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

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? and and

2.3 The “+/-” Connection Focus Question: How are the algorithms for addition & subtraction of integers related?

2.3 The “+/-” Connection

2.3 The “+/- Connection 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 Negative signs and subtraction signs are the same. So when you are subtracting a negative, we usually use parentheses to avoid confusion 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 = 10? = – 4 = 6 10 – 6 = 4

2.4 Fact Families