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