I. Human Rights as Politics II. Human Rights as Idolatry

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Description

• cours magistral
• revision
• exposé
• cours - matière : law

I. Human Rights as Politics II. Human Rights as Idolatry MICHAEL IGNATIEFF The Tanner Lectures on Human Values Delivered at Princeton University April 4–7, 2000

• man rights
• virtual war
• moral progress
• universal declaration
• crimes
• states
• international relations
• human rights
• state

Sujets

• Cours magistral
• Révision
• Exposé
• Cassin
• Lauren
• Alain Finkielkraut
• Helmuth von Pannwitz
• Sewall

Informations

• Publié par: usse0
• Nombre de lectures: 14
• Langue: English

Extrait

Page 1.
A Five Day Exploration of
Polynomials
Using Algebra Tiles and the TI-83
Plus
Graphing Calculator
Pre- Algebra
Grade Seven
By: Cory SavardPage 2.
Overall Unit Objectives
Upon completion of this unit, students will be able to do the following things:
1. Both identify and classify polynomials and find their degree.
Standards met:
NCTM: #1 (Mathematics as problem solving), #2 (Mathematics as communication),
#3 (Mathematics as reasoning), #4 (Mathematical connections), and #9 (Algebra).
NYS: #1 (Mathematical Analysis, part 1a).
2. Evaluate polynomials.
Standards met:
NCTM: #1 – 4, 9
NYS: #3 (Mathematical Reasoning).
3. Use algebra tiles to represent polynomials.
Standards met:
NCTM: #1 – 4, 9
NYS: #6 (Models).
4. Add, subtract and multiply polynomials using algebra tiles.
Standards met:
NCTM: #1 – 4, 9
NYS: #1 (Analysis).
5. Use the TI-83 Plus graphing calculator to graph polynomials.
Standards met:
NCTM: #1 – 4, 9Page 3.
NYS: #2 (Information Systems)
6. Identify the degree of a polynomial based on the shape of its graph, and identify
the shape of a graph based on the degree of its polynomial equation.
Standards met:
NCTM: #1 – 4, 9
NYS: #2 (Information Systems).Page 4.
Resources Used
1. “Pre-Algebra: An Integrated Transition To Algebra and Geometry”, by Price,
Rath, Leschensky, Malloy and Alban; Copyright 1997 by Glencoe/The McGraw
Hill Companies, Inc. Material used includes Chapter 14 (pp. 706-730).
2. “Curriculum and Evaluation Standards for School Mathematics”, Copyright 1989
by The National Council of Teachers of Mathematics, Inc.Page 5.
Materials and Equipment Needed
1. A class set of “homemade” algebra tiles.
2. One set of algebra tiles for use with the overhead projector.
3. An overhead projector.
4. A class set of TI-83 plus graphing calculators, as well as an overhead projector kit
to display the calculator screen on the overhead.
5. Handouts #1 – 9
6. Answer keys for handouts #1-4, 6-9.
7. Bookwork answer keys #1-5.
8. “Pre-Algebra: An Integrated Transition To Algebra and Geometry”, by Price,
Rath, Leschensky, Malloy and Alban; Copyright 1997 by Glencoe/The McGraw Hill
Companies, Inc.Page 6.
Polynomials: A Unit Overview
1. Introducing Polynomials
a. Monomials, binomials and trinomials
b. The constant
c. Finding the degree
d. Evaluating polynomials
2. Adding Polynomials with algebra tiles
a. Introduce algebra tiles
i. Explain that each tile has a value based in its area.
ii. Explain negative tiles
iii. Practice modeling polynomials with the tiles.
b. Explain some characteristics of polynomials.
i. The coefficient
ii. Like terms
c. Begin adding polynomials with the tiles.
i. Explain “zero pairs”
ii. Practice problems
3. Subtracting polynomials with algebra tiles
a. Explain that subtracting is simply adding the additive inverse.
i. Distribution
ii. Additive inverse and how to find itPage 7.
b. Practice finding the additive inverse
c. Practice subtracting polynomials
4. Multiplying Polynomials with algebra tiles
a. Using rectangles
b. Multiplying a polynomial by a monomial
i. Distribution
ii. Commutativity
c. Practice problems
5. More multiplying with algebra tiles
a. Multiplying binomials
b. Combining like terms
c. Introducing word problems
d. Practice problemsPage 8.
Day #1
Introducing Polynomials
Concept: Identifying, classifying, finding the degree of and evaluating polynomials.
Objectives: By the end of the day students should be able to identify monomials,
binomials and trinomials. Students should also be able to find the degree of a monomial,
binomial, trinomial or constant. Finally, students should be able to evaluate polynomials
when given a value for the variable.
Materials: One copy of Handout #1 per group of five students, Handout #1 answer key,
one copy of Handout #2 for each student, Handout #2 answer key, Bookwork answer key
#1.
Opening Activity: Introduce the terms monomial, binomial, trinomial, polynomial and
constant.
Developmental Activity:
1. Identifying monomials, binomials, trinomials and the degree of each.
2. Evaluating polynomials for a given variable value.
Closing Activity: Pose questions to verify student understanding in the form of a “relay”.Page 9.
Day #1
Teacher Notes
Opening Activity: Have students recall the definitions of the terms monomial, binomial,
trinomial, polynomial and constant. Use words in which the prefixes are familiar, such
as bicycle and tricycle, to help the students understand the definitions.
Developmental Activity:
Ask the students to identify each of the following expressions as a monomial,
binomial or trinomial, or not a polynomial at all.
1. x + 4 Answer: binomial
2. x Answer: monomial
3. x + 4x + 4 Answer: trinomial
4. 2x + Answer: not a polynomial
Introduce the term constant and ask the students to identify the constant term of
each of the following:
1. x + 1 Answer: 1
2. x + 3x + 5 Answer: 5
Introduce the term degree and explain how to find the degree of a monomial,
binomial, trinomial or constant. Ask students to find the degree of the following: (Recall
that the exponent of x is 1.)
1. 3x Answer: 1
2. 2xy Answer: 3
Inform students that the degree of a constant term is zero.
2
2
x
1
2
3
2Page 10.
Explain to students how to find the degree of a polynomial. Ask the students to
find the degree of the following polynomial by finding the degree of each monomial
within the polynomial: x + xy + 5
Answer: x = Degree 3
xy = Degree 2
5 = Degree 0, Since 5 is a constant
x + xy + 5 = Degree 3, Since 3 is the highest monomial degree in
the polynomial.
Ask the students to find the degree of the polynomial x y + x + y . Answer:
4
Show students how to evaluate polynomials for given variable value/values.
Solve the following equation with the students: x + xy + 1 when x=3 and y=2.
1. Plug in 3 for x and 2 for y.
2. Solve, obtaining 16.
Ask the students to evaluate xy + y + 3 for x=7 and y=5. Answer: 63.
Closing Activity: Conduct a relay with the students. Separate the students into rows of
five, if they are not already in such rows. Cut up one copy of handout #1 per row of
students and distribute question #1 to the first student in each row, question #2 to the
second student in each row, etc. Student #1 will solve his/her question and pass that
answer on to student #2, who will use the answer from student #1 to solve his/her
question, and so on. There should be no talking allowed. Upon completion of the last
2
3
2
3
3
2
2
2
3