Operations With Integers

1
Operations With Integers

• _____________________________________________

-4

• _________________
• Middle Grades
• Mathematics Methods

-8
2
MinusWhat does it mean?

• In algebra, the minus sign can mean three things.
• In front of a number, the minus sign means
  negative.
• In front of any expression, the minus sign means
  the opposite of.
• Between two expressions, the minus sign means
  subtract or take away.

3
Adding Integers

• Teaching the Idea
• Integers are positive and negative whole numbers
  and zero.
• _________________________________________
• When you add opposites, such as 3 and -3, the
  result is 0.

4
Adding Integers

• Teaching the Idea
• Integers are positive and negative whole numbers
  and zero.
• _________________________________________
• When you add opposites, such as 3 and -3, the
  result is 0.

Three zero pairs. No counters are left, so the
result is 0.
5
Example Problems

• To model addition of integers, put on the first
  number,
• put on the second number, cancel what you can,
  and then count.
• -10 (-3)
• -8 9
• 4 (-7)
• -12 (-6)
• 4 3
• -5 2

What patterns do you notice?
6
Subtracting Integers

• To model subtraction, put on the first number,
  take off the second number, and count.
• (Sometimes there are not enough blocks to take
  off, so zero may be added until there are
  enough counters to remove.)

-2 - 5
Negative 2 put on, not enough to take five, so
add five zero pairs, and then take five, count
what is left.
7
Subtracting Integers

• To model subtraction, put on the first number,
  take off the second number, and count.
• (Sometimes there are not enough blocks to take
  off, so zero may be added until there are
  enough counters to remove.)

-2 - 5
Negative seven left
8
Subtraction Examples

• Put on, add zero as needed, take off, count.
• -10 - 3
• 6 - 9
• 4 - (-7)
• -12 (-6)
• 7 - 3
• -5 - 2

What patterns do you notice?
9
Multiplication of Integers

• Consider the four cases

3(-2)
3(2)
3 sets of negative two is -6
3 sets of two is 6

• -3(2)

• -3(-2)

Opposite of 3 sets of two is -6
Opposite of 3 sets of negative two is 6
10
MinusWhat does it mean?

• In algebra, the minus sign can mean three things.
• In front of a number, the minus sign means
  negative.
• In front of any expression, the minus sign means
  the opposite of.
• Between two expressions, the minus sign means
  subtract or take away.

11
Division of Integers

• Recall there are four ways to write a division
  expression.
• Relate division of integers to multiplication
• For example
• 12/3

What times 3 equals 12?