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


Power Base – 4 Exponent – 5 Simplify – replace a

numerical expression with its single numerical value

Evaluate – replace a variable with a given number

54


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


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


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


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


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


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


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


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


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


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


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


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

chapter 1. pg. 4-9 obj: learn how to write algebraic expressions. content standard: a.sse.1.a

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