NCTM goals state that all students should:

Learn to value math.Become confident in their ability to do math.Become mathematical problem solvers.Learn to communicate mathematically.Learn to reason mathematically.

Writing enables students to engage in problem solving activities that require them to question, explore, summarize, clarify, predict, verify, and communicate their findings through written and oral language.

1. They must stop and think about what was done;2. They must construct ideas.3. They are challenged to examine their ideas.4. They become actively involved in thinking and learning.

1. Journals2. Solving Math Problems3. Explaining Mathematical Ideas4. Creative Writing/General Writing Assignments

1. Use a separate notebook to be used only as a math journal.

2. It is best to take the last 5 minutes of class for journal writing while the lesson is still fresh.

3. Journal assignments can be to write (1) what they thought about the day’s lesson; (2) what they learned today; (3) write about difficulties they are having; (4) write to a friend who missed the lesson; or (5) definitions and illustrations of new terms. Also, give them a sense of audience and a purpose for writing.

4. Journals should never be graded or corrected for grammar, spelling. etc., however, if a statement is unclear the teacher should ask the student to rewrite.

5. Journals must be read by the teacher (once a week), and students need to know they are being read.

Journal writing helps the teacher assess how well students are understanding or NOT understanding the math concepts being taught. It also helps the teacher assess his/her instruction.

1. Have students generate their own descriptions, explanations, or examples. No word-for-word copies from text or dictionary.

2. Have students represent each term or phrase using a graphic representation, picture, illustration, or pictograph.

3. Periodically review the terms and phrases. One good way to accomplish this is by using a “Word Wall.”

For a complete description of this project and a list of words see: http://state.tn.us/education/ci/ Click on “Resources” then open the file for TN Academic Vocabulary

Students should explain the reasoning process (either in writing or verbally) to show how and why they solved a problem they way the did. Encourage the use of drawings or diagrams.

This is not problem solving. It is prompted by a straightforward request such as “Explain what ¾ means?” or “Show me what you know about the relationship of fractions, decimals, and percents?”

Spot

Each month John weighs his puppy Spot, with the results shown below.

1. If the pattern of the puppy’s weight gain continues, how much will he weigh at 5 months?

2. How much do you think Spot will weigh when he is fully-grown?

Explain how you arrived at your answers-tell me STEP-BY-STEP, writing in complete sentences AND showing your work along the way.

BE SPECIFIC AND INCLUDE DETAILS!!!Spot’s Age Spot’s Weight

1 month 10 lbs.

2 months 15 lbs.

3 months 19 lbs.

4 months 22 lbs.

5 months ?

How you will be GradedFormat:

_____ Neatness (5pts)

_____ Correct Heading (5 pts)

Pattern Recognition and Extension:

_____ All work provided (10 pts)

_____ Accuracy

No awareness of the pattern. (10 pts)

Recognition that there is a pattern but incorrect conclusion as to what it is. (20 pts)

Correct recognition of pattern, but inability to extend (30 pts)

Correct recognition and extension of pattern (40 pts)

Explanation:

_____ Clarity

No or wholly inadequate explanation provided. (10 pts)

Explanation unclear. (20 pts)

Explanation clear. (30 pts)

Explanation very clear and well articulated (40 pts)

Variable Dilemma

Each letter in the equations below stands for a different number (0-9). Look at each equation carefully. Think about what you know about how numbers work. Find the value of each letter (A-J).

Write a brief summary of how you found your answer. It should describe EVERY STEP IN DETAIL, and it should enable a reader to understand the approach you used to find the solution for EVERY VARIABLE.

1. G+G+G=D

2. J+E=J

3. G2=D

4. B+G=D

5. F-B=C

6. I/H=A (H>A)

7. A•C=A

How You Will be Graded

Format:

_____ Neatness (5pts)

______ Correct Heading (5 pts)

Accuracy:

_____ No findings or a few correct answers (10 pts)

Some recognition of applicability of principles of number theory; some/most answers correct. (20 pts)

All answers correct based on complete application of principles of number theory. (30 pts)

Approach/Method of Solution:

_____ Random and disorganized; no systematic approach. (10 pts)

Some system apparent in the approach, but not well organized/use of trial and error. (20 pts)

Highly systematic and organized approach; no reliance on trial and

error. (30 pts)

Explanation:

___ Little or no explanation given. (10 pts)

Explanation attempted, but difficult to understand/thinking process not always easy to follow. (20 pts)

Explanation very clear, and thinking process easy to follow. (30 pts)

Outfits

Maria is going to visit her cousins for the weekend. She packs a pair of purple pants, a pair of jeans, and a pair of blue shorts. For shirts she takes a blue tee shirt, a white tank top, a yellow blouse, and a green shirt. In addition, she has three pairs of socks: White, yellow, and blue.

How many different outfits can she make?

Use a picture or table to organize the information.

Write a detailed and specific description of how you figured out your answer.

How you will be GradedFormat:

_____ Information is randomly presented-there is no apparent method of organization. (5pts)

Some attempt to organize the information; however the system is inefficient (15 pts)

Organization of information shows recognition of the patterns inherent in the situation. (25 pts)

Method of solution:

_____ Either no method used or method completely inappropriate. (5 pts)

Appropriate method used, but either not fully executed or based on rote application only. (15 pts)

Method used highly elegant and efficient, revealing comprehensive understanding. (30 pts)

Explanation:

_____ Description either missing or reveals an approach to the problem only by trial and error. (5 pts)

Description reveals limited attempt to use a systematic approach, but only by trial and error. (15 pts)

Description is efficient and clear, revealing understanding of a systematic approach. (25 pts)

Describe the following situations in writing.

1. Divide 18 balloons among 4 people.

2. Divide 18 cookies among 4 people.

3. Divide $18.00 among 4 people.

4. Divide 18 by 4 on a calculator.

What are the similarities and differences?

R—Role from which to writeA—Audience to addressF—Format in which to writeT—Topic about which to writeS—Stronge Verb that suggests the purpose of writing

R.A.F.T.S. prompts can be used in any content area.

R.A.F.T.S. prompt:

You keep your weekly grades in a notebook. This week your teacher asked you to average your grades to arrive at a mean score to share with your parents at a parent/teacher conference. Do this calculation, then write a reflections to share with your parents on how well you are succeeding in math.

RoleAudienceFormatTopicStrong Verb

Youyour parentsreflectionaverage your grades to arrive at mean scoreshare and write

1. Make it easy for students to speak in class.2. Use discussion to determine what knowledge students bring

to the subject of your lesson.3. Get students to explain their answers.4. If they truly understand, they can write it.5. Notice what is right, not just what is wrong.

A final word from Kaye Toliver:

“When your students feel it is safe to talk; whey they know that what they say will be listened to; they see that what they have to communicate is considered to be valuable by the teacher; you will have opened windows into their minds.”