52 West Main Street

Washingtonville, NY 10992

Phone: 845.497.4000

Fax: 845.497.4030

Washingtonville, NY 10992

Phone: 845.497.4000

Fax: 845.497.4030

Topic of the Week:

Mr.Chin's Class: Distributive Property of Multiplication Over Addition. Complete Distance on a Coordinate Plane.

Quiz on Math Properties, Algebra Rules, and Distributive Property on Tuesday.

Quiz on Math Properties, Algebra Rules, and Distributive Property on Tuesday.

Mr. Andersen's Class: Review notes on Algebra Rules and Math Properties.

Quiz on Math Properties, Algebra Rules, and Distributive Property on Tuesday.

A. PEMDAS Arrow. The order in which we evaluate expressions is: Parenthesis, Exponents, Multiplication or Division, and Addition or Subtraction. All expressions should be evaluated from left to right.

B. When calculating area or volume, be sure to follow these steps.

First: Select a formula for your figure and write it.

Second: Replace your variables with your appropriate corresponding numbers.

Third: Calculate - be sure to follow your PEMDAS Arrow rules.

Fourth: Express your answer using proper units - area uses square units, volume uses cubic units.

C. Formulas

1. area of a rectangle: a = l x w

2. area of a triangle: a = b x h ÷ 2

3. area of a square: a = s (squared = s x s)

4. area of a paralellogram: a = b x h

5. area of a trapezoid: a = b1 + b2 ÷ 2 x h

6. volume of a rectangular prism: v = l x w x h

7. volume of a cube: v = s (cubed = s x s x s)

1. Commutative Property of Addition: a + b = b + c

2. Commutative Property of Multiplication: a x b = b x c

3. Associative Property of Addition: (a + b) + c = a + (b + c)

4. Associative Property of Multiplication: (a x b) x c = a x (b x c)

5. Additive Identity Property of Zero: a + 0 = a

6. Multiplicative Identity Property of One: a x 1 = a

7. Distributive Property of Multiplication over Addition: a (b + c) = (a x b) + (a x c)

E. **Distance on a Coordinate Plane**

If you are trying to find the distance between two points on a coordinate plane there are two strategies that you should consider.

1. If you have the points plotted on a coordinate plane, you can count the units between them. The distance will be found by counting the units.

2. If you don't have the points plotted on a coordinate plane, you can still find the distance, but it will help a lot if you know in which quadrant your points are plotted.

a. If the points are plotted in the same quadrant, then cross off your matching coordinates (either the x or the y), and then find the absolute value of the appropriate coordinate. Subtract to find the difference between these two values. This will be the distance.

b. If the points are plotted in different quadrants, then cross of your matching coordinates (either the x or the y), and the find the absolute value of the appropriate coordinate. Add the absolute values to find the sum. This will be the distance between the two points.

F. The Four Basic Rules of Algebra

1. Equations have an equal sign, expressions do not. Whatever you do to one side of the equation, you must do to the other so that it stays balanced (or equal).

2. Variables always follow the numbers.

3. Variables should always be written in alphabetical order when you have the chance.

4. When solving for the value of a variable, use opposite operations in order to isolate the variable.

constant- a number in a math statement (it doesn't change value; it is constant); in 5 x e = 20, 5 is a constant

coefficient - a constant factor in a variable term; in 3e + 4hm, 3 is a coefficient and 4 is a coefficient

factor - numbers multiplied to form a product; in 3 x 4 = 12, 3 and 4 are factors; in 3e + 4hm, 3 and e are factors and 4h and m are factors

product - the result of multiplication; the answer in a multiplication operation; in 3 x 4 = 12, 12 is the product

term - part of an expression that can be added to or subtracted from the rest of the expression; any value, or variable together with its operation, or any variable linked to a value by multiplication or division; in

3e + 4hm, 3e is a term; 4hm is a term

3e + 4hm, 3e is a term; 4hm is a term

variable - a letter or other symbol that stands for a number or quantity; in 3e + 4hm, e, h, and m are variables