2.6 Order of Operations (p.48-51)

I. Follow this order for evaluating expressions with more than one operation.
1. First, perform operations in parentheses.
2. Clear exponents by replacing with the real value.
3. Multiply and divide, working from left to right.
4. Add and subtract, from left to right.

Ways to Remember

• Parentheses - Exponents - Multiply and Divide - Add and Subtract
  P-E-(MD)-(AS) or "PEMDAS "
• Please (parentheses) Excuse (exponents)My Dear (multiply and divide) Aunt Sally (add and subtract)
  
  Example:
  285+93÷(3-2) x 3 x4²
  285+93÷ 1 x 3 x4² parentheses
  285+93÷1x 3 x16 exponents
  285+93÷1 x3x16 multiply and divide from left to right
  93 x3= 279
  279 x 16 = 4464
  285 + 4464 = 4749 add and subtract
  
  285+93÷(3-2) x 3 x4² =4749
  

For a description of how order of operations works try this link that includes an explanation and practice problems from mathgoodies.com

Here is a game from Harcourt to see how well you know your operations.
Play Rags to Riches to test what you know.

Take this Quiz from math6.org

2.5 Exponents (p.46-47)

I. Exponent: a symbol of repeated multiplication
A. An exponent shows how many times a number is multiplied by itself.
B. Exponent can also be called a "power"

II. Base: the number being multiplied (used as a factor) when working with exponents.
Examples:
The exponent "2" is telling us to multiply the base "4" "2" times. 4x4 =16
III. Rules:
A. Using the power of 1, makes the value equal to the base (original) number
B. Using "0" power of any number, expcept zero, is defined to be 1

IV. Reading exponents: aⁿ or a^n

• a raised to the n-th power,
• a raised to the power [of] n or possibly a raised to the exponent [of] n,
• a to the n-th power or a to the power [of] n,
• a to the n.

A. Some exponents have their own pronunciation: for example, a^2 is usually read as a squared and a^3 as a cubed.

Here is a brief description of exponents from About.com.
Check what you know on this short quiz and get immediate feedback from regentsprep.org.

September 8-21 Activities

Please take advantage of this time and work on your math facts using one of the following tools

• Math Magician
• Academic Skill Builder racing games
• Math Facts Cafe: Really good for 2 and 3 digit mental math facts practice
• Kids Games facts practice
• WildMath.com

This skill is very important for your future success with math. Please challenge yourself to improve your facts knowledge regardless of how well you think you already know them. Pros can still improve their 2 and 3 digit mental math flashcards at Math Facts Cafe.

There will be a facts test the week we get back :) Enjoy!

2.4 Mental Math: Use the Properties (p.42-45)

Lesson 2.4 is practice for applying the properties knowledge we learned in lesson 2.3. Today we learned about one new strategy called compensation

I. Compensation
A. Used for addition and subtraction
1. For addition: change one number to a multiple of 10 and then adjust the other number by
doing the opposite to keep the balance.
Example: 44 +57 = (44 +6) +(57 - 6) = 50 + 51 = 101
Because 50 + 51 is easier to add together.

2. For subtraction: change each number in the same way, so that the last number being
subtracted is a multiple of 10 that ends in 0.
Example: 128 - 56 = (128 +4) - (56 +4) = 132 - 60 = 72
II. Divide Mentally
A. Divide a number by breaking it into smaller,more managable parts.
Example: 396 ÷ 4
396 = 360 + 36 (break it into parts that can be divided by 4)
360 ÷ 4 = 90 and 36 ÷ 4 = 9 (mentally divide the parts by 4)
90 + 9 = 99
So, 396 ÷ 4 = 99.

2.3 Algebra Properties (p.40-41)

Click on the the names of each property to see them explained using models at europa.com
I. Commmutative Property: A property of addition and multiplication that states that if the ORDER of addends or factors is CHANGED, THE SUM OR PRODUCT STAYS THE SAME.

• Addition: 3+9 = 12 = 9 + 3
• Multiplication: 8 x 3 = 24 = 3 x 8
• Watch this video from eHow that explains the commutative property.

II. Associative Property: When adding or multiplying three or more numbers, it doesn't matter the order or how you group your addends or factors because it will not change the sum or product (answer) - it's a lot like the commutative property, but involves more numbers.

• Addition: (8 + 5) + 4 = 8 + (5 + 4) = 17
• Multiplication: (6 x 7) x 2 = 6 x (7 x 2) = 84

III. Distributive Property: When multiplying a sum by a number it is the same as multiplying each addend by the number and then adding the products.

• 4 x (7 +3) = (4 x 7) + (4 x 3) = 40

IV. Identity Property of Addition: the sum of any number and zero is that number.

• 3 + 0 = 3
• 0 + 5 = 5

V. Identity Property of Multiplication: the product of any number and 1 is that number.

• 15 x 1 = 15
• 1 x 9 = 9

Test what you know with this Jeopary style game on Quia.com

2.2 Algebra Mental Math and Equations (p.38-39)

I. Equation: is a statement showing that two quantities are equal (all equations have an equal sign). Examples:
6+7=13
k-3=1
a+b=11

II. Solution: find the solution is finding the value of a variable (a letter or symbol representing a number) in an equation. For example in the following equation:
16=c+9
The solution is c=7

Watch this Explanation of Equations from Harcourt math.

2.1 Algebra: Expressions (p.36-37)

Expressions
--Expressions are combinations of mathematical symbols that express a value.
I. Numerical Expression: an expression that includes only numbers and operations
Examples: 47-38 30+12+9
II. Algebraic Expression: an expression that includes a variable.
Examples: k-3 5+n 6x5xb
A. Variable: A variable is a letter or symbol that can stand for one or more numbers.
Examples: the letters "k" "n" and "b" from the algebraic expressions above are varialbes
B. Evaluate: replacing the variable with a number and then finding the value of the express
a + 150, for a = 8
replace a with 8
a + 150
8 + 150 add
158 : the value of the algebraic expression "a + 150, for a = 8" is 158

Here is an external linke with an introduction to algebra