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Mathematics

I.                    Title:  Operations and Coordinates: The Coordinate System

II.                 Organization:  Whole group / pairs

III.               Objectives:

·        The students will be able to name and plot ordered pairs on a coordinate system.

·        The students will perform operations with positive and negative numbers.

IV.              Standards Covered:

·        2.1.5 F:  Use simple concepts of negative numbers on a number line.

·        2.1.8 F:  Use the number line model to demonstrate integers and their applications.

·        2.8.5 H:  Locate and identify points on a coordinate system.

V.                 Materials:

·        Math In Context: Operations Workbook

·        Pencil

·        Graphing paper

VI.              Procedure:

a.       Intro/Motivation:  I will begin the lesson by placing a graph on the overhead projector with two labeled points on it.  I will ask the students what they think is the fastest way to get to the two points.  I will ask the students to share their ideas.

b.      Developmental Activities:  I will ask the students to open their workbooks to page 45 to begin the new section titled “The Coordinate System”.  I will explain to the class that today we will begin to learn how to plot points on a graph.  The number line we have been working with in class moves only left and right, which is in one dimension.  Today we are going to look at what is called a coordinate plane.  A coordinate plane has two dimensions.  You can move left, right, up or down.  I will use the graph on the overhead projector to draw the x-axis.  I will show the students that the number line can also be called the x-axis.  We have learned that when you move left of the zero on the number line the numbers are positive or negative?  (negative)  Call on student for answer.  What about if we move to the right of the zero?  (positive)  Call on student for answer.  Now let’s look at a new axis called the y-axis.  The y-axis moves up and down, rather than left to right.  When you move up the y-axis from the zero, do you think the numbers will be positive or negative?  (positive)  How about when you move down on the y-axis?  (negative)

Can someone read the first two paragraphs on page 45?  Call on

student to read.  The point on the graph where the x and y axes intersect is

called the origin.  The origin can be labeled with a capital O.

Can someone read the last paragraph on page 45?  Call on student

to read.  When we worked with the number line, or the x-axis as we now

know it as, we only needed to know one number to mark a point on the

line.  In the coordinate plane, since we have 2 axes, we need to know 2

numbers to make a point.  These two numbers are called coordinates or

an ordered pair.  Ordered pairs are always written in the form (x, y).

The first number of the ordered pair is called the x-coordinate.  What

axis do you think we could find the x-coordinate on?  Call on student for

answer.  The x-coordinate tells us how many spaces or units to move on

the x-axis.  The second number of the ordered pair is called the

y-coordinate.  What axis do you think this number lies on?  EVERYONE!

The y-coordinate tells us how many spaces or units to move on the y-axis.

On page 45 in your books, point F is labeled with the ordered pair (+2, -1).  Who can tell me what the x-coordinate of the ordered pair is?  Call on student for answer.  How did you figure that out?  So what would the y-coordinate be?  On the graph, if point A is at the origin, which is always labeled with the ordered pair (0, 0), who can tell me how to get to point B?  Try using only two numbers to get there.

The x and y axes divide the coordinate plane into 4 separate

We start in the upper right hand corner, and move counter-clockwise

around the graph.  I will label the quadrants on the graph on the overhead.

After introducing the students to the coordinate system, I will hand out

Battleship game boards to each student.  I will explain the directions to the

class:  place one battleship (made of 3 points) and one submarine (made of

vertically, horizontally, or diagonally.  I will begin by calling a point and

list it in the “points called” box on the game board.  The students need to

record the points called on their game board also and declare whether it

was a hit or a miss (and if the ship is sunk).  The student with the least

amount of hits wins the game.

Closure: At the end of the period, I will ask the class if they enjoyed

playing the game, and if it helped with their understanding of the

coordinate system.

·        For ESL students, allow them to work on problems with a buddy who can help with the language.

·        For special needs students, repeat key concepts in the lesson.

·        During the Battleship game, repeat points called.

