Chapter 1. Pg. 4-9 Obj: Learn how to write algebraic expressions. Content Standard: A.SSE.1.a.
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Transcript of Chapter 1. Pg. 4-9 Obj: Learn how to write algebraic expressions. Content Standard: A.SSE.1.a.
Foundations for Algebra
Chapter 1
1.1 Variables and Expressions
Pg. 4-9 Obj: Learn how to write algebraic
expressions. Content Standard: A.SSE.1.a
1.1 Variables and Expressions
Quantity – anything that can be measured or counted
Variable – a symbol, usually a letter, that represents the value(s) of a variable quantity
Algebraic expression – a mathematical phrase that includes one or more variables
Numerical expression – a mathematical phrase involving numbers and operation symbols, but no variables
1.2 Order of Operations and Evaluating Expressions
Pg. 10 – 15 Obj: Learn how to simplify
expressions involving exponents and use the order of operations to evaluate expressions.
Content Standard: A.SSE.1.a
1.2 Order of Operations and Evaluating Expressions
Power Base – 4 Exponent – 5 Simplify – replace a
numerical expression with its single numerical value
Evaluate – replace a variable with a given number
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1.2 Order of Operations and Evaluating Expressions
Order of Operations P – Please – Parentheses E – Excuse – Exponents M – My – Multiplication D – Dear – Division A – Aunt – Addition S – Sally - Subtraction
1.3 Real Numbers and the Number Line
Pg. 16 – 22 Obj: Learn how to classify, graph,
and compare real numbers and find and estimate square roots.
Content Standard: (prepares) N.RN.3
1.3 Real Numbers and the Number Line
Square Root A number a is a square root of number b
if a²=b. Radicand – the expression under the
radical symbol Radical – the radical symbol and
radicand together Perfect Square – the square of an
integer Set – a well-defined collection of
objects Element of a set – each object in a
set
1.3 Real Numbers and the Number Line
Subset – consists of elements from the given set – can be listed within brackets {}
Inequality – a mathematical sentence that compares the values of two expressions using an inequality symbol
1.3 Real Numbers and the Number Line
Real NumbersRational Numbers– any number that can be
written as a fractionIrrational
Numbers – those numbers which cannot be written as
fractions
Integers – negative, positive numbers and zero (no decimals)
Whole Numbers – positive integers and zero
Natural Numbers – positive integers
1.4 Properties of Real Numbers
Pg. 23 – 28 Obj: Learn how to identify and use
properties of real numbers. Content Standard: (prepares) N.RN.3
1.4 Properties of Real Numbers
Equivalent Expressions – two algebraic expressions that have the same value for all values of the variable(s)
Deductive Reasoning – the process of reasoning logically from given facts to a conclusion
Counterexample – an example showing that a statement is false
1.4 Properties of Real Numbers
Commutative Properties Addition – a+b=b+a Multiplication – ab = ba
Associative Properties Addition – (a + b) + c = a + (b + c) Multiplication – (ab)c = a(bc)
Identity Properties Addition – a + 0 = a Multiplication – a(1) = a
1.4 Properties of Real Numbers
Zero Property of Multiplication a(0) = 0
Multiplication Property of -1 -1(a) = -a
1.5 Adding and Subtracting Real Numbers
Pg. 30 – 36 Obj: Learn how to find sums and
differences of real numbers. Content Standard: (prepares) N.RN.3
1.5 Adding and Subtracting Real Numbers
Absolute Value- the distance a number is from 0 (always positive)
Opposites – two numbers that are the same distance from zero on a number line, but in opposite directions
Additive Inverse – a number and its opposite
1.5 Adding and Subtracting Real Numbers
Adding Real Numbers Like Signs – Add the absolute values and
keep the sign Different Signs – Subtract the absolute
values and keep the sign of the larger absolute value
Subtracting Real Numbers Change subtraction to addition, change
the sign of the second number, and follow the addition rules
1.6 Multiplying and Dividing Real Numbers
Pg. 38 – 44 Obj: Learn how to find the products
and quotients of real numbers. Content Standard: (prepares) N.RN.3
1.6 Multiplying and Dividing Real Numbers
Multiplying and Dividing Real Numbers Like signs – positive answer Different signs – negative answer
Multiplicative Inverse For every nonzero real number a, there
is a multiplicative inverse 1/a such that a(1/a) = 1
Reciprocal – a nonzero real number of the form a/b is b/a
1.7 The Distributive Property
Pg. 46 – 52 Obj: Learn how to use the
Distributive Property to simplify expressions.
Content Standard: A.SSE.1.a
1.7 The Distributive Property Distributive Property
a(b + c) = ab + ac (b + c)a = ba + ca a(b – c) = ab = ac (b – c)a = ba – ca
Term – a number, a variable, or the product of a number and one or more variables
Constant – a term that has no variable Coefficient – a numerical factor of a term Like Terms – have the same variable
factors
1.8 An Introduction to Equations
Pg. 53 – 58 Obj: Learn how to solve equations
using tables and mental math. Content Standard: A.CED.1
1.8 An Introduction to Equations
Equation – a mathematical sentence that uses an equal sign
Open sentence – an equation that contains one or more variables and may be true or false depending on the values of its variables
Solution of an equation – a value of the variable that makes the equation true
1.9 Patterns, Equations, and Graphs
Pg. 61 – 66 Obj: Learn how to use tables,
equations, and graphs to describe relationships.
Content Standard: A.REI.10 and A.CED.2
1.9 Patterns, Equations, and Graphs
Graphing in the Coordinate Plane Coordinate Plane – two number lines that
intersect at right angles X-axis – the horizontal axis Y-axis – the vertical axis Origin – the point at which the axes intersect Quadrants – the four sections formed by the
x- and y-axes Ordered Pair – names the location of a point
in the plane
1.9 Patterns, Equations, and Graphs
Graphing in the Coordinate Plane Coordinates – the numbers in an ordered
pair▪ X-coordinate – first number – the number of
units left or right of the origin▪ Y-coordinate – second number – the number
of units up or down of the origin
1.9 Patterns, Equations, and Graphs
Solution of an Equation – any ordered pair that makes the equation true
Inductive Reasoning – the process of reaching a conclusion based on an observed pattern