GeoGebra applets

# Magic Figure

## Practice all four operations (version 1)

Teaser and introduction goes here. Sample problem here.

## Comparing and locating integers

Integers are a lot like the whole numbers that you already know.  The main difference is that there are negative integers as well as positive integers.  Zero is also an integer, but it is neither positive nor negative.  Here is one way we can picture the set of integers:

## Dividing positives and negatives

Take a look at the following four expressions:

## Multiplying positives and negatives

 (+10) x (+3) = +30 (+10) x (-3) = -30

We know that $5\times~2=10$, but what about $-5\times~-2$? Or $5\times~-2$?

To learn how to multiply positive and negative numbers, we will make a table and look for patterns. We will also begin with simple problems that we definitely know the answer to. Starting with answers we know, we will follow the pattern to discover the answers to unfamiliar questions.

## Finding the subtraction rules

Here are some very important things we have discovered so far:

## Subtracting with number lines

 We will use hops on a number line to model subtraction of positive and negative numbers. When subtracting a positive number we move to the left on the number line. When subtracting a negative number we move to the right on the number line. Why is this? Read on...

## Adding with a number line

 Using the number line to solve addition problems will always work. However, it might be considered a little childish if you are still using a number line to answer questions while in high school! In this lesson you will find two rules to make adding negative numbers (especially ones with large absolute values) easier. Consider the following problems. Solve them with a number line and then look for patterns that will allow you to solve the problems without the number line.

We will use hops on a number line to model addition of positive and negative numbers. When adding a positive number we move to the right on the number line. Adding negative numbers moves us to the left on the number line.

Why do we move to the left when adding negative numbers? Read on…