VIII.         Evaluation:

Student:

·        Do the students understand what the x and y axes are?

·        Can the students name and plot points on the plane?

·        Do the students understand how to use positives and negatives when plotting points on the graph?

Teacher:

·        Was the class enthusiastic about the lesson?  Was there a lot of participation?

·        Did the students understand the difference between the x and y axes?

·        Did the students understand how to name and plot points on the graph?

·        Did the students seem to enjoy the Battleship game?

IX.       Follow-Up:

·        Give students an extra Battleship game board, and ask them to

play a game with someone at home.

Daily Lesson Plan 2

Mathematics

I.                    Title:  Introduction to Integers

II.                 Organization:  Whole group

III.               Objectives:

·        The students will be able to define what an integer is.

·        Students will be able to identify a positive and negative number.

·        The students will be able to identify where the positive and negative numbers are located on the number line.

IV.              Standards Covered:

·        2.1.5 F:  Use simple concepts of negative numbers on a number line.

·        2.1.8 F:  Use the number line model to demonstrate integers and their applications.

V.                 Materials:

·        Pencil

·        Paper

·        Number line

VI.              Procedure:

a.       Intro/Motivation:  Begin the lesson with a word problem:

Problem:  The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level.  The lowest elevation is Death Valley, which is 282 feet below sea level.  What is the distance from the top of Mt. McKinley to the bottom of Death Valley?

Solution:  The distance from the top of Mt. McKinley to sea level is 20,320 feet and the distance from sea level to the bottom of Death Valley is 282 feet.  The total distance is the sum of 20,320 and 282, which is 20,602 feet.

b.      Developmental Activities: The problem that we just solved uses the notion of opposites.  Above sea level is the opposite of below sea level.  Here are some other examples of opposites:

Top, bottom ;  Increase, decrease ; Forward, backward ;  Positive, negative

We could solve the problem above using integers.  Integers are the set of whole numbers and their opposites.  The number line can be used to represent the set of integers.  Look carefully at the number line (draw on board) :

Now, let’s take a look at some key terms for this unit:

Positive Integers are whole numbers which are greater than zero.  These numbers are to the RIGHT of zero on the number line.

Negative Integers are whole numbers which are less than zero.  These numbers are to the LEFT of zero on the number line.

The integer zero is NEUTRAL.  It is neither positive or negative.

Two integers are OPPOSITES if they are each the same distance away from zero, but on opposite sides of the number line.  One will have a positive sign and the other will have a negative sign.  On our number line, -3 and +3 would be labeled opposites.

Let’s go back to the problem we started class with:

Problem:  The highest elevation in North America is Mt. McKinley, which is 20,320 feet above sea level.  The lowest elevation is Death Valley, which is 282 feet below sea level.  What is the distance from the top of Mt. McKinley to the bottom of Death Valley?

Solution: We can represent each elevation as an integer:

 Elevation Integer 20,320 feet above sea level +20,320 sea level 0 282 feet below sea level -  282

The distance from the top of Mt. McKinley to the bottom of Death Valley is the same as the distance from +20,320 to -282 on the number line.  We can add the distance from +20,320 to 0, and the distance from 0 to -282, for a total of 20,602 feet.

Let’s look at a few more examples:

Ex 1)  Name the opposite of each integer:

a)      - 41

b)      +9

c)      +67

d)      -50

Ex 2)  Write an integer to represent each of the following situations:

a)      14 degrees above zero

b)      10 steps backward

c)      a loss of \$12.00

d)      gaining 40 points

Allow the students to break into pairs to work on the following exercises:

Write an integer to represent the following situations:

1. Earnings of 15 dollars.
2. A loss of 20 yards.

What is the opposite of:

1. -231
2. +1096
3. -98532

Solve the following problem using integers.  Jenny has \$2.00.  She earns \$5.00, spends \$10.00, earns \$4.00, then spends \$3.00.  How many dollars does she have or owe?

