integer1

Day 1: What are Integers?
//__**Integers**__ are the set of whole numbers and their opposites.// For examples: ..., -3, -2, -1, 0, 1, 2, 3, ... One of the way to represent integers with manipulatives (aka "Math Toys") is by using Algebra tiles. These are the tile that we bought for you last year. If you can't find them, you can click on the of the documents below to print off your own set of Integer Tiles.

colored paper or want to color with crayons.|| Use the one below if you have colored ink in your printer. ||
 * Use the one below if you have
 * [[file:Algebra Tile - Units.doc]] || [[file:Algebra Tile - Units with Color.doc]] ||

Each square represents one unit (either positive or negative). So, grouping the units together will make a larger number. (See the example below.)
 * [[image:pu.jpg]] || [[image:nu.jpg]] ||

Try using your Algebra Tiles to model what 3 would look like. What about -8? 11? -7? Answers

*Any questions? (Post them to this page's discussion board.)*
Numbers can also be shown on a number line. **Be sure to start at zero!!!** When you compare integers, values that are further to the left on a number line are smaller. So, numbers that are further to the right are larger. (Remember that we can use < "less than" and > "greater than" to compare numbers and integers.)
 * [[image:numberline.JPG]] ||

Let's put the following set of numbers in order from least to greatest. {-12, 9, -3, 2, -6, 17, 0} Begin by plotting each integer on a number line. Then right down the numbers in order from left to right. So, in order from least to greatest {-12, -6, -3, 0, 2, 9, 17}.
 * [[image:numberline_compare.JPG]]||

*Any questions? (Post them to this page's discussion board.)*
Where are some places that you might use integers outside of a math class? How about... Picture by [|matchity] || Picture by [|William Wilkinson]|| Picture by [|gautsch.i]|| Picture by [|Tracy O] || Just to name a few.
 * Temperature||Stock Market||Football||Money||
 * [[image:thermometer2.jpg]]

*Any questions? (Post them to this page's discussion board.)*
Knowing //how far a number is away from zero// can be useful. Here is a video that helps to explain that distance. (It's called //__**absolute value**__//.)
 * media type="custom" key="731119" ||
 * Video by [|clanahan]. ||

Absolute value is a type of Grouping Symbol. When **__evaluating expressions__** (which means finding a number answer to the problem), remember to follow the **__Order of Operations__**.


 * P** - **P**lease - **P**arenthesis & Grouping Symbols
 * E** - **E**xcuse - **E**xponents & Roots
 * M****D** - **M**y **D**ear - **M**ultiplication & **D**ivision from left to right
 * A****S** - **A**unt **S**ally - **A**ddition & **S**ubtractions from left to right

So, this means that |5| is 5 (5 spaces away from zero). What about |-12|? It would be 12 (twelve spaces away from zero). What about -|6|? This would be -6 (The //opposite// of six spaces away from zero). What about -|-14|? This would be -14 (The //opposite// of fourteen spaces away from zero).

We can also do other operations involving absolute value.
 * 10| + |3| = 10 + 3 = 13
 * -6 | + |9| = 6 + 9 = 15
 * -15| - |4| = 15 - 4 = 9

*Any questions? (Post them to this page's discussion board.)*
When you're ready, here's your [|homework assignment]. Have fun with it!

Day 1: What are Integers? Day 2: Adding Integers Day 3: Subtracting Integers Day 4: Multiplying Integers Day 5: Dividing Integers Day 6: Test