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Published byHerbert Turner Modified over 9 years ago
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Chapter 1
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Pg. 4-9 Obj: Learn how to write algebraic expressions. Content Standard: A.SSE.1.a
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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
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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
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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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Order of Operations P – Please – Parentheses E – Excuse – Exponents M – My – Multiplication D – Dear – Division A – Aunt – Addition S – Sally - Subtraction
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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
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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
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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
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Real Numbers Rational Numbers– any number that can be written as a fraction Irrational 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
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Pg. 23 – 28 Obj: Learn how to identify and use properties of real numbers. Content Standard: (prepares) N.RN.3
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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
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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
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Zero Property of Multiplication a(0) = 0 Multiplication Property of -1 -1(a) = -a
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Pg. 30 – 36 Obj: Learn how to find sums and differences of real numbers. Content Standard: (prepares) N.RN.3
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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
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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
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Pg. 38 – 44 Obj: Learn how to find the products and quotients of real numbers. Content Standard: (prepares) N.RN.3
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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
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Pg. 46 – 52 Obj: Learn how to use the Distributive Property to simplify expressions. Content Standard: A.SSE.1.a
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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
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Pg. 53 – 58 Obj: Learn how to solve equations using tables and mental math. Content Standard: A.CED.1
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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
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Pg. 61 – 66 Obj: Learn how to use tables, equations, and graphs to describe relationships. Content Standard: A.REI.10 and A.CED.2
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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
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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
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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
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