Math 300: Mathematics Concepts for Teachers, Spring 2016

Reading and Homework Assignments

Week 3

HOMEWORK #4: Due Monday, February 15th:

 

Reading Assignment:

·       Read sections 1.4 and 2.1 for understanding and write notes (for yourself) of all the relevant information.  The reading questions below are meant to help you.  Turn in the answers to these questions as part of the homework.

 

Reading Questions:

1.  Learn or remind yourself of the following (no need to write them down on the homework, but learn them well): weight, capacity, angle, area, volume, conversions, gram, ounce, pound, ton, metric ton, milliliter, liter, cup, pint, quart, gallon, angle (two definitions), full turn, degree, radian, protractor, acute angle, right angle, obtuse angle, straight angle, reflex angle, arc, adjacent angles, bisector, supplementary angles, complementary angles, measure of an angle, vertical angles, parallel lines, perpendicular lines, set square, circle, radius (radii), diameter, tangent, compass, straightedge,. 

2.  Find examples and non-examples for each of the following:  angle, adjacent angles, parallel lines, perpendicular lines.

For each of the characteristics in the definition of the object, try to find a non-example that satisfies all the characteristics but that one.

3.  Practice measuring angles with a protractor (follow the instructions on page 21).

4.          What are some mistakes people may make while measuring an angle with a protractor.

5.          Explain the angle measurement facts on page 24.

6.          Use a set square to draw parallel lines and perpendicular lines.

7.          Use a compass and a straightedge to draw two circles which are tangent to each other.

8.          Write questions and comments you have on the readings for today.

 

Homework Assignment:.

·       Homework Set #1: 6,7,8,9 (Optional: 1-5—if you need or would like the practice.)

·       Homework Set #2: 6,7,8,10,11,12,13,14 (Optional: 1-5,9—if you need or would like the practice.)

·       Homework Set #3: 4,5,8,9 (Optional: 1,2,3,6,7,10,11—if you need or would like the practice.)

 

Pen Pal Letter/Video:

o   Select a partner for the pen pal communication with the 4th-5th grade students.

o   Select whether you want to write a letter or create a video to communicate with the students.

o   Revise the videos you have created to include with your letter or video communication.

o   Write or videotape your first “letter” to be sent to the students via email.  You can address the students as “Dear Pen pals” for now, since you do not yet know their names.

o   Submit your letter/video to

 

Here is some information:

Mathematics Letter/Video Pen-pal Information

 

Each week you will correspond via video with children in 4th and/or 5th grade about mathematics.  You and a partner will describe and explain the concepts you are learning in class and from the book, and will hear about the mathematics the children are learning.   You will typically receive the children’s letter/video by the end of the day on Tuesday and your video/letter (one video/letter from the pair of teachers for a group of children) will be due the following Tuesday.  

 

The purpose of this experience is for you to interact with the children mathematically.  You need to create opportunities to explain mathematics and to have the children explain mathematics to you.  Each letter/video should include at least:

·     A pleasant greeting and some getting acquainted conversation (example: sharing some weekend activities, your favorite books, your pastimes, your family background, and asking the children about theirs).

·     Careful/thoughtful responses to the children’s questions and problems (you may say or write notes to the individual children within your letter).

·     A description/explanation of one of the concepts you are learning in class: “Talk” to the children about the concepts.  You can also ask questions about these topics, or ask them what they think they are.

·     A worthwhile mathematical problem for the children related to the concepts we are learning in class.

·     Questions about the mathematics the children are learning in order to find out about their understanding.

You may also include puzzles, drawings, math games, etc.

 

Benefits for you:

·       Making connections between the mathematics you are learning and that which is taught in elementary school. 

·       Reinforcing your understanding by writing about your learning and composing explanations and solutions to children’s questions.

·       Practicing formulating explanations appropriate for school-age children.

·       The satisfaction of becoming the children’s role model; helping them reinforce their understanding and become more successful in mathematics.

·       You may include this activity in a job application, résumé, school application, etc.

 

Your commitment:

·       Communicate with your pen-pals each week throughout the semester.  Turn in your letter/video on time every other week, as the children look forward to receiving them. 

·       Learn about the children’s mathematical thinking and share your insights with the class.

·       Turn in the letters/videos and a reflection paper at the end of the semester.

