Introduction to Integers Today you will begin the first steps in conquering the Algebra Mystery Maze competition! The first chain and maze require you to have an understanding of integers. Make sure you READ all slides and use your mouse or enter key to advance slides!!
So…What are integers? Integers are the set of counting numbers, their opposites, and zero. Huh??? If you remember, counting numbers are the numbers we use to count (1,2,3,4,5). Sometimes they are called natural numbers.
1, 24, 378, and 4,672 are counting numbers. 3.14, -2, 0, and 2 7/9 are not counting numbers. Click the hyperlink below to learn more and quiz yourself! Click here
Ok. So now you know that integers is just a fancy way of describing positive and negative numbers. Check out the following web page linked to the dancing skeleton to review how to compare integers and learn about Absolute Value. Stop after you complete Work Exercise 2 Practice with Absolute Values. Click here The web page is called Yo Quiero Math which means I Love Math in Spanish!! Don’t let the teacher or her parakeet intimidate you! Try practice questions as they are provided! FYI: When you get to the section on Absolute Value you may need to select the back button to get to all 3 practice sessions. Make sure you do all 3 practice sessions because the 3 rd one in the best to prepare you for adding integers!
Ok, so Absolute Value is the number of units away from zero a counting number is on the number line and it is always positive. Why? Because we are measuring a chunk of space between zero and the number and that’s all for now! This algebraic equation may look terrifying but think about it. Really all it says is that the absolute value of some number (x) and 1 added together is the same distance away from zero as five would be! What number(s) could you plug in to make it true? What if x=4? What if x= -6? Remember Absolute Value is space from zero and is always positive! Just a thought!!!
Moving on to Adding and Subtracting Integers So now that we have reviewed counting numbers, integers and absolute value we are ready to begin doing some serious calculations ! Click the Cartoon Below! Work through: 1. Adding Integers on the Number Line 2. Work Exercise 3 3. Rules For adding Integers 4. Work Exercise 4 Yo Quiero Math again!! Watch out for the parakeet in her collar!! Click Tutorial button to access all 4 exercises! Click The Cartoon Below!
Now we can see why the Absolute Value stuff was important! By figuring out the amount of units the two numbers are talking about, we just need to figure out what sign to use! Quick Rules to Memorize: Signs the same combine and use that sign! + plus + = + - plus - = - Signs different, find the difference in their absolute values and use the sign of the larger unit! - plus + = difference between and sign of largest Piece of cake!
So…What about Multiplication and Division??? Use absolute value again! |5| Then…If the signs are the same it is ALWAYS a positive product or quotient! -5 X -6 =+30 32 ÷ 8 = +4 If the signs are different it is ALWAYS a negative product or quotient! -5 X 9 = -45 36 ÷ -6 = -6 Ignore the signs (for now!) and multiply or divide the absolute values! -25 ÷ 5 = or |25| ÷ |5| = 5
Check out the videos links for more info! Click on each image below!
Practice! Practice! Practice! When you feel you have mastered Integers, ask for your integer practice worksheet. If not go to www. coolmath .com and find some independent practice!