Principles of Economics

Tom Giambrone

Description

• cours magistral
• leçon - matière potentielle : supply
• cours - matière potentielle : on the principles of economics
• expression écrite
• revision
• cours - matière : economics - matière potentielle : economics
• leçon - matière : economics

Principles of Economics N. Gregory Mankiw Harvard University January 2000

• macroeconomics
• classical assumption of price flexibility
• demand curve
• run assumptions of price flexibility
• short run
• behavior of a firm
• behavior of the firm
• economics
• theory
• questions

Sujets

• Cours magistral
• Supply
• Révision
• Economics
• Jordan
• Department of Justice

Informations

• Publié par: usse0
• Nombre de lectures: 15
• Langue: English

Extrait

th7 Grade Integer Arithmetic
7-Day Unit Plan
by
Brian M. Fischer
Lackawanna Middle/High School
Page 1 of 20Table of Contents
Unit Objectives …………………………………………...…………………………..…... 3
NCTM Standards …………………………………………………………….…………... 3
NYS Standards ………………………………………………………….………………....3
Resources and Materials ……………………………..…………………………………… 3
Overview of daily objectives ……………………………………….……………………. 4
Day 1 ……………………………………………….……………….…………………….5
Day 2 ……………………………………………….……………….…………………….8
Day 3 ……………………………………………….……………….…………………….9
Day 4 ……………………………………………….……………….…………………….12
Day 5 ……………………………………………….……………….…………………….14
Day 6 ……………………………………………….……………….…………………….15
Day 7 ……………………………………………….……………….…………………….17
Page 2 of 20Unit Objectives - Students will be able to
§ add, subtract, multiply, and divide integers.
§ use algebra tiles to model the addition and subtraction of integers.
§ add and subtract integers using an interactive internet site that simulates algebra tiles.
§ find the average of a set of integers.
NCTM Standards for Grades 6 - 8
§ Number and Operations Standard
§ Problem Solving Standard
§ Reasoning and Proof Standard
§ Communication Standard
§ Connections Standard
§ Representation Standard
NYS Standards for Grades 7 - 8
§ Key Idea 1 – Mathematical Reasoning
§ Key Idea 3 – Operations
§ Key Idea 4 – Modeling/Multiple Representations
§ Key Idea 5 – Measurement
§ Key Idea 7 – Patterns/Functions
Resources & Materials
§ Textbook: Middle School Math Course 2 by Foresman - Wesley, 1999.
§ Supplemental worksheets from the Foresman – Wesley textbook..
§ Algebra tiles – minimum 10 yellow tile and 10 red tiles per student/pair.
§ Computer lab with internet access. Students may work in pairs.
§ Student worksheets.
§ MATHO boards and MATHO problem cards.
§ Scientific Calculator.
Page 3 of 20Overview of Daily Objectives
Day 1 – Students will
§ understand the definition of additive inverse and the zero property of addition.
§ be able to use algebra tiles to represent integer addition problems and determine their sums.
§ develop rules for adding a pair of integers.
Day 2 – Students will
§ be able to use an interactive internet site to represent integer addition problems with algebra
tiles and determine their sums.
§ be able to use an interactive internet site to represent integer subtraction problems with
algebra tiles and determine their differences.
Day 3 – Students will
§ be able to use algebra tiles to represent integer subtraction problems and determine their
differences.
§ rewrite integer subtraction problems as addition problems.
Day 4 – Students will
§ be able understand the concept of a negative times a negative by using a visual aid.
§ develop integer multiplication rules by developing patterns.
Day 5 – Students will be able to divide integers.
Day 6 – Students will be able to solve problems that involve finding the average of a set of
integers.
Day 7 – Students will practice to integer arithmetic in a game format.
Page 4 of 20Day 1
Objective – Students will be able to:
§ Understand the definition of zero pairs and the Zero Property of Addition.
§ Use algebra tiles to represent integer addition problems & determine their sums.
§ Develop rules for adding a pair of integers.
Materials – algebra tiles, worksheets, overhead projector, algebra tiles for the overhead.
Opening Activity – Distribute worksheets. Have them copy the definitions of Additive Inverse
and Zero Property of Addition. While they are doing this distribute the algebra tiles.
Activity #1 – Discuss the above definitions and zero pairs. Explain that a yellow tile represents
+1 and a red tile represents -1. Demonstrate zero pairs using the tiles.
Activity #2 – Model worksheet problems 1 and 2 together and discuss question #3.
Activity #3 – Model worksheet problems 4 and 5 together and discuss.
Activity #4 – Have students model and solve problems 6 thru 9 on their own. Monitor their
progress by observing. After they have completed the problems have them discuss their
solutions with their group members. Students will then be selected to model and explain their
solutions to the class using the overhead. Leave enough time to formalize the rules.
Closing Activity – Discuss the solution to question 10 and review the solution to question 3.
Compare and contrast how to add integers with like and unlike signs. Collect the tiles.
Homework – page 453: 2, 6-18 even. Have them sketch algebra tiles.
Page 5 of 20Adding Integers
Additive Inverse -
The Zero Property of Addition -

