### Accentuate the Negative

Focus Question: How can you find the total value of a combination of positive and negative numbers?

Problem 1.2

Focus Question: How can you use the number line to compare two numbers?

#### Comparing Integers

Focus Question: How can you write a number sentence to represent a change on a number line, and how can you use a number line to represent a number sentence?

Focus Question: How can you use a chip model to represent addition and subtraction?

In this investigation, we will be using chips to represent positive and negative integers.

You may have heard the terms, "In the red" (meaning you owe or have a negative amount of money) and "In the black"(meaning have a positive amount of money)

In the image above, there are black positive chips and red negative chips on the board. Some red and black chips have already been put together in "zero pairs" that cancel each other out. Is this image "in the black" or "In the red"? How do you know?

Now try for yourself:

Focus Question: How can you predict whether the result of an addition of two numbers will be positive, negative, or zero?

#### Decimals and Fractions

Focus Question: How is a chip model or number line useful in determining an algorithm for subtraction?

Problem 2.3

Focus Question: How are the algorithms for addition and subtraction of integers related?

Focus Question: What related sentence is equivalent to 4 + n = 43 and makes it easier to find the value of n?

Focus Question: How is multiplication of two integers represented on a number line and a chip board?

Focus Question: What algorithm can you use for multiplying integers?

Problem 3.3

Focus Questions: What algorithm can you use for dividing integers?How are multiplication and division of integers related?

Focus Question: What pattern do you notice on the game board for the Integer Product Game that can help you win?

Focus Question: Does the Order of Operations work for integers? Explain.

Problem 4.2

Focus Question: How can you use the Distributive Property to expand an expression or factor an expression that involves integers?

Focus Question: What information in a problem is useful to help you decide which operation to use to solve a problem?