Ch. 2 Test Prep

Complete the Ch. 2 practice test at home. Use the Ch. 2 notes, games, and tutorials from the blog to help you. The test is has been moved to Wednesday, September 30. to accomodate changes in schedule due to the 12:30 release time.

2.7 Problem Solving: Multiple Steps (p.52-53)

I.To solve a multi step problem, break it down into single steps.
1. Organize the important information (don't use unnecessary info).
2. Follow the steps in the appropriate order.
3. Pay attention to the order of operations within each step.
4.Make sure you are answering the question being asked.
5. Use a label when writing your answer.

Try these activities from Math Playground to check your understanding. You can also watch these videos that explain how to do some different kinds of words problems.

• Complete PW12 in your Practice Workbook

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.

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.

2.2 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