Ø We will be using algebra tiles to model the addition of integers.
§ Yellow tiles represent positive integers (unshaded squares in our diagrams).
§ Red tiles represent negative integers (shaded squares in our diagrams).
§ By the Zero Property of Addition, a yellow tile plus a red tile equals .
1. Use algebra tiles to model the addition problem (+5) + (+3). Sketch your model below.
What is the sum of +5 and +3?
2. Use algebra tiles to model the addition problem (-2) + (-7). Sketch your model below.
What is the sum of -2 and -7?
3. Describe how to find the sum of a pair of integers with like signs.


4. Write the addition problem for the model below.
Circle the zero pairs, a positive and a
negative tile paired up equals zero.
What is the sum of the above model?
Page 6 of 205. Write the addition problem for the model below.
Circle the zero pairs, a positive and a
negative chip paired up equals zero.
What is the sum of the above model?
6. Use algebra tiles to find the sum of (+3) and (-8). Show your model below.
7. Use algebra tiles to find the sum of (+5) and (-2). Show your model below.
8. Use algebra tiles to find the sum of (-6) and (-3). Show your model below.
9. Use algebra tiles to find the sum of (-6) and (+8). Show your model below.
10. Describe how to find the sum of a pair of integers with different signs.



Page 7 of 20Day 2
Objective – Students will be able to:
§ Use algebra tiles to represent integer addition/subtraction problems & determine
their sums/differences.
Materials – computers connected to the internet and a video display so that the students can
observe the teacher’s interaction with the computer.
Opening Activity – Have the students seated at a computer in pairs and have them observe the
teacher work with the algebra tiles on the computer. Go to the web site
http://matti.usu.edu/nlvm/nav/frames_asid_161_g_2_t_1.html and go through 2 demonstration
problems. Have this web site written on the chalkboard and/or stored in favorite places. Always
check a web site prior to using it.
Activity #1 – Have the students access this website and solve some integer addition problems.
Have them write these problems and their solutions on a sheet of paper. Let each student solve
about 3 problems.
Activity #2 – Review the rules for adding integers.
Activity #3 – Go to the web site http://matti.usu.edu/nlvm/nav/frames_asid_162_g_2_t_1.html
and go through 2 demonstration problems. Have this web site written on the chalkboard and/or
stored in favorite places.
Activity #4 – Have the students access this website and solve some integer subtraction problems.
Have them write these problems and their solutions on a sheet of paper. Let each student solve
about 3 problems.
Closing Activity – Discuss integer subtraction. See if they made a connection to addition.
Homework – page 453: 2, 20-30 even, 33, and 36.
Page 8 of 20Day 3
Objective – Students will be able to:
§ Use algebra tiles to represent integer subtraction & determine differences.
§ Develop rules for subtracting a pair of integers.
Materials – algebra tiles, worksheets, overhead projector, algebra tiles for the overhead.
Opening Activi