1. Math Journal Chapters 5, 8, and 10 Math Journal Chapters 5, 8, and 10 Jaxon Sharp Block: F Dec. 13

2. Notation When you multiply a variable and number the number goes first and then the variable. A variable is a letter or symbol. We use this notation because it makes things much easier and more simple. If there is more than one variable, then just put the variables in alphabetical order. Examples: 1. 3(a)+4=7a. 2. 4(n)+8(m)=12mn 3. 54(y)+45(x)+71(n)=170nxy

3. Rule for Finding a Pattern Step 1: First you have to find the difference between each term, (like 5. 8, 3, 57 etc.) Whatever the change is; that is the number you multiply to the n for the nth term. So, if the change between to numbers is 3, than it would be 3n. Step 2: Multiply the change to the few n terms and see what the difference is. That number will be what you add or subtract for the pattern. Like 5n-3 or 7n+2 Examples: 1) Pattern: 3, 5, 7, 9, 11. +2 each time, but add 1 at the beginning. So, by following my rules, the pattern is M=2n+1. 2) Pattern: 7, 10, 13, 16, 19. +3 each time, but add 4 at the beginning. So, by following my rules, the pattern is M=3n+4. 3) Pattern: 11, 20, 29, 38, 47. +9 each time, but add 2 at the beginning. So, by following my rules, the pattern is M=9n+2.

4. Function Machine Function: Is any rule that takes an input value and converts it to an output value. Like patterns, the function machine takes a input number and finds an output number. Examples: Find output using input. Z=7y-6 1. y=7=43 2. y=19=127 3. y=73=505

5. Finding Input of a Number using the Output of a Number If we already know the output of a number and the method we used to get it. You just do everything backwards. Addition is subtraction and multiplication is division. Don’t forget to use Order of Operations. Examples: 1. Method: +4-1 output number: 5 input number: 2 2. Method: -9+4 output number: 8 input number: 13 3. Method: -13+7 output number:12 input number: 18

6. Substitution Substitution is when we substitute a number or variable with a something worse. “Like substituting Mr. Turner with a less attractive substitute teacher.” Just like replacing something. Examples: 1. Substitute a with 5: 8(a)+7(a)=75 8(5)=40 7(5)=35 40+35=75 2. Substitute n with 4: 4(n)+n= 20 4(4)=16+4=20 3. Substitute m with 11: m(m)+m(9)=220 11(11)=121 11(9)=99 99+121=220

7. Evaluate VS. Simplifying Evaluating is finding the value of an expression when you put in a number or substitute a number in for a variable, while simplifying is putting together the terms with the exact same variable by adding or subtracting the coefficients. Evaluating is finding an exact answer while simplifying is narrowing down the answer. Expression is one or more terms put together with an operation, but NO equal sign, while an equation is two or more expressions with an equal sign. A term is a variable or number put together with the addition sign or subtraction sign that’s in front of it. Examples of Evaluating: 1. 8(9)+7(2) is 86 2. 7(6)+5(5) is 67 3. 6(12)+3(12) is 108 Examples for Simplifying: 1. 6a+5a=11a 2. 4a+7y+3a+11y=18y+7a 3. 7n+3a+2y+23n+12a+9y=30n+15a+11y

8. Simplifying Expressions When simplifying expression using like terms you add the like terms and add the other along with it. Like terms are terms that have the exact same variable. Examples: 1. 8a+7n+9n=16n+8a 2. 19a+47y+21n+13y=60y+19a+21n 3. 34+21z+7n+99z=120z+34+7n

9. Constant VS. Coefficient A constant is just a plain number with no variable. A coefficient is the number in front of a variable. They’re both numbers, it’s whether its in front of a variable or not. Examples:Constants: 1. 65 2. 39 3. 97 Coefficients: 1. 3a=3 2. 54z=54 3. 43y=43