Chapter 1
1-1: Using a Problem Solving Plan
OBJECTIVES:
Use a four step plan to solve problems
Choose an appropriate method of computation
VOCABULARY:
Conjecture: educated guess
Inductive Reasoning: a conjecture based on a pattern of examples or past events
Four Step Problem Solving Plan:
Read the problem quickly once to get a general understanding.
Reread the problem and underline important facts.
Plan how to solve the problem.
Get an idea of what the answer should be.
Use your plan to solve the problem.
Reread the problem again and make sure your answer makes sense.
VERY IMPORTANT:
Reasonableness: Always make sure your answer is reasonable, if your answer doesn’t seem right, solve it again!!
1-2: Numbers and Expressions
Objectives:
Use the Order of Operations to evaluate expressions.
Translate verbal phrases into numerical expressions.
VOCABULARY:
Numerical Expression: a combination of numbers and operations
Evaluate: Find a numerical value or “a number answer”
Order of Operations: the order in which we perform mathematical operations.
Order of Operations:
Step 1: Simplify the expressions inside grouping symbols.
Step 2: Simplify all exponential expressions.
Step 3: Do all multiplications and divisions from left to right.
Step 4: Do all additions and subtractions from left to right.
Short cut way to remember: “PEMDAS”
Translating Verbal Phrases into Numerical Expressions
Addition
Sum
Plus
More Than
Increased By
In All
Subtraction
Difference
Minus
Less Than
Subtract
Decreased By
Less
Multiplication
Product
Times
Multiplied
Each
Of
Factors
Division
Quotient
Divided
Per
Rate
Ratio
1-3: Variables and Expressions
Objectives:
Evaluate expressions containing variables.
Translate verbal phrases into algebraic expressions.
VOCABULARY:
Variable: A letter used to represent any value, or an unknown value.
Algebraic Expression: An expression that contains sums and/or products of
variables and numbers.
Defining a Variable: Choosing a variable and a quantity for the variable to
represent.
Notes:
Any letter can be used to represent a variable.
The most used letter for variables is X.
Representing multiplication and division with variables:
4x +2 : 4x means 4 times x; the number comes before the letter in 4x!!!
xy:
means x times y
x/3:
means x divided by 3
Usually variables are written with lower case letters. Capitals are only used in special circumstances.
Replacing a variable with a number demonstrates the:
Substitution Property of Equality. If two quantities are equal then one quantity can be replaced by the other.
When you evaluate expressions you use this property.
1-4: Properties
Objectives:
Identify and use properties of addition and multiplication.
Use properties of addition and multiplication to simplify
algebraic expressions.
VOCABULARY:
Property: statement that is true for any numbers.
Counterexample: an example that shows a conjecture is not true.
Simplify: to write an expression in simpler form
Properties of Addition and Multiplication:
Commutative Property of Addition: the order in which numbers are added
Does not change the sum. 3+4 = 4+3
Commutative Property of Multiplication: the order in which numbers are
Multiplied does not change the product: 3 × 4 = 4 × 3.
Associative Property of Addition: the way in which numbers are grouped when
Added does not change the sum.
Associative Property of Multiplication: the way in which numbers are grouped
When multiplied does not change the product.
Additive Identity: When 0 is added to any number the sum is the number
Multiplicative Identity: When any number is multiplied by 1 the product is the number.
1-5: Variables and Equations
Objectives:
Identify and solve open sentences.
Translate verbal sentences into equations.
VOCABULARY
Equation: a mathematical sentence that contains an equal sign.
Open Sentence: an equation that contains a variable.
Solution: a value for the variable that makes the equation true.
Solving the Equation: the process of finding the value that makes the equation true.
Properties:
Symmetric Property: If a = b then b = a.
We can switch around the equal sign.
Transitive Property: If a = b and b = c, then a = c.
If two things are equal to the same thing, then they are equal to each other.
1-6: Ordered Pairs and Relations
Objectives:
Use Ordered Pairs to Locate Points
Use Tables and Graphs to Represent Relations
VOCABULARY
Coordinate System: Used to locate points and is formed by the intersection of two number lines that meet at right angles at their zero points.
x-axis: the horizontal number line
y-axis: the vertical number line
coordinate plane: another word for the coordinate system
origin: Where the lines intersect: (0,0)
ordered pair: pair of numbers used to locate any point on the coordinate plane.
x-coordinate: the first number in the ordered pair, tells you where to go on the x-axis.
y-coordinate: the second number in the ordered pair, tells you where to go on the y-axis.
graph: draw a dot at the point that corresponds to the ordered pair.
relation: a set of ordered pairs
domain: the set of x-coordinates
range: the set of y-coordinates
1-7: Scatter Plots
Objectives:
Construct Scatter Plots
Interpret Scatter Plots
VOCABULARY
Scatter Plot: graph that shows the relationship between two sets of data. Two sets of data are graphed as ordered pairs on a coordinate
system.
There are three types of relationships that exist between two sets of data:
Positive relationship: as x increases, y increases
Negative relationship: as x increases, y decreases
No relationship: There is no obvious pattern.
We can use scatter plots to make predictions of what will happen in the future.
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