Central Bankers Courses 2008 Advanced Topics in Monetary Economics I

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Description

• cours - matière : economics

Central Bankers Courses 2008 Advanced Topics in Monetary Economics I February 4 – 15, 2008 Argentina Mr. McCandless George T. Austria Mr. Ragacs Christian Belgium Mr. Ide Stefaan Bolivia Mr. Rodriguez Gonzales Hugo Adolfo Brasil Mr. Jorge Marcos Valli Czech Republic Ms. Hájková Dana Europe Mr. Roma Moreno France Mr. Frappa Sébastien Germany Mr. Setzer Ralph Hong Kong Mr. Ng Hoi Tak Hungary Mr. Vonnák Balázs Iceland Ms. Sveinsdóttir Rósa Björk Jamaica Mr. Murray André D. Mexico Mr. Amoroso Plaza Nicolás E. Mongolia Mr. Doojav Gan-Ochir Morocco Mr. Saidi Youssef Poland Ms.

• plaza nicolás e. mongolia
• national bank
• sveinsdóttir rósa björk jamaica
• turkey koray alper turkey date
• section head
• mexico
• date
• education

Sujets

• Economics
• University of Banja Luka
• National Bank of Rwanda
• Germany

Informations

• Publié par: usse0
• Nombre de lectures: 12
• Langue: English

Extrait

th8 Grade Algebra
5 Day Lesson Plan
*Computer*
*Pan Scale*
*Algebra Tiles*
*Equation Mat*
*TI-83 Plus/ TI-73*
Karen KmiotekObjectives
• Students will be able to solve equations by using algebra and the properties of
equality, graphs and tables on the calculator, and an equation mat and algebra
tiles.
• Students will experiment with various models to solve equations.
• Students will work with others to solve equations.
• Students will be able to present mathematical concepts using mathematical
language.
NYS Key Ideas: 1A, 1B – Mathematical Reasoning
2A – Number & Numeration
3A, 3E - Operations
4B, 4D, 4E, 4F-Modeling/ Multiple Representation
5E - Measurement
7E – Patterns/ Functions
NCTM Standards: Number & Operations
Algebra
Problem Solving
Communication
Representation
2Resources
• Lynch, Chicha and Eugene Olmstead. Math Matters Book 2- An
Integrated Approach, South-Western Educational Publishing, 1998.
Chapter 5, pp. 180-187.
• Ellis, Wade, Kathleen Hollowell, Paul Kennedy, and James Schultz.
Algebra 1, Holt, Rinehart and Winston Publishing, 2001. Chapter 3, pp.
114-139.
• Cuevas, Gilbert J., editor. Navigating Through Algebra in Grades 3-5.
Reston, Va: National Council of Teachers of Mathematics, 2001. Pan-
balance applet. (Uses Internet Explorer)
• www.quia.com, Mathematics
• TI-83 Plus/ TI-73 Application, Algebra 1Chapter 2
3Materials
• Pan Scale
• Chips
• Algebra Tiles
• Equation Mat
• TI-83 Plus/ TI-73
• Computers
• Overhead Unit
• Calculator Overhead Screen
4Overview of Unit
Day 1- Properties of Equality
-Opening Activity: Students will experiment with a pan scale and equality
-Main Activity: A lesson on the Properties of Equality will be given using the TI-83
Plus/TI-73 calculator
-Closing Activity: Students will use Navigations Series applet to further experiment
with pan scales
Day 2- One – Step Equations, Addition and Subtraction
-Opening Activity: Show and discuss cartoon on overhead
Show equality on pan scales using the calculator application on
the TI-83 Plus
-Main Activity: Use calculator program to see that equations can be solved by
graphing both sides of the equations, and by viewing a table.
-Closing Activity: Students will experiment with solving word problems.
Day 3- One – Step Equations, Multiplication and Division
-Opening Activity: In groups, students will determine solutions by graphing
equations and reading a table.
-Main Activity: Students will be assigned a group and a method for which they
must prepare a presentation on solving equations.
-Closing Activity: Students will do presentations in their groups.
Day 4- Two – Step Equations
-Opening Activity: In groups, students will determine the equation that is modeled
by the equation mat and algebra tiles.
-Main Activity: Examples will be done on solving two-step equations by using an
equation mat. Then the students will have to solve the equations
they found in the opening activity.
-Closing Activity: Students will have a choice of three games to play on their
calculators to review all the properties of equality.
Day 5- Review and Assessment
-The first half of class will be spent reviewing for the test with the internet.
-The students will take a test for the second half of the period.
5Day 1
Objectives:
• Students will experiment with pan scale and equality.
• Students will be able to use the properties of equality to find equivalent
expressions.
Opening Activity:
In groups of two, students will experiment with a pan scale and weighted
chips. From what they see by placing the chips on both sides, they will make
conjectures about equality.
Main Activity:
I will present all of the properties of equality to the students on the overhead.
Students will follow through the program on their calculators.
• When two expressions are equal, you can add the same number to each
expression and the resulting sums will be equal. This is called the
addition property of equality.
F or all real number’s a, b, and c, if a = c, then a + b = c + b.
- For example, if x – 6 = 10, then x – 6 + 6 = 10 + 6 or x = 16

