Transcript Negatiges_Investivation2

Get ready before the bell rings!
 Take out homework and a pencil to prepare for the
homework quiz!
 Check the file folder for your class to pick up graded
work
 Located by the bookshelf, blue crate.
 Look behind the tab for your class period and take home
anything with your name on it.
Chapter 2 - Accentuate the Negative
2.1 Extending Addition to Rational
Numbers
 What techniques do we have to add integers?
 Chip Board
 Number Line
Chip Board
 How can we model this problem using chips?
Problem 2.1
Number Lines
 How can we use number lines to solve this problem?
2.1 Reflection
 How do you solve addition problems in which both
signs are the same?
 How do you solve addition problems in which the
signs of the numbers are different?
 For what types of expressions did you get a
negative number?
2.1 Reflection
 How can you write a sum of two numbers that results
in a sum of -5?
2.2 Extending Subtraction to
Rational Numbers
 Vocabulary
 Additive Inverses

The sum of two opposites is zero
 Additive Identity

The sum of any number and zero
is the original number
Kim’s Chip Model
Otis’s Chip Model
Otis’s Chip Model
Number Line
 The Arroyo Family just passed mile 25 on the highway.
They need to get to the exit at mile 80. How many
more miles do they have to drive?
2.2 Reflection
 How do you compute subtraction problems in
which both signs are the same?
 How do you compute subtraction problems in
which the signs of the numbers are different?
 How do you know if the difference is positive or
negative?
 When you are subtracting with integers, must you
always think of the operation as subtraction?
On your own…
 Consider the following pairs of expressions.
Without computing any of the answers, predict
how the expressions within each pair compare to
teach other. Will the two answers in each pair be
the same or different? If they are different, which
will be greater?
 -7 + -8 and -7 - +8
 -12 - -4 and -4 - -12
2.3 The “+/-” Connection
 Focus Question: How are the algorithms for addition &
subtraction of integers related?
2.3 The “+/-” Connection
-6
+6
2.3 The “+/- Connection
+6
-6
•Subtracting a positive number is the same operation as adding a
negative number.
•Subtracting a negative number is the same thing as adding a
positive number.
2.3 The “+/-” Connection
 Algorithms for Addition & Subtraction
 A – B = A + -B
 A + B = A - -B
A note on notation…
 You’ve been writing rational numbers with raised
signs, to avoid confusion with the symbols.
 However, most writing in mathematics do not use
raised signs.
 Positive numbers are always written without a sign.
 +3
= 3 and +7.5 = 7.5
 Negative signs and subtraction signs are the same. So
when you are subtracting a negative, we usually use
parentheses to avoid confusion.
 -5
- -8 becomes -5 – (-8)
2.4 Fact Families
 Focus Question: What related sentence is equivalent
to 4 + n = 43 and makes it easier to find n?
 Fact Family Video
2.4 Fact Families
 What are the other three number sentences that make
a fact family with 4 + 6 = 10?
 6 + 4 = 10
 10 – 4 = 6
 10 – 6 = 4
2.4 Fact Families