Closure: As we have discussed, integers are the set of whole numbers and their opposites.  Whole numbers greater than zero are called positive integers and are labeled with a + sign.  Whole numbers less than zero are called negative integers and are labeled with a – sign.  The integer zero is neither positive nor negative and has no sign.  Two integers are opposites if they are each the same distance away from zero, but on opposite sides of the number line.  A positive integer may be written with or without a sign.

·        For ESL students, allow them to work on problems with a buddy who can help with the language.

·        For special needs students, repeat key concepts in the lesson.

VIII.         Evaluation:

Student:

·        The students will be evaluated by the work they do in pairs.

·        The teacher may also walk around the room while students are working and listen to their responses.  This can be used as a way of evaluating the effectiveness of the lesson.

Teacher:

·        Was there a missing element to my planning?

·        Did things turn out better or worse than expected?

·        Did the students understand how to use the number line to calculate integers?

·        If students did not work well in their groups, try assigning different groups for the next cooperative learning assignment.

IX.  Follow-Up:

Assign problems from the text for homework.

Daily Lesson Plan 3

Mathematics

I.                    Title:  Growing Interest

II.                 Organization:  Whole group / pairs

III.               Objectives:

·        The student will be able to apply percents as operators by solving problems about savings accounts and interest rates.

·        Students will identify what is meant by an interest-bearing savings account.

·        Students will be able to solve interest rate problems after one year.

·        Students will be able to solve compound interest problems to determine how many years it takes for an initial savings account to double.

IV.              Standards Covered:

·        2.2.8:  Add, subtract, multiply and divide different kinds and forms of rational numbers including integers, decimal fractions, percents and proper and improper fractions.

·        2.5.8:  Invent, select, use and justify the appropriate methods, materials and strategies to solve problems.

·        2.5.8:  Justify strategies and defend approaches used and conclusions reached.

V.                 Materials:

·        Calculators (one per student)

·        Math In Context: More or Less Workbook p.37-38

·        Pencil

·        paper

VI.              Procedure:

a.       Intro/Motivation:  I will ask the students: Do any of you have bank accounts?  Why do you have a bank account?  Where do you get the money to save?  What if I told you that Mr. Karamis and I are both opening a new bank.  Mr. Karamis will give you a new pen if you put your money in his bank.  If you put your money in my bank I will give you an extra \$10.00.  Who would you rather bank with?  Why?  Banks want your business so they pay each account holder an interest rate.

b.      Developmental Activities:  Open your books to page 37 on the section called “Growing Interest”.  Call on students to read the introductory paragraph.  Discuss what is meant by an interest-bearing savings account.  Model example:

If I put \$100.00 in a savings account with a 5% interest rate, how much money will I have after one year?  I will show the students different ways to find the answer to the problem on the board.

1)      100 x .05 = 105

2)      10% of 100 is 10

5% of 100 is 5

Therefore, 100 + 5 = 105

What if the bank offered me a 15% interest rate?  How much money would I have after one year?  Call on the students to come to the board and show their solutions.  Call on a student to read the second paragraph on p. 37.  Allow students to work in pairs to answer question 18.  Call on students to explain which strategy they used to solve the problem.  Read and explain problem 19 to the students.  Assign problem 19 for homework.

c.       Closure:  So now you know that when you are looking for a bank to put your money in, you want to look for a bank that is going to give you the highest interest rate.

·        For ESL students, allow them to work on problems with a buddy who can help with language.

·        For special needs students, allow them extra time to work on problems and repeat key concepts in the lesson.

VIII.         Evaluation:

Student:

·        Do the students understand what an interest-bearing savings account is?

·        Can the students calculate interest rates after one year?

Teacher:

·        Did I keep the students attention throughout the entire lesson?

·        Did the students understand how to calculate interest rates?

IX.              Follow-Up:

·        Assign homework problem 19 out of the student workbook on p. 37.      "Mathematics is the alphabet with which God has written the universe." -- Galileo Galilei This site is written and maintained by Tiffany Young