What you should learn

To state the coordinate of a point on a number line

To graph integers on a number line

To add integers by using a number line

NCTM Curriculm Standards 1, 2, 6 - 10

 

In doing this the teacher wants to make sure that the following words are incorporated into the introductory lesson:

Number line

Whole Numbers

Negative Number

Integers

Venn Diagrams

Graph

Coordinate

Introduction: Do you like to play board games? In order to play one popular board game you must know how to move playing pieces around the board. To do this, you add the numbers rolled on dice and then move your playing piece the corresponding number of spaces forward. You also need to know how to move your playing piece backward when directed to do so. Understanding how to add and subtract integers can help you to play.

Nidi, Lynn, Michael, and Domingo are playing the game described above. The chart below shows a turn for each player. How can you represent Nidi's moves using numerals?

You can solve problems like the one above by using a number line. a number line is drawn by choosing a starting position, usually 0, and marking off equal distances from that point. The set of whole numbers is often represented on a number line. This set can be written {0, 1, 2, 3, ...}, where "..." means that the set continues indefinitely.

Although only a portion of the number line is shown, the arrowhead indicates that the line and the set of numbers continue.

The number line below shows that the value of 2 - 3 should be 1 less than 0. However, there is no whole number that corresponds to 1 less than 0. You can write the number 1 less than 0 as -1. This is an example of a negative number.

To include negative numbers on the number line, exstend the number line to the left of zero and mark off equal distances. The points to the right of zero are named using the positive sign (+). The points to the left of zero are named using the negative sign (-). Zero is neither positive nor negative.

The set of numbers used on the number line above is called the set of integers. This set can be written {..., -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, ...}.

Venn Diagrams are figures often used to represent sets of numbers.

Notice that the natural numbers are a subset of the whole numbers and the whole numbers are a subset of the integers.

To graph a set of numbers means to draw, or plot, the points named by those numbers on a number line. The number that corresponds to a point on a number line is called the coordinate of that point.

Exercise 1: Name the set of numbers graphed.

a.

The set is {-5, -4, -3, -2, -1, 0, 1, 2, ...}

 

b.

 

Exercise 2: At 4:08 AM, the temperature in Casper, Wyoming, was -10 degrees Farenheit. By 1:30 PM, the temperature had risen 17 degrees to the daytime high. What was the high temperature? (Draw and label a number line)

Activity: Modeling Mathematics: Adding Integers

To find the sum of -7 and -5, follow the steps below.

Step 1: Draw an arrow starting at 0 to -7, the first addend.

Step 2: Starting at -7, draw an arrow and go to the left 5 units long. This represents the second addend, -5.

Step 3: The arrow ends at the sum, -12. So -7 + (-5) = -12

YOUR TURN

a. What addition sentence is modeled on the number line shown below?

b. Draw a number line to show the addition sentence -3 + (-2) = -5.

c. Use a number line to find -4 + 5.

Closing Activity: Check for understanding by using this as a quick review before class is over. It should take about the last five to ten minutes. I would use it for my students as their 'ticket out the door'. Click Here.

Homework: The homework to be assigned for tonight would be: 17 - 39 odd, 40, 41, 43, 45 - 52

Alternative Homework: Enriched: 16 - 38 even, 40 - 52

Extra Practice: Students book page 759 Lesson 2-1

Extra Practice Worksheet: Click Here.

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