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Math 8 and 9 Unit 1: Integers TEST Coming soon!
Math Modelling:
What is modelling? Modelling is a way to show how to get an answer, or explain how it works. Early in Math it means using objects to count, or using your fingers, a number line, cubes/tiles, or pictures. Teachers often teach math "their way" and kids just learn "that's how to do math." WRONG! There are many ways to show what you know...they all work some of the time.
The idea is to learn how to do the math, eventually NOT needing the modelling when you've figured it out!
Addition/Subtraction modelling:
example #1: Thermometer number line
7 + 4 =____
For basic addition and subtraction questions, start at the first number by putting your pencil on it (7). Addition means "go up" subtraction means "go down"
+4 means go up 4 from where you started (7). The answer? 11
The model shows others what you did to get the answer! It's necessary so the teacher can help "fix" your broken model sometimes, or for students to make sure their model works in that situation!
Draw a Thermometer! Make it go from -10 to +10...use 20 lines on your page! Make it BIG!
Write ADD goes up SUBTRACT goes down
put a zero in the middle, then 1, 2, 3...10 up and -1, -2, -3...-10 all the way down.
Answer the following:
4 + 2 =
8 - 5 =
7 + 1 =
5 - 3 =
Easy, right? You've been using the model soooo long, you don't need it anymore! Great. If you do still need it...keep using it:)
When it gets more useful is when we start to use integers (like the negatives). The model is still the same! Add go up, subtract go down!
Try these:
3 - 5 = -7 + 10 = -1 - 4 = +3 + 2 = + 6 - 9 =
When does this model break down? Why?
As we learn more, teachers make the math harder. Some peopl are ready! Some people are not ready... The goal of learning a new language is to master small steps and NOT move on until you're ready. SADLY, in a classroom, the teacher decides when to move on! Some kids are bored and can move faster (1/3 of the class), while some aren't ready to move (1/3). That means only about 1/3 of the class is moving at the same pace as the teacher! That's not good for anyone!
Mr. White's Philosophy!
If you get math quickly, let's advance you quickly so you can get "extending" on your report cards (like you probably had last year). This means you get the stuff so well you can explain it (teach it) to others. I'll put you to the test!
If you get math, but it takes more time, let's help you work through at your speed, and have you ask a peer as needed to just check to see if you're on the right track.
If you struggle with math, let's set you up with material at your current level, and progress you with the teacher's support, mini-lessons, and quizzes as you become ready. This does mean you might need to spend some of YOUR OWN TIME with me for tutorials. Trust me... it's worth it! AND no matter how the math goes, at least you'll be demonstating to your teacher that you're working your butt off regardless of the level of success.
The "PUT IN" and "TAKE OUT" Model!
ADDITION means put in, SUBTRACTION means take out!
(+3) + (-2)
(-7) - (-2)
(+4) - (+1)
(+5) + (+2)
Example: (+3) + (+2) =
Step 1: Draw a circle
Step 2: use + to mean +1, ++ to mean +2, etc...each + is one positive and the same with - is -1, and - - - - is -4
so put 3 plus signs in the circle
Add means put in, so PUT IN 2 more plus signs...
You had 3, then you added 2, so what's in the circle?
5 plus signs = +5!
Try these practice questions...
Try these...
(-3) + (-5) = (+6) + (+3) = (-7) - (-3) =
But this model breaks sometimes, and we need to know how to fix it...
Modelling Addition and Subtraction of Integers
What is a "zero pair"?
when we have a + and a - together it means a +1 and a -1...and they cancel each other out, or equal ZERO...hence a ZERO PAIR!
Adding zero pair (easy)
(+7) + (-2)
(-5) + (+3)
(+2) + (-6)
(-2) + 8
Subtracting zero pair breaks the model a bit...
(+3) - (+2)
(+5) - (+ 6)
(-4) - (+3)
(-5) - (-7)
We need Zero Pair to make things work...but it's confusing at first...
you can add a zero pair to any circle at any time...since it equals zero! so we can add it at the beginning, or we can add it half way through...
A zero pair is + and - together concel each other out...and equal ZERO! hence zero pair
Start with a circle, and put 2 plus signs in
add means put in, so PUT IN 3 negative signs...
since a positive next to a negative equals zero, we can cancel them out!
What's left? one negative...or -1
EASY!
medium!
This worksheet has easier at the top...then some middle, and at the bottom...HARD!
Once you have Integers figured out with great success (using whatever models you need), you're ready to show the teacher what you can do!
QUIZ TIME!
Part II of Integers
Multiplication and Division
WAY easier than adding and subtracting!
Use this same chart that we used for helping simplify addition and subtraction questions
(-3) - (-2) becomes (-3) + 2 = -1
To multiply and divide we use it DIFFERENTLY!
sign of the first integer X sign of the second integer = sign of answer!
Ways of showing multiplication and division...
Time for another
SWEET QUIZ!
Add, Subtract, Multiply AND Divide!
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