• When two expressions are equal, you can subtract the same number from
each expression and the resulting differences will be equal. This is called
the subtraction property of equality.
F or all real number’s a, b, and c, if a = c, then a – b = c – b.
- For example, if x + 1 = 4, then x + 1 – 1 = 4 – 1 or x = 3
6
• You can also multiply two equal expressions by the same number. When
you do this, the resulting products will be equal. This is called the
multiplication property of equality.
F or all real number’s a, b, and c, if a = c, then ab = cb.
- For example, if 2x = 10, then 1/2(2x) = 1/2(10) or x = 5
• Finally, you can divide two equal expressions by the same number. When
you do this, the resulting quotients will be equal. This is called the
division property of equality.
For all real number’s a, b, and c, with b 0, if a = c, then a = c .
b b
- For example if 3x = 27, then 3x = 27 or x = 9
3 3

• Next on the calculator, the students will see that we can use these
properties to solve one and two step equations.
7
Closing Activity:
Using the Algebra Navigations Series Pan Balance applet on the computer,
the students will experiment with the pan scale and different weighted shapes. They
will explore the differences in the weights of four different shapes. As they play
along they will have to be thinking about the relationships of the weights between
the different shapes.
After going through all possibilities, the students will be asked to record the
chart on a separate piece of paper. The students will then compare their data with the
rest of the class.
Homework:
8Do a write up on what you observed from the pan scale model. Make sure to
include the method you used to determine the relationships between the different
weights, what the relationships are (list from heaviest to lightest), and what your
feelings were as you placed the shapes on the scale.
Also, using your previous knowledge and the Properties of Equality, come up
with two examples that demonstrate each property.
Sample Student Work:
In order to determine the relationships between the weights of the shapes, I
began by placing one shape on the right hand side of the scale and a different shape
on the left hand side. I kept adding one shape to the side that was higher until the
sides were balanced. I did this for each combination of shapes. After doing all six
experiments, I made a chart on which shape was heavier in each case. I then
compared all six charts to determine that the heaviest shape was the diamond, then
the circle, then the square, and lightest was the upside down triangle.
Sometimes I felt frustrated while placing the shapes on the scale because one
side would always be heavier than the other and I had to keep going back and forth
to make the scale balance. But most of the time I thought this was pretty cool and
helps me visually understand equality.
Examples on Equality
+ 6x+2 = 4x-5, 6x+2+10 = 4x-5+10
+ -x+1 = 2x-6, -x+1+1 = 2x-6+1
- 10x+7 = x+1, 10x+7-2 = x+1-2
- x-5 = 3x-6, x-5-11 = 3x-6-11
* x+2 = 4x, 2(x+2) = 2(4x)
* 7x+1 = x-2, 6(7x+1) = 6(x-2)
/ 3x = 21, 3x = 21
5 5
/ x+4 = 2x-1, x+4 = 2x-1
6 6
Overhead Transparency
9Addition Property of Equality
For all real number’s a, b, and c, if a = c,
then a + b = c + b.
Subtraction Property of Equality
For all real number’s a, b, and c, if a = c,
then a – b = c – b.
Multiplication Property of Equality
then ab = cb.
Division Property of Equality
For all real number’s a, b, and c, with b 0, if a = c,
then a = c .
b b
10