
• Students get sleepy or inattentive if they are only observers. Try to make your lesson interactive. Maybe have them try some problems.
• Each group should create an outline of their lesson, including the sequencing you plan and intended problems you'll use, with solutions too.
• Each group will have about 15 min to teach. This includes time for the class to try problems and ask questions. If you think your group will need more time, let me know.

1. One copy of your group's lesson plan. (Put all names, first and last on one copy)
2. Two 1/2 page typed reflections on the lessons taught in week 10.

   One reflection should be on how your group's lesson went. What did you like/dislike? What did you learn? What would you still like to learn about your topic? What did you thinking about playing the role of teacher? (You can answer any or all of these)

   One reflection must be done on a group presenting on the day you are not presenting. What did you like/dislike? What did you learn about the topic? What would you still like to learn? What did you think about the teaching? (You can answer any or all of these)

   Limit yourself to half a page.

3. Be present (physically and mentally) both days of presentations.

• Anything from the first two exams
• Any of the presentation topics, #1-10 (listed above)
• Special focus on "why does the math work", not just "how do I compute that".
• Special focus on student errors. This will be one of the biggest responsibilities you will have as a teacher. If a student makes a mistake, what does that tell you about what they _are_ understanding, and how do you get them past any misconceptions? As with most of our topics, this relies heavily on visual models and manipulatives. Explanations of "why" instead of "how" are needed here.

  ex) In multiplying the tens place by the tens place, instead of saying "put the number in the hundreds place", explain why that is the appropiate location, based on the meaning of the numbers multiplied and the meaning of the resulting number. Consider a visual model.