Transcript Document

Models and Pictorials
Warm-up
Baby It’s Cold Outside
Powerpoint
Division of Integers
Guided Practice
Are We There Yet?
Baby It’s Cold Outside!
(Warm Up)
On Tuesday, the temperature changes -2°F per
hour from noon until 10:00am the next morning.
The temperature at noon on Tuesday is 75°F.
1. What is the temperature at 4:00p.m. on
Tuesday? There are 4h between noon and
4:00pm, so 4 x (-2) = -8; 75° + (-8°) = 67°F.
2. What is the temperature at 9:00a.m. on
Wednesday? There are 21h between noon and
9:00am, so 21 x (-2) = -42; 75° + (-42°) = 33°F.
Division of Integers
We learned in an earlier lesson that addition
and subtraction are inverse operations. What
would be the inverse of multiplication? Division
Write the fact family for the following
multiplication problem.
5 x 3 = 15
3 x 5 = 15
15
15 ÷ 3 = 5 or 3 = 5
15
15 ÷ 5 = 3 or 5 = 3
Division of Integers
Write the fact family for each of the following
multiplication problems.
2x3=6
3x2=6
-2 x 3 = -6
3 x (-2) = -6
6
6 ÷ 2 = 3 or 2 = 3
6
6 ÷ 3 = 2 or = 2
3
2 x -3 = -6
(-3) x 2 = -6
-6
-6 ÷ 2 = (-3) or 2 = -3
-6
-6 ÷ (-3) = 2 or -3 = 2
6
-6 ÷ (-2) = 3 or2 = 3
6
-6 ÷ 3 = (-2) or 3 = -2
-2 x (-3) = 6
-3 x (-2) = 6
6
6 ÷ (-2) = (-3) or -2 = -3
6
6 ÷ (-3) = (-2) or -3 = -2
Division of Integers
What patterns do you see in the fact families?
Answers will vary.
Use what you know about the relationship
between multiplication and division facts and
the patterns you discovered to help you solve
these problems:
-6 = -48
1. 8 x ___
2. ___
-12 x (-9) = 108
3. 6 x (-13) = -78
___
Division of Integers
We can further reinforce this by using chips.
-12 ÷ 4 = -3
How can we interpret this?
-12 divides into 3 sets of 4 negative
chips
Division of Integers
Try this one.
-12 ÷ -4 = 3
How can we interpret this?
-12 divides into 3 sets of 4 positive chips
(they are positive because the 12 and 4 are
both negative).
Division of Integers
Try another example.
-8 ÷ 2 = -4
How can we interpret this?
-8 divides into 4 sets of 2 negative chips
Division of Integers
Try another example.
-8 ÷ -2 = 4
How can we interpret this?
-8 divides into 4 sets of 2 positive chips
(they are positive because the 8 and 2 are
both negative).
Division of Integers
Work with your partner to construct an
algorithm for dividing integers?
When dividing integers, if the signs are alike,
the quotient is positive, if the signs are
different, the quotient is negative.
What is the relationship between the
multiplication algorithm and the division
algorithm?
Regardless of how the algorithms are
worded, students should notice that
multiplication and division are the same.
Are We There Yet?
(Guided Practice)
Write a number sentence to represent each situation
and then solve your number sentence.
1. The Extraterrestrials have a score of -300. They
answer four 50-point questions incorrectly. What
is their new score?
-300 + [4 x (-50)] = -500 points
2. The Super Computers answer three 100-point
questions incorrectly. They now have 200 points.
What was their score before answering the three
questions?
n + [3 x (-100)] = 200; 500 + (-300) = 200;
500 points
Are We There Yet?
(Guided Practice, cont.)
3. The Bigtown Bears football team is at the 25-yard
line. In the next three plays, they lose an
average of 4 yards per play. Where are the
Bears after the three plays?
25 – (3 x 4) = 13 yard line.
4. A new convenience store wants to attract
customers. For a one-day special, they sell
gasoline for $0.25 below their cost. They sell
5,750 gallons that day. How much money do
they lose?
5,750 ÷ (-0.25) = -$1,437.50 loss