Properties and Operations with Integers (negative numbers)
Intro Lessons (fraction concepts):
To begin the year, we start by discussing and reinventing some common fraction concepts. Seventh grade math relies heavily on fraction knowledge, and specifically a thorough understanding of equivalent fractions. Therefore, this is a perfect place to start as we get used to being back in school. :)
Types of numbers:
Before we delve into negative numbers, we must first create some common understandings of numbers. We will learn some new vocabulary that we can later use to describe different values throughout the year. In class, I had you categorizing a list of seemingly random numbers. Below is a short list of a select few "new" vocabulary that we discussed:
Absolute Value and Opposites:
Once we have some basic vocabulary down we will discuss a few basic concepts that we need to understand before we dive into operations with negative numbers.
Addition and Subtraction with Negative numbers pt. 1
For simple addition and subtraction involving negative numbers we can use a number line. Observe the three examples below for to model this:
(Note that you can also think of how a thermometer works)
Adding a negative number
Now that we see how to do simple addition and subtraction we can start talking about some trickier problems. Think about it..... If you can add to move right, and subtract to move left, what about adding a negative??? Or what about subtracting a negative???
Take note that the commutative property helps us when we are starting with a positive number and adding a negative. However, notice below how the commutative property isn't so helpful when starting with a negative number:
Notice how when we start with a negative and use the commutative property to change the order of the terms, that we still end up "adding a negative". Therefore, the commutative property idea is helpful, but only when we are starting with a positive term.
Take a look at the video below for the 3 main concepts we use for adding a negative number:
Subtracting a negative is a little tricky to envision mentally. Therefore, I like to make this an entirely different concept rather than "cram" it all into one lesson with 'adding a negative'. That being said, watch the video below:
Multiplying and Dividing Negative numbers:
Multiplying and dividing with negatives implements, or rather expands upon, the rules we have already learned. Watch the short video below to see how we create these rules.
Exponents with Negative Bases:
Recall how we write and read exponents below:
Another concepts that we discuss with this section is dividing by zero: