1. Title: The Power of One – math in a different angle

“We are all woven together in a single garment of destiny.” Dr. Martin Luther King

Grade level / Class size / Time/Duration
6 / 35 / 2 period of 50 minutes

2.

  1. Subject: Mathematics

(After lesson on powers and exponents.)

4. Objective:

  • Using at least 3 different numbers students will create a mathematical model of the exponential power of a number
  • Using math manipulative material students will explore the concrete model of the power of a number (grains of rice doubled each square of a chess board)
  • Students will participate actively in a discussion about the exponential power of a historical event, a personality, an idea, a scientific fact, a word such as “ahimsa” and “satyagraha”
  • Students will write a personal commitment statement to reflect the collective brainstorming
  • Students will apply the notion to the power of their own beliefs by making a small piece of a classroom self-discipline quilt called “everyone counts”.

Goal: To extend the concept of the immense scope of the exponential power of a unit.

5. Standards:

CaliforniaState Standards:

Algebra and functions

1.3 Apply algebraic order of operations and the commutative, associative, and distributive properties to evaluate expressions; and justify each step in the process.
1.4 Solve problems manually by using the correct order of operations or by using a scientific calculator.

Number sense

2.3 Solve addition, subtraction, multiplication, and division problems, including those arising in concrete situations that use positive and negative integers and combinations of these operations.

Mathematical reasoning

1.0 Students make decisions about how to approach problems:

1.1 Analyze problems by identifying relationships, distinguishing relevant from irrelevant information, identifying missing information, sequencing and prioritizing information, and observing patterns.
1.2 Formulate and justify mathematical conjectures based on a general description of the mathematical question or problem posed.
1.3 Determine when and how to break a problem into simpler parts.

2.0 Students use strategies, skills, and concepts in finding solutions:

2.1 Use estimation to verify the reasonableness of calculated results.
2.2 Apply strategies and results from simpler problems to more complex problems.
2.3 Estimate unknown quantities graphically and solve for them by using logical reasoning and arithmetic and algebraic techniques.
2.4 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.
2.5 Express the solution clearly and logically by using the appropriate mathematical notation and terms and clear language; support solutions with evidence in both verbal and symbolic work.
2.6 Indicate the relative advantages of exact and approximate solutions to problems and give answers to a specified degree of accuracy.
2.7 Make precise calculations and check the validity of the results from the context of the problem.3.0 Students move beyond a particular problem by generalizing to other situations:

3.1 Evaluate the reasonableness of the solution in the context of the original situation.
3.2 Note the method of deriving the solution and demonstrate a conceptual understanding of the derivation by solving similar problems.
3.3 Develop generalizations of the results obtained and the strategies used and apply them in new problem situations.

Language Arts:

Reading:

1.0Word Analysis, Fluency, and Systematic Vocabulary Development

Students use their knowledge of word origins and word relationships, as well as historical and literary context clues, to determine the meaning of specialized vocabulary and to understand the precise meaning of grade-level-appropriate words.

Vocabulary and Concept Development
1.2 Identify and interpret figurative language and words with multiple meanings.
1.3 Recognize the origins and meanings of frequently used foreign words in English and use these words accurately in speaking and writing.
1.4 Monitor expository text for unknown words or words with novel meanings by using word, sentence, and paragraph clues to determine meaning.
1.5 Understand and explain "shades of meaning" in related words (e.g., softly and quietly).

Literary Response and Analysis

Students read and respond to historically or culturally significant works of literature that reflect and enhance their studies of history and social science. They clarify the ideas and connect them to other literary works.

Narrative Analysis of Grade-Level-Appropriate Text3.2 Analyze the effect of the qualities of the character (e.g., courage or cowardice, ambition or laziness) on the plot and the resolution of the conflict.3.3 Analyze the influence of setting on the problem and its resolution.
1.0 Writing Strategies
Students write clear, coherent, and focused essays. The writing exhibits students' awareness of the audience and purpose. Essays contain formal introductions, supporting evidence, and conclusions. Students progress through the stages of the writing process as needed.
2.4 Write responses to literature:
  1. Develop an interpretation exhibiting careful reading, understanding, and insight.
  2. Organize the interpretation around several clear ideas, premises, or images.
  3. Develop and justify the interpretation through sustained use of examples and textual evidence.
Speaking Applications (Genres and Their Characteristics)
2.3 Deliver oral responses to literature:
  1. Develop an interpretation exhibiting careful reading, understanding, and insight.
  2. Organize the selected interpretation around several clear ideas, premises, or images.
  3. Develop and justify the selected interpretation through sustained use of examples and textual evidence.

