GEOMETRY LESSON

1. Chapter 1
Chapter 1
Using Algebra to work with Data
Using Algebra to work with Data
Lesson 1.4
Working with Integers

2. CA Standard
CA Standard
• Number Sense
• Grade 7 Standard 2.5
• Understand the meaning of the absolute value of a
number;
• interpret the absolute value as the distance of the
number from zero on a number line; and
• determine the absolute value of a real number.

3. What are we going to learn today:
What are we going to learn today:
• Find the absolute value of a number
• Add and subtract integers
• Use negative numbers to find differences on
number scales

4. Natural numbers
Natural numbers
• Counting numbers like 1, 2, 3 …

5. Whole Numbers
Whole Numbers
• 0, 1, 2, 3 …

6. Integers
Integers
• Negative and Positive numbers
• Zero
• … -5, -4, -3, -2, -1, 0, 1, 2, 3, 4 …

7. Rational Numbers
Rational Numbers
• Numbers that can be expressed as fractions

8. Irrational Numbers
Irrational Numbers
• Numbers that are not rational
• √2
• 0.303003…

9. Real Numbers
Real Numbers
• All rational and irrational numbers

10. Classification of Numbers
Classification of Numbers
Irrational Numbers Rational Numbers
Real Numbers
Natural
Whole
Integers
1 2
5 7
0
-7
-29
-0.7
1
2
3
√2
0.303003…
π
-√17

11. Number Line Terms
Number Line Terms
• Numbers under the line are called coordinates
• What is a special name for point C on the number line?
• Origin
• Does 5.3 lie to the left or right of 5?
• right
• Does -5.3 lie to the left or right of -5?
• left

12. Number Line
Number Line
• How far from the origin is the point labeled E?
• 9.5
• How far from the origin is the point labeled B?
• 5.5
• Are the coordinates of these points and the distance they are from the origin
the same?
• No
• What do the coordinates of these points have to do with these distances?”
• Tells you the distance and direction from 0
• “Does anyone know an operation that would turn any number’s coordinate
into the distance that number is from the origin?”
• Absolute value

13. Absolute Value
Absolute Value
• Distance of a number from zero on a
number line
• Always positive

14. Distance between points
Distance between points
• What is the distance betweens points C and D?
• What is the distance between points D and E?
• What is the distance between points A and B?
• You can use absolute value to find these distances

15. Example
Example
• The Marianas Trench in the Pacific
Ocean is one of the deepest places on
earth at an elevation of – 35840 feet.
Mount Everest is the highest place with
an elevation of 29,035 feet.
• Which is further from sea level?
• Write the distance from the highest to the
lowest point on the earth using absolute
value and evaluate.

16. Example
Example
• IBM stock started the day at 192.5 but by
the end of the day it was down to 190.3.
• Write the distance between these two quotes
as an absolute value and evaluate.

17. Order of operations
Order of operations
• Absolute value is same as parenthesis
• Do the operations inside the bars first

18. Property of Opposites
Property of Opposites
• For every number a, there is a number –a
such that a + (-a) = 0
• -a is the opposite of a
• What is the opposite of 3?
• -3
• What is the opposite of 0?
• 0

19. Adding and Subtracting Negatives
Adding and Subtracting Negatives
• Subtracting a number is the same as adding
its opposite
• 5 – 3 = 5 + (-3)
• 700 – (-100) = 700 + 100