 

In order to make this pen-pal experience worthwhile and satisfying for all pen-pals, please keep in mind the following items as you write/speak your letters:

1)     Children learn from what they read/see.  Make sure your letter/video is mathematically correct, grammatically correct and free of spelling errors.  Proofread the wording you use for your letter/video and have a friend read it and give feedback.  Rewrite it as necessary.  I will be happy to proofread/view your letter/video if I get it in enough time and make comments/give ideas.

2)     Be a great role model:

·       Write (or speak) thoughtful, meaningful, beautiful letters. These letters/videos may be the first the children have ever received.  Schedule enough time each week (at least one to two hours) to write/video for to your pen-pals.  Get together with your partner to write/video the letter.  You should write/video the letter together.

·       Let the letters/videos show that you have a strong desire to learn.  For example, you may admit that sometimes you get frustrated while working through a problem, but, when you persevere, you feel a great sense of accomplishment.  Also, let the children know that when you did not know the answer to a question, you kept working on it or did some research (tell them how).  If you are still working on finding the answer, let the children know. 

·       Children may mirror the attitudes they encounter.  Speak positively of mathematics and learning.

3)     Make sure your explanations are directed towards the children asking the questions.  If you are not sure of their level of knowledge, give an initial explanation, but also ask specific questions to find out what they know.  The children’s responses will give you a starting point for your next explanation.  Make sure you always try to address “why” and not just “how.”

4)     If you do not know how to answer a question/solve a problem, spend time to do some research.  Do not give up!  I am always happy to help.   

 

Pen-pal Information for Elementary School Students

 

Dear Students,

 

This semester you will communicate with college students who intend to become elementary school teachers.  Your pen-pals look forward to communicating with you about your mathematical learning throughout the year.  The goal is to deepen the pen-pals’ and your understanding of mathematics and your ability to explain concepts, while developing a relationship via correspondence or video communication—whichever you prefer.

 

The purpose of this experience is to interact mathematically.  Your pen-pals will explain mathematics to you and will look forward to your explanations.  Each letter/video should include at least:

a) A pleasant greeting and some getting-acquainted conversation (for example: sharing some of your weekend activities, your favorite books, your pastimes, your family background, and asking your pen-pals about theirs).

b) Responses to your pen-pals’ questions and problems.

c) A description/explanation of the concepts you are learning in class.  You can also ask questions about these topics.

d) A mathematical problem for your pen-pals related to the concepts you are learning in class.

e) Mathematics questions about which you are curious.

You may also include puzzles, drawings, math games, etc.

 

In order to make this pen-pal experience wonderful for all pen-pals, please keep in mind the following items as you write your letters:

 

1. Proofread/check your letter/video and have a friend/teacher/parent read/watch it and give you input.  Rewrite/re-record it as necessary.  Please:

    1. Schedule enough time each week to create a thoughtful, meaningful, beautiful letter/video.
    2. Describe your learning and understanding of mathematical concepts in as much detail as you can.  Let your pen-pals know about successes and challenges while solving problems.  Share when you get an “aha” moment and when you become frustrated while working through a problem, and tell them about the process that helped you understand or overcome a challenge.  
    3. Let your pen-pals know how you feel about the mathematics you are learning.

 

  1. Tell your pen-pals what you know, and ask specific questions.  That way your pen-pals will be best able to provide an explanation that will make sense to you.  If the explanations are not clear to you, please be specific about what you did not understand.

 

  1. When your pen-pals ask you a question, and you do not know the answer, keep trying!  Describe where you got stuck, and your pen-pal may be able to provide some guidance.  Please remember that getting the answer to a mathematical problem is only part of the process of doing mathematics.  If you think about the mistakes you made in the process, about other problems you can solve in a similar way, and about other strategies to solve the problem, you gain more understanding.  Let your pen-pals know about the mistakes you made and what you learned from them, and about other thoughts and ideas you had once you got an answer. 

 

Pen-pal checklist

 

Our pen-pal letter/video includes at least:

 

_______A pleasant greeting and some getting-acquainted conversation.

 

_______Careful/thoughtful responses to all of our pen-pals’ questions and problems.

 

_______A detailed description/explanation of one of the concepts we are learning in class.

 

_______At least one worthwhile mathematical problem for my pen-pals to solve.

 

_______At least one question about mathematics.

 

 

Other issues to consider:

 

_______Our letter/video is grammatically correct and free of spelling errors.

 

_______We spent an adequate amount of time and effort creating this letter/video.

 

_______We have fun communicating with our pen-pals and make our pen pals look forward to getting our letter/video every week.

 

_______Our letter/video includes the date.

 

_______ Please name the letter/video using your names and the letter/video number.

 

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