2.4 Deliver persuasive presentations:

  1. Provide a clear statement of the position.
  2. Include relevant evidence.
  3. Offer a logical sequence of information.
  4. Engage the listener and foster acceptance of the proposition or proposal.

2.5 Deliver presentations on problems and solutions:

  1. Theorize on the causes and effects of each problem and establish connections between the defined problem and at least one solution.
  2. Offer persuasive evidence to validate the definition of the problem and the proposed solutions.

District character education guidelines:

6. Summary of the lesson:

Students will explore the exponential power of a number in several modalities and transfer the concept to real life experience and commitment. They will expand the connection of the power of a unit to the scientific, historical and character-building areas. They will discuss and write about their personal power to maintain the nonviolence in their environment. Finally, they will create a classroom quilt with each one adding a piece with their personal statement on promoting “respect and responsibility” in the classroom community. The quilt, the concept and the music will be used all year as a reminder and symbol of the personal and communal commitment.

7. Questions to consider:

  • What is my understanding of the power of a number?
  • What is the collective scope of every unit?
  • How does this math concept apply to my life?
  • How does each individual force become a collective power?
  • Is my voice valid? Does it count? Does it have a value?
  • How do my thoughts/ words/actions affect others? All of us? Me?
  • What are my micro and macro responsibilities?
  • As a child, do I have the strength to affect change in my environment?

8. Materials needed:

Pattern blocks

Beans/rice or other counters

Teacher or student made copy of a chessboard

9. Vocabulary

Power unit

Base collective

Exponent factor

Responsibility commitment

10.Interdisciplinary approach:

Science: Examine the impact of individual gain versus its impact on the environment.

Social studies: Analyze the different nonviolent movements in history to study the collective power of one thought, one resolve, one person, one nation

Language Arts: Write essays, poems, rap songs. Read biographies of Mahatma Gandhi, Dr.Martin Luther King, Cesar Chavez or any other person who has made a significant positive contribution that has benefited many.

Arts: Make posters, murals, write music.

Current events: identify the individuals who are trying to overcome injustice today. What are the issues? What are the methods? How effective are these methods?

  1. Assessment:
  1. Point system:

3 points for the math problems

1-10 points can be assigned for the personal statement

1-10 points can be assigned for the completion of the quilt piece

Instructional Agenda

Teacher instruction / Student response
  1. Introduction/Hook
As students walk into the classroom there is a question on the board for bell-work: “For an 8-day job, how would you like to be paid? A. $10 for each day or B. $1 doubled for eight days?
Next, teacher will read them the book, One grain of rice by Demi
  1. Lesson/Activity
Students are asked to show the exponential growth of any three numbers.
Students are encouraged to use math manipulative and demonstrate the concept.
Teacher leads discussion as to where we see this phenomenon in other areas of our lives:
Nature- the power of a seed
the power of a drop of water
Body – the power of a cell
Politics- the power of a vote
Sports- the power of a second
History- the power of a idea
the power of a song “This little light of mine I am going to let it shine”
  1. Conclusion
Teacher will apply the notion of the power of each individual to –
*Respect for themselves and others. *Nonviolence towards self and others. *The power of nonviolence.
Teacher will read poem from ‘Tao Te Ching’
“The softest stuff in the world
Penetrates quickly the hardest;
Insubstantial, it enters
Where no room is.
By this I know the benefit
Of something done by quiet being;
In all the world but few can know
Accomplishment apart from work,
Instruction when no words are used.” / Students will be asked to give a spontaneous response and then justify it by solving the two problems.
Students will start making the connection as to the immense scope of a unit.
Students will write the exponential powers of 3 numbers of their choice and share with class.
Students will share chessboards with partners to place grains of rice on squares. They will begin with one grain of rice and keep doubling the number for each square after that.
Students will contribute to the collective intelligence by giving other examples.
Students will hear the song and interpret the lyrics.
Student will write a paragraph summarizing the group discussion and their personal understanding of it.
Students will design a small piece of a paper/fabric to be later added to the class quilt of “everyone counts”. On the piece they will write their personal commitment to promote the class motto of respect and responsibility.
  1. Reflection: Students will be empowered with the notion of their personal role as an effective part of the whole group. Students will stretch their time concept from ‘here and now and about me’ to ‘then and later and about us’
  1. References of all sources

Internet:

Bibliography of primary or secondary sources

One grain of rice: A mathematical folktale by Demi

Sing For Freedom: The Story Of The Civil Rights Movement Through Its Songs
A life like mine – D K Publishing

Tao Te Ching –R.B. Blakney (1955, Mentor Books New York, poem #43)