Chapter 1 Foundations for Algebra 1 1 Variables

Chapter 1 Foundations for Algebra

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

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 Numbers Rational Numbers– any number that can be written as a fraction Integers – negative, positive numbers and zero (no decimals) Whole Numbers – positive integers and zero Natural Numbers – positive integers Irrational Numbers – those numbers which cannot be written as fractions

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 – 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 